phd in mathematics scope

Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

• Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
• Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
• Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
• Complete a seminar, giving a talk of at least one-hour duration
• Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
• Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

Maths is a vast subject, both in breadth and in depth. As such, there’s a significant number of different areas you can research as a math student. These areas usually fall into one of three categories: pure mathematics, applied mathematics or statistics. Some examples of topics you can research are:

• Number theory
• Numerical analysis
• String theory
• Random matrix theory
• Graph theory
• Quantum mechanics
• Statistical forecasting
• Matroid theory
• Control theory

Besides this, because maths focuses on addressing interdisciplinary real-world problems, you may work and collaborate with other STEM researchers. For example, your research topic may relate to:

• Biomechanics and transport processes
• Evidence-based medicine
• Fluid dynamics
• Financial mathematics
• Machine learning
• Theoretical and Computational Optimisation

What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:

• Continually read literature – This will be to help develop your knowledge and identify current gaps in the overall body of knowledge surrounding your research topic.
• Undertake research specific to your topic – This can include defining ideas, proving theorems and identifying relationships between models.
• Collect and analyse data – This could comprise developing computational models, running simulations and interpreting forecasts etc.
• Liaise with others – This could take many forms. For example, you may work shoulder-to-shoulder with individuals from different disciplines supporting your research, e.g. Computer scientists for machine learning-based projects. Alternatively, you may need frequent input from those who supplied the data for your research, e.g. Financial institutions or biological research colleagues.
• Attend a wide range of lectures, seminars and events.

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

The average programme duration for a mathematics PhD in the UK is 3 to 4 years for a full-time studying. Although not all universities offer part-time maths PhD programmes, those that do have a typical programme duration of 5 to 7 years.

Again, although the exact arrangement will depend on the university, most maths doctorates will require you to first register for an MPhil . At the end of your first year, your supervisor will assess your progress to decide whether you should be registered for a PhD.

Additional Learning Modules

Some Mathematics departments will require you to enrol on to taught modules as part of your programme. These are to help improve your knowledge and understanding of broader subjects within your field, for example, Fourier Analysis, Differential Geometry and Riemann Surfaces. Even if taught modules aren’t compulsory in several universities, your supervisor will still encourage you to attend them for your development.

Most UK universities will also have access to specialised mathematical training courses. The most common of these include Pure Mathematics courses hosted by Mathematics Access Grid Conferencing ( MAGIC ) and London Taught Course Centre ( LTCC ) and Statistics courses hosted by Academy for PhD Training in Statistics ( APTS ).

What Are the Typical Entry Requirements for A PhD in Maths?

In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master’s degree (or international equivalent) in Mathematics or Statistics [1] .

However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor’s degree in any math-related subject. The highest entry requirement is a first-class (1st) honours Master’s degree in a Mathematics or Statistics degree only.

It’s worth noting if you’re applying to a position which comes with funding provided directly by the Department, the entry requirements will usually be on the higher side because of their competitiveness.

In terms of English Language requirements, most mathematics departments require at least an overall IELTS (International English Language Testing System) score of 6.5, with no less than 6.0 in each individual subtest.

Tips to Consider when Making Your Application

When applying to any mathematics PhD, you’ll be expected to have a good understanding of both your subject field and the specific research topic you are applying to. To help show this, it’s advisable that you demonstrate recent engagement in your research topic. This could be by describing the significance of a research paper you recently read and outlining which parts interested you the most, and why. Additionally, you can discuss a recent mathematics event you attended and suggest ways in how what you learnt might apply to your research topic.

As with most STEM PhDs, most maths PhD professors prefer you to discuss your application with them directly before putting in a formal application. The benefits of this is two folds. First, you’ll get more information on what their department has to offer. Second, the supervisor can better discover your interest in the project and gauge whether you’d be a suitable candidate. Therefore, we encourage you to contact potential supervisors for positions you’re interested in before making any formal applications.

How Much Does a Maths PhD Typically Cost?

The typical tuition fee for a PhD in Maths in the UK is £4,407 per year for UK/EU students and £20,230 per year for international students. This, alongside the range in tuition fees you can expect, is summarised below:

Note: The above tuition fees are based on 12 UK Universities [1]  for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value.

In addition to the above, it’s not unheard of for research students to be charged a bench fee. In case you’re unfamiliar with a bench fee, it’s an annual fee additional to your tuition, which covers the cost of specialist equipment or resources associated with your research. This can include the upkeep of supercomputers you may use, training in specialist analysis software, or travelling to conferences. The exact fee will depend on your specific research topic; however, it should be minimal for most mathematic projects.

What Specific Funding Opportunities Are There for A PhD in Mathematics?

Alongside the usual funding opportunities available to all PhD Research students such as doctoral loans, departmental scholarships, there are a few other sources of funding available to math PhD students. Examples of these include:

You can find more information on these funding sources here: DiscoverPhDs funding guide .

What Specific Skills Do You Gain from Doing a PhD in Mathematics?

A doctorate in Mathematics not only demonstrates your commitment to continuous learning, but it also provides you with highly marketable skills. Besides subject-specific skills, you’ll also gain many transferable skills which will prove useful in almost all industries. A sample of these skills is listed below.

• Logical ability to consider and analyse complex issues,
• Commitment and persistence towards reaching research goals,
• Outstanding verbal and written skills,
• Strong attention to detail,
• The ability to liaise with others from unique disciple backgrounds and work as part of a team
• Holistic deduction and reasoning skills,
• Forming and explaining mathematical and logical solutions to a wide range of real-world problems,
• Exceptional numeracy skills.

What Jobs Can You Get with A Maths PhD?

One of the greatest benefits maths PostDocs will have is the ability to pursue a wide range of career paths. This is because all sciences are built on core principles which, to varying extents, are supported by the core principles of mathematics. As a result, it’s not uncommon to ask students what path they intend to follow after completing their degree and receive entirely different answers. Although not extensive by any means, the most common career paths Math PostDocs take are listed below:

• Academia – Many individuals teach undergraduate students at the university they studied at or ones they gained ties to during their research. This path is usually the preferred among students who want to continue focusing on mathematical theories and concepts as part of their career.
• Postdoctoral Researcher – Others continue researching with their University or with an independent organisation. This can be a popular path because of the opportunities it provides in collaborative working, supervising others, undertaking research and attending conferences etc.
• Finance – Because of their deepened analytical skills, it’s no surprise that many PostDocs choose a career in finance. This involves working for some of the most significant players in the financial district in prime locations including London, Frankfurt and Hong Kong. Specific job titles can include Actuarial, Investment Analyst or Risk Modeller.
• Computer Programming – Some students whose research involves computational mathematics launch their career as a computer programmer. Due to their background, they’ll typically work on specialised projects which require high levels of understanding on the problem at hand. For example, they may work with physicists and biomedical engineers to develop a software package that supports their more complex research.
• Data Analyst – Those who enjoy number crunching and developing complex models often go into data analytics. This can involve various niches such as forecasting or optimisation, across various fields such as marketing and weather.

What Are Some of The Typical Employers Who Hire Maths PostDocs?

As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:

• Education – All UK and international universities
• Governments – STFC and Department for Transport
• Healthcare & Pharmaceuticals – NHS, GSK, Pfizer
• Finance & Banking – e.g. Barclays Capital, PwC and J. P. Morgan
• Computing – IBM, Microsoft and Facebook
• Engineering – Boeing, Shell and Dyson

The above is only a small selection of employers. In reality, mathematic PostDocs can work in almost any industry, assuming the role is numerical-based or data-driven.

How Much Can You Earn with A PhD in Maths?

As a mathematics PhD PostDoc, your earning potential will mostly depend on your chosen career path. Due to the wide range of options, it’s impossible to provide an arbitrary value for the typical salary you can expect.

However, if you pursue one of the below paths or enter their respective industry, you can roughly expect to earn [3] :

Academic Lecturer

• Approximately £30,000 – £35,000 starting salary
• Approximately £40,000 with a few years experience
• Approximately £45,000 – £55,000 with 10 years experience
• Approximately £60,000 and over with significant experience and a leadership role. Certain academic positions can earn over £80,000 depending on the management duties.

Actuary or Finance

• Approximately £35,000 starting salary
• Approximately £45,000 – £55,000 with a few years experience
• Approximately £70,000 and over with 10 years experience
• Approximately £180,000 and above with significant experience and a leadership role.

Aerospace or Mechanical Engineering

• Approximately £28,000 starting salary
• Approximately £35,000 – £40,000 with a few years experience
• Approximately £60,000 and over with 10 years experience

Data Analyst

• Approximately £45,000 – £50,000 with a few years experience
• Approximately £90,000 and above with significant experience and a leadership role.

Again, we stress that the above are indicative values only. Actual salaries will depend on the specific organisation and position and responsibilities of the individual.

Facts and Statistics About Maths PhD Holders

The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.

Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

Alan Turing was a British Mathematician, WW2 code-breaker and arguably the father of computer science. Alongside his lengthy list of achievements, Turning achieved a PhD in Mathematics at Princeton University, New Jersey. His thesis titled ‘Systems of Logic Based on Ordinals’ focused on the concepts of ordinal logic and relative computing; you can read it online here . To this day, Turning pioneering works continues to play a fundamental role in shaping the development of artificial intelligence (AI).

Ruth Lawrence

Ruth Lawrence is a famous British–Israeli Mathematician well known within the academic community. Lawrence earned her PhD in Mathematics from Oxford University at the young age of 17! Her work focused on algebraic topology and knot theory; you can read her interesting collection of research papers here . Among her many contributions to Maths, her most notable include the representation of the braid groups, more formally known as Lawrence–Krammer representations.

Emmy Noether

Emmy Noether was a German mathematician who received her PhD from the University of Erlangen, Germany. Her research has significantly contributed to both abstract algebra and theoretical physics. Additionally, she proved a groundbreaking theorem important to Albert Einstein’s general theory of relativity. In doing so, her theorem, Noether’s theorem , is regarded as one of the most influential developments in physics.

Other Useful Resources

Institute of Mathematics and its Applications (IMA) – IMA is the UK’s professional body for mathematicians. It contains a wide range of useful information, from the benefits of further education in Maths to details on grants and upcoming events.

Maths Careers – Math Careers is a site associated with IMA that provides a wide range of advice to mathematicians of all ages. It has a section dedicated to undergraduates and graduates and contains a handful of information about progressing into research.

Resources for Graduate Students – Produced by Dr Mak Tomford, this webpage contains an extensive collection of detailed advice for Mathematic PhD students. Although the site uses US terminology in places, don’t let that put you off as this resource will prove incredibly helpful in both applying to and undertaking your PhD.

Student Interviews – Still wondering whether a PhD is for you? If so, our collection of PhD interviews would be a great place to get an insider perspective. We’ve interviewed a wide range of PhD students across the UK to find out what doing a PhD is like, how it’s helped them and what advice they have for other prospective students who may be thinking of applying to one. You can read our insightful collection of interviews here .

[1] Universities used to determine the typical (median) and range of entry requirements and tuition fees for 2020/21 Mathematics PhD positions.

• http://www.lse.ac.uk/study-at-lse/Graduate/Degree-programmes-2020/MPhilPhD-Mathematics
• https://www.ox.ac.uk/admissions/graduate/courses/dphil-mathematics?wssl=1
• https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdpms
• https://www.ucl.ac.uk/prospective-students/graduate/research-degrees/mathematics-mphil-phd
• http://www.bristol.ac.uk/study/postgraduate/2020/sci/phd-mathematics/
• https://www.surrey.ac.uk/postgraduate/mathematics-phd
• https://www.maths.ed.ac.uk/school-of-mathematics/studying-here/pgr/phd-application
• https://www.lancaster.ac.uk/study/postgraduate/postgraduate-courses/mathematics-phd/
• https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
• https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05325/phd-pure-mathematics/
• https://warwick.ac.uk/study/postgraduate/research/courses-2020/mathematicsphd/
• https://www.exeter.ac.uk/pg-research/degrees/mathematics/

[2] Higher Education Leavers Statistics: UK, 2016/17 – Outcomes by subject studied – https://www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education-leaver-statistics-subjects

[3] Typical salaries have been extracted from a combination of the below resources. It should be noted that although every effort has been made to keep the reported salaries as relevant to Math PostDocs as possible (i.e. filtering for positions which specify a PhD qualification as one of their requirements/preferences), small inaccuracies may exist due to data availability.

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• Mathematics, Ph.D.

The department offers the doctor of philosophy degree with a major in mathematics and a master of arts degree in mathematics.

The Ph.D. degree requires proficiency in basic and advanced graduate mathematics and the completion of a dissertation containing a significant piece of original research in some area of mathematics. The scope of the research program in mathematics is broad. The Ph.D specialty and dissertation may be in any area of mathematics, including but not limited to algebra, algebraic geometry, applied mathematics, combinatorics, computational mathematics, complex analysis, differential equations, differential geometry, dynamical systems, harmonic analysis, logic, mathematical biology, number theory, probability, and topology. A complete list of faculty and their areas of expertise is available through the department website .

Students in the Ph.D. program also have the option to earn a master of arts degree .

Please consult the table below for key information about this degree program’s admissions requirements. The program may have more detailed admissions requirements, which can be found below the table or on the program’s website.

Graduate admissions is a two-step process between academic programs and the Graduate School. Applicants must meet the minimum requirements of the Graduate School as well as the program(s). Once you have researched the graduate program(s) you are interested in, apply online .

Admission is competitive. Applicants to the Ph.D. program are automatically considered for financial support. For more information about application to the Ph.D. and M.A. programs, see the department's admission website .

Graduate School Resources

Resources to help you afford graduate study might include assistantships, fellowships, traineeships, and financial aid.  Further funding information is available from the Graduate School. Be sure to check with your program for individual policies and restrictions related to funding.

Program Resources

Prospective students should see the program website for funding information .

Minimum Graduate School Requirements

Major requirements.

Review the Graduate School minimum academic progress and degree requirements , in addition to the program requirements listed below.

MODE OF INSTRUCTION

Mode of instruction definitions.

Accelerated: Accelerated programs are offered at a fast pace that condenses the time to completion. Students typically take enough credits aimed at completing the program in a year or two.

Evening/Weekend: ​Courses meet on the UW–Madison campus only in evenings and/or on weekends to accommodate typical business schedules.  Students have the advantages of face-to-face courses with the flexibility to keep work and other life commitments.

Face-to-Face: Courses typically meet during weekdays on the UW-Madison Campus.

Hybrid: These programs combine face-to-face and online learning formats.  Contact the program for more specific information.

Online: These programs are offered 100% online.  Some programs may require an on-campus orientation or residency experience, but the courses will be facilitated in an online format.

CURRICULAR REQUIREMENTS

Required courses.

Take a total of 51 graduate credits, or generally 18 courses . This includes courses in math and in breadth. In the Ph.D. program, math courses numbered above 700 are for graduate credit. Math courses below 700 must be approved by the academic advisor.

There are five general and overlapping areas of specialization 1 within the department:   

• Algebra, Algebraic Geometry, Combinatorics and Number theory
• Analysis, Differential Equations and Probability
• Applied and Computational Mathematics
• Geometry, Topology, and Dynamics

There is also a specialty in Mathematics Education 1 . The course requirement is the same as for the other specialties except that the required 51 credits should include 18 credits in courses that relate to mathematics education, and at least one of the courses must be on research techniques in education. The 18 credits may come (wholly or in part) from courses included in breadth.

These pathways are internal to the program and represent different curricular paths a student can follow to earn this degree. Pathway names do not appear in the Graduate School admissions application, and they will not appear on the transcript.

Graduate School Policies

The  Graduate School’s Academic Policies and Procedures  provide essential information regarding general university policies. Program authority to set degree policies beyond the minimum required by the Graduate School lies with the degree program faculty. Policies set by the academic degree program can be found below.

Major-Specific Policies

Prior coursework, graduate work from other institutions.

With program approval, students in the Ph.D. program are allowed to count no more than 19 credits of graduate coursework from other institutions. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

UW–Madison Undergraduate

No more than 7 credits from a UW–Madison undergraduate degree are allowed to count toward the degree. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

UW–Madison University Special

With program approval, students are allowed to count no more than 15 credits of coursework numbered 300 or above taken as a UW–Madison Special student. Coursework earned ten years or more prior to admission to a doctoral degree is not allowed to satisfy requirements.

This program follows the Graduate School's Probation policy.

• Good standing (progressing according to standards; any funding guarantee remains in place).
• Probation (not progressing according to standards but permitted to enroll; loss of funding guarantee; specific plan with dates and deadlines in place in regard to removal of probationary status).
• Unsatisfactory progress (not progressing according to standards; not permitted to enroll, dismissal, leave of absence or change of advisor or program).

ADVISOR / COMMITTEE

Students who are not yet working with a dissertation advisor are required to meet semiannually with their academic advisor. All students must have a dissertation advisor by the end of the sixth semester.

CREDITS PER TERM ALLOWED

15 credits. Minimum of 6/semester, other than dissertators.

Time Limits

Students must complete all program requirements within eight years of beginning the program . Extensions have to be approved by the program.

A candidate for a doctoral degree who fails to take the final oral examination and deposit the dissertation within five years after passing the preliminary examination may be required to take another preliminary examination and to be admitted to candidacy a second time.

Doctoral degree students who have been absent for ten or more consecutive years lose all credits that they have earned before their absence. Individual programs may count the coursework students completed prior to their absence for meeting program requirements; that coursework may not count toward Graduate School credit requirements.

grievances and appeals

These resources may be helpful in addressing your concerns:

• Bias or Hate Reporting  
• Graduate Assistantship Policies and Procedures
• Office of the Provost for Faculty and Staff Affairs
• Dean of Students Office (for all students to seek grievance assistance and support)
• Employee Assistance (for personal counseling and workplace consultation around communication and conflict involving graduate assistants and other employees, post-doctoral students, faculty and staff)
• Employee Disability Resource Office (for qualified employees or applicants with disabilities to have equal employment opportunities)
• Graduate School (for informal advice at any level of review and for official appeals of program/departmental or school/college grievance decisions)
• Office of Compliance (for class harassment and discrimination, including sexual harassment and sexual violence)
• Office of Student Conduct and Community Standards (for conflicts involving students)
• Ombuds Office for Faculty and Staff (for employed graduate students and post-docs, as well as faculty and staff)
• Title IX (for concerns about discrimination)

Students should contact the department chair or program director with questions about grievances. They may also contact the L&S Academic Divisional Associate Deans, the L&S Associate Dean for Teaching and Learning Administration, or the L&S Director of Human Resources.

Take advantage of the Graduate School's  professional development resources to build skills, thrive academically, and launch your career. 

• Learn a substantial body of mathematics in introductory and research level graduate courses in mathematics.
• Complete a dissertation under the guidance of an advisor. The dissertation should make an original and substantive contribution to its subject matter.
• Demonstrate breadth within the learning experiences.
• Present research in seminar talks, conferences or publications.
• Communicate complex ideas in a clear and understandable manner.
• Foster ethical and professional conduct.

Please visit the Math Department website for a complete list of faculty and instructional academic staff .

• Requirements
• Professional Development
• Learning Outcomes

Contact Information

Mathematics College of Letters & Science math.wisc.edu

Kathie Brohaugh, Graduate Coordinator [email protected] 608-263-8884 203 Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706

Autumn Kent, Director of Graduate Studies [email protected]

Tullia Dymarz, Director of Admissions [email protected]

Graduate Program Handbook View Here

Graduate School grad.wisc.edu

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Best Doctorates in Mathematics: Top PhD Programs, Career Paths, and Salaries

Given that only a small proportion of the general population holds a PhD in Mathematics, there aren’t many people pursuing doctoral studies in the math field. It requires a high level of intelligence and mathematical ability which a typical person doesn’t possess. It also requires a decent work ethic and the ability to commit five to seven years to research and study.

However, PhD in Mathematics salaries are high. If you’re interested in pursuing a PhD in Mathematics, check out our article to find the best mathematics PhDs and what mathematics jobs you can get. First, let’s find out what a PhD in Mathematics is.

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What is a phd in mathematics.

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

How to Get Into a Mathematics PhD Program: Admission Requirements

The requirements to get into a mathematics PhD program typically include application fees, school transcripts, a professional resume, three letters of recommendation, and a statement of academic purpose. The admission process for most mathematical PhD programs is similar.

Some schools also require that students have mastered the material roughly equivalent to the undergraduate mathematics major, such as several semesters of calculus and experience with differential equations. Other doctoral math programs require applicants to submit essays or a minimum GPA score as entrance requirements.

PhD in Mathematics Admission Requirements

• Professional CV or resume
• Statement of academic purpose
• Application fee
• At least three recommendation letters
• Undergraduate and graduate school transcripts

Mathematics PhD Acceptance Rates: How Hard Is It to Get Into a PhD Program in Mathematics?

It is extremely hard to get into a PhD program in Mathematics. For example, the Harvard PhD acceptance rate is 4.59 percent and the University of Wisconsin has a zero percent PhD acceptance rate over a five-year median. Doctoral studies in mathematics are rigorous and have a low acceptance rate, making it difficult to get into and obtain a Doctorate in Mathematics.

How to Get Into the Best Universities

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Best PhDs in Mathematics: In Brief

Best universities for mathematics phds: where to get a phd in mathematics.

The best universities for mathematics PhDs are Harvard University, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California, Berkeley, and Yale University.

Other universities also have excellent PhD in Mathematics programs that we haven’t mentioned in our list, like Johns Hopkins University, Colorado State University, University of California, Los Angeles, and University of Chicago.

Columbia University is a private Ivy League research university founded in 1754 as King's College. It is among the top five national universities and is known as the oldest institution of higher education in New York. At Columbia University, students can find doctoral studies in biological sciences, astronomy, chemistry, economics, music, psychology, and religion.

Mathematics PhD

The PhD mathematics program is designed for full-time students interested in research and teaching at the university level. It is an intense course also meant for students that seek careers in quantitative research and development in business or government. It covers subjects like analysis and probability, Riemann surfaces, cumulative algebra, and modern geometry.

Mathematics PhD Overview

• Program Length: 4 years
• Acceptance Rate: 6%
• Tuition and Fees: $25,248/semester
• PhD Funding Opportunities: Department of Defense Funding, NIH Fellowship Parent Funding 

Mathematics PhD Admission Requirements

• A completed online application form at the Online Application System
• $120 application fee
• Statement of purpose
• A video essay (to be completed in the Online Application System)
• A current resume or CV
• Official transcripts from each university you attended
• Two letters of reference

Harvard University was established in 1636 by the Puritan clergyman John Harvard. It is known as the oldest institution of higher learning in the US and as one of the most prestigious universities in the world. It offers many PhD programs in subjects such as anthropology, statistics, virology, physics, neuroscience, mathematics, immunology, and history of science.

This doctoral program is intended for students who aspire to be research mathematicians and have demonstrated a strong interest in this field. The math graduate courses cover topics like commutative algebra, advanced real analysis, differential geometry evolution dynamics, Riemann surfaces, and Hodge theory.

• Program Length: 4-5 years
• Acceptance Rate: 7%
• Tuition and Fees: $50,928/first two years of study; $13,240/second two years of study
• PhD Funding Opportunities: Hertz Foundation, National Defense Science and Engineering Graduate Fellowship Program, National Physical Science Consortium for Minorities and Women, National Science Foundation
• Application
• $105 application fee 
• Transcripts
• Letters of recommendation
• Demonstration of English proficiency (for non-native speakers)

Massachusetts Institute of Technology (MIT) is a land-grant research university in Cambridge. Founded in 1861, MIT is best known for its programs in physical science and engineering. It offers a wide array of doctoral studies in aeronautics and astronautics, physics, political science, economics, chemical engineering, biology, brain, and cognitive sciences.

Doctor of Philosophy or Doctor of Science Mathematics Degree

In addition to choosing between a Doctor of Philosophy and a Doctor of Science program, students can choose to apply to the Pure or Applied Mathematics programs. Geometry, number theory, algebra, logic, statistics, topology, astrophysics, combinatorics, analysis, probability, numerical analysis, and theoretical physics, are covered in the Pure and Applied Mathematics curricula.

Doctor of Philosophy or Doctor of Science Mathematics Degree Overview

• Acceptance Rate: N/A
• Tuition and Fees: $27,755/term
• PhD Funding Opportunities: Postdoctoral and Senior Research Awards, Faculty Early Career Development Program, Mathematical Sciences Postdoctoral Research Fellowships (MSPRF)

Doctor of Philosophy or Doctor of Science Mathematics Degree Admission Requirements

• Fill out the online application
• Transcripts including grades in math/science/engineering courses
• At least three names and email addresses of recommendation letter writers
• Educational and work history
• Statement of objectives
• Outside financial support and potential outside support
• Credit/debit card payment of the $75 application fee
• Self-reported grades
• Arrange for submission of official transcripts and letters of recommendation

Princeton University is a private Ivy League research university that was founded in 1746. It is known as the fourth-oldest institution of higher education in the US. Princeton University has many PhD programs in subjects like philosophy, mechanical and aerospace engineering, electrical and computer engineering, and neuroscience.

Applied and Computational Math PhD

In this program, students gain a thorough understanding of areas of mathematics critical to scientific and engineering applications, such as numerical analysis and other computational approaches. In the first year, students choose three topics from six applied mathematics categories. At the end of the first year, students need to take a preliminary exam. 

Before the third year, students need to pass the general examination which culminates in a seminar on a research topic. The final requirement for this program is the doctoral dissertation which can be a mathematical contribution to one field of science or engineering.

Applied and Computational Math PhD Overview

• Tuition and Fees : $58,790/year 
• PhD Funding Opportunities: University, departmental, and program fellowships, research and teaching assistantships, external financial support

Applied and Computational Math PhD Admission Requirements

• $75 application fee
• Recommendation letters
• Fall semester grades (for students currently enrolled in master’s degree programs)
• English language tests (for international students)

Established in 1829, Rochester Institute of Technology is known for its excellent technology, engineering, and computing programs. It offers PhDs in Astrophysical Sciences and Technology, Biomedical and Chemical Engineering, Color Science, Imaging Science Sustainability, and many more disciplines.

Mathematical Modeling PhD

Students in this program plan their own trajectory based on required coursework, research, and their selected concentration. They can select from concentrations in the areas of applied inverse problems, biomedical, and discrete mathematics, among others. Some of the program’s courses cover subjects like numerical analysis and computing for mathematical modeling. 

Mathematical Modeling PhD Overview

• Acceptance Rate: 74%
• Tuition: $54,176/year 
• PhD Funding Opportunities: Federal loans, Outside Scholarships, Yellow Ribbon Program, employment through co-ops, internships, or assistantships

Mathematical Modeling PhD Admission Requirements

• Online graduate application
• Copies of official transcripts of all previously completed undergraduate and graduate courses
• Bachelor’s degree from an accredited university or college
• Current resume/CV
• Two letters of recommendation
• Personal statement of educational objectives
• TOEFL, IELTS, or PTE score (international students)
• $65 application fee

Stanford University is well-known for its enterprising student population and high return on investment. Founded in 1885 by California senator Leland Stanford, Stanford University is consistently ranking in the top 10 national universities. Stanford offers many PhD programs in its Graduate School of Engineering, including programs in engineering, medicine, and education.

Mathematics PhD Program

Students in this PhD program take courses in algebraic topology, differential topology, differential geometry, algebraic geometry, theory of probability, real analysis, modern algebra, and mathematical methods of imaging. In the first year, the coursework prepares the students for the qualifying examinations which test them on their skills in algebra and real-world analysis. 

Students must have a dissertation advisor and seek candidacy in their second year. Students will take their Area Examination during their third year, which must be completed by the conclusion of the Winter Quarter. In the fourth and fifth years, students are expected to finish their dissertation research.

Mathematics PhD Program Overview

• Acceptance Rate: 5.7%
• Tuition and Fees: $56,487
• PhD Funding Opportunities: Federal programs, university fellowships, research assistantships, teaching assistantships

Mathematics PhD Program Admission Requirements

• Bachelor’s degree from a regionally accredited US college or university 
• Unofficial transcripts/academic records
• Names and contact information of those who can provide between three and six letters of recommendation
• Online application
• $125 application fee or fee waiver

University of California, Berkeley was founded in 1868. UC Berkeley is known for strict academic criteria for its undergraduate programs. The school has more than 130 academic departments and 80 multidisciplinary research areas. UC Berkeley is among the top universities in the world.

PhD Program in Applied Mathematics

The applied mathematics program requires doctoral students with previous graduate study in mathematics must demonstrate exceptional mathematical research skills. Students in this course can learn about linear algebra and differential equations, multivariable calculus, and discrete mathematics. There are also major electives like mathematical biology and statistics.

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PhD Program in Applied Mathematics Overview

• Program Length: 5-6 years
• Acceptance Rate: 18%
• Tuition and Fees: $10,248.75/semester (resident); $17,799.75/semester (non-resident)
• PhD Funding Opportunities : Berkeley Fellowships, Chancellor’s Fellowships, Cota-Robles Fellowships, Mentored Research Awards, UC Dissertation-Year Fellowships, Conference Travel Grants, Parent and Caregiver Grants

PhD Program in Applied Mathematics Admission Requirements

• A bachelor’s degree or equivalent from an accredited institution
• A minimum GPA of 3.0
• Enough experience in your undergraduate program to complete the program
• At least three letters of recommendation
• $120 application fee (California residents); $140 application fee (all other applicants)

The University of Michigan - Ann Arbor is among the top 30 national universities. It was founded in 1817 in Ann Arbor. Some of the most popular majors from this university are business administration, experimental psychology, and economics. It also has good PhD level programs in education, electrical and computer engineering, and computer and information science.

Applied & Interdisciplinary Mathematics PhD

This PhD degree's purpose is to create graduates who are well-prepared to pursue successful careers in the mathematical sciences, whether in government or academia. Students in the applied and interdisciplinary mathematics course can learn about risk management and modeling of financial losses, mathematical theory of probability, and modern mathematics.

Applied & Interdisciplinary Mathematics PhD Overview

• Program Length: 5-6 years 
• Acceptance Rate: 26%
• Tuition and Fees: $25,230.38 (in state); $50,646.38 (out of state)
• PhD Funding Opportunities: Graduate Student Instructorship (GSI): Mathematics Graduate Student Instructor Teacher Training Program, and Graduate Student Research Assistantship (GSRA)

Applied & Interdisciplinary Mathematics PhD Admission Requirements

• Three letters of recommendation
• Personal Statement (500-word limit)
• TOEFL or IELTS Exam (non-native English speakers)
• Three semesters of calculus
• One or two semesters of differential equation courses
• One semester course in modern algebra, linear algebra, geometry or topology
• Advanced calculus of one and several variables 
• $75 application fee (US citizens); $90 application fee (international applicants)

Nelson Dewey, the first governor of Wisconsin, founded the University of Wisconsin in 1848. It has one of the best engineering and business majors. It also has several good graduate degrees from its Department of Mathematics like Doctor of Philosophy, Master of Arts – Foundations of Advanced Studies, and Master of Arts – Foundations for Research.

Mathematics, PhD

The University of Wisconsin’s Doctor of Philosophy program offers a foundation in fundamental and advanced graduate mathematics. Students in this PhD program can learn about linear algebra, abstract algebra, differential equations, knot theory, and real analysis.

Mathematics, PhD Overview

• Program Length: 5 years
• Acceptance Rate: 16%
• Tuition and Fees: $12,176/year (in state); $25,504/year (out of state)
• PhD Funding Opportunities: Graduate assistantships, fellowships, traineeships, student loans, student jobs, research and travel grants

Mathematics, PhD Admission Requirements

• Application to the UW–Madison Graduate School
• Master’s degree in mathematics or a related field
• Official transcripts
• Supplementary information form
• Three academic letters of recommendation and one additional letter
• Proof of English proficiency (for non-native speakers)
• One-page statement of purpose

Yale University was founded in 1701 in New Haven, Connecticut. It is among the top 10 national universities and is known for its Ivy League reputation . Yale has many PhD programs like anthropology, applied physics, architecture, biomedical engineering, chemical, and environmental engineering. 

PhD in Applied Mathematics

The applied mathematics program entails the study and application of mathematics to issues prompted by a diverse set of application fields. Students study and apply mathematics concepts to questions driven by a variety of applicable fields.

It covers topics such as discrete algorithms, linear and nonlinear partial differential equations, statistical theory and applications, information theory, econometrics, and classical and modern applied harmonic analysis. This program also covers topics like financial statistics, financial mathematics, econometrics probability theory, and information theory. 

PhD in Applied Mathematics Overview

• Acceptance Rate: 6.2%
• Tuition and Fees: $45,700/year
• PhD Funding Opportunities: Financial aid, university fellowships, dissertation fellowships, teaching fellowships

PhD in Applied Mathematics Admission Requirements

• A list of all the prior colleges or universities you’ve attended 
• Unofficial transcripts from each school
• TOEFL scores (non-native English-speaking applicants)

Can You Get a PhD in Mathematics Online?

Yes, you can get a PhD in Mathematics online. However, there aren’t many online PhD math programs out there because of two reasons. The first reason is that there isn’t a big demand for PhDs in Mathematics, so online universities are not inclined to find ways to make those programs more accessible.

The second reason is that in traditional doctoral studies graduate students in mathematics are used as research and teaching assistants. Usually, math doctoral studies take place within a community in which PhD students are apprentices learning alongside instructors and one another.

Best Online PhD Programs in Mathematics

How long does it take to get a phd in mathematics.

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree .

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

Is a PhD in Mathematics Hard?

Yes, a PhD in Mathematics is hard. Doctoral studies that require advanced knowledge of mathematics would be extremely difficult for most people. Whether you choose to pursue a PhD in Applied Mathematics or Pure Mathematics, you will encounter complex theoretical concepts.

How Much Does It Cost to Get a PhD in Mathematics?

On average, it costs $12,171 per year to get a PhD in Mathematics . This data is based on the National Center for Educational Statistics’s (NCES) report for the average costs of postgraduate studies at public institutions from 2018 to 2019. According to this data, it would cost a total of $48,684 for four years of studies. The cost to get a PhD in Mathematics has likely risen since 2019.

How to Pay for a PhD in Mathematics: PhD Funding Options

The PhD funding options that students can use to pay for a PhD in Mathematics include research fellowships, teaching assistantships, and tuition waivers. In the previous section, we mentioned the cost of doctoral degrees , but this number is with a deduction in the tuition.

These funding options enable students to lower the cost of tuition. For example, domestic students receive lower tuitions. Without funding options or deductions, a PhD can cost from $20,000 to $30,000 per year.

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What Is the Difference Between a Mathematics Master’s Degree and PhD?

The difference between a Master’s Degree in Mathematics and a PhD is the career opportunities they provide graduates. People who pursue a PhD in Mathematics usually seek jobs in research and academia, while people who pursue master’s degrees are more interested in advancing their professional careers.

A PhD in Math is more research-intensive and focused on historical and current perspectives within the mathematics field. Master’s degrees are a bit broader. Master’s degrees can take up to three years to complete, while PhD can take up to six years. Math PhD students also teach and engage in departmental activities, while master’s students do not.

Master’s vs PhD in Mathematics Job Outlook

It is usually required for postsecondary teachers to have PhDs. According to the Bureau of Labor Statistics (BLS), these professionals have a job outlook of 12 percent , four percent higher than the average for all occupations.

Mathematics and statisticians are usually required to hold a master’s degree and they have a job outlook of 33 percent , nearly three times the average for all occupations. According to these numbers, the job outlook for Master’s Degrees in Mathematics is higher than for PhDs in Mathematics. However, these are just two examples of careers available to master’s and PhD holders.

Difference in Salary for Mathematics Master’s vs PhD

According to PayScale, mathematicians with a master’s degree earn $85,000 per year, and mathematicians with a PhD degree earn $110,000 a year. This is a difference of $25,000 per year for mathematics master’s vs PhD holders.

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Why You Should Get a PhD in Mathematics

You should get a PhD in Mathematics because it expands your academic career opportunities and salary options. With a PhD in Math, you can work for private businesses or government agencies. Many PhD grads work in engineering, medicine, and software development, where they apply the advanced mathematical knowledge they acquired from their doctoral programs.

Reasons for Getting a PhD in Mathematics

• Specialized skills. A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.
• Higher salary. A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.
• Career opportunities. One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.
• Research opportunities. Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

Getting a PhD in Mathematics: Mathematics PhD Coursework

Getting a PhD in Mathematics is not an easy task. Students need to learn different math courses, some of which require advanced knowledge of mathematics. There is some standard mathematics PhD coursework, like classes in mathematical analysis or mathematical logic. Find out more details on common mathematics PhD courses below.

Mathematical Analysis

These kinds of courses explain the principles of mathematical analysis, including differentiability, continuity, sequence and series convergence, the Riemann integral, function sequences, and series. Students can also learn real applications of real-world analysis, including the estimation of indeterminate integrals, Laurent series, WKB theory, Cauchy theorem, and residual theorem.

Differential Topology

Courses in differential topology are a part of the theory of differential forms and De Rham’s theory. Somer differential topology courses teach about multilinear algebra, Stokes’ theorem, and an introduction to cohomology. But, in most cases, these courses teach about winding numbers, vector fields, index, smooth maps, transversality, and differential manifolds.

Discrete Mathematics

Courses in discrete mathematics usually cover finite geometry, finite groups, finite topology, finite fields, fundamental algebraic topology, combinatorics, and graph theory. Students can learn about the symmetry group of the regular icosahedron because it is a reoccurring subject throughout the course.

Theory of Probability

Theory of probability courses introduce students to discrete and continuous random variables, independent random variables, conditional probability, distribution functions, Poisson distributions, Bayes theorem, and joint distribution. Students in this course will learn how to use math principles in the analysis of random phenomena.

Algebraic Geometry

In most cases, algebraic geometry courses teach students about complex algebraic varieties, cohomology, affine, and projective algebraic geometry. They also cover the fundamental concepts of complex analytic varieties, Bezout’s theorem, algebraic curves, and surfaces, the language of schemes, and properties of morphisms.

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How to Get a PhD in Mathematics: Doctoral Program Requirements

Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs. Keep reading to find out more.

PhD students must finish eight or nine-term courses at the graduate level, in most cases maintaining at least a C average grade. The time for completion of a PhD math coursework is four to five years.

The residency requirement can vary from university to university. For most math PhD candidates, the usual residency requirement is around three years. The whole point of residency is to continue the education and training of students in a specialized field of mathematics.

A committee of three faculty members administers the Qualifying Examination, which is an oral test. Each student selects three qualifying test subjects and discusses them with appropriate examiners. Subjects must be in separate, reasonably broad mathematical fields. 

Typically, the primary topic is decided in cooperation with the potential thesis advisor. After completing the qualifying test, students must choose a thesis advisor, who is usually the primary topic examiner.

In academic positions, teaching is important, especially in mathematical doctoral studies. Many people in math PhD programs aspire to academic positions, so teaching is one of the best ways to learn about the mathematics academic profession. It is an excellent way to learn public presentation skills by completing at least one semester of classroom teaching.

Writing and defending a thesis for a PhD in Mathematics is the culmination of this graduate program. Usually, a thesis is anticipated to contain original research of a high enough quality to be published in a high-level research journal. The defense is usually held in the classroom of the Institute and is presented to the Thesis Examination Committee.

Potential Careers With a Mathematics Degree

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PhD in Mathematics Salary and Job Outlook

People with a PhD in Mathematics earn above the average annual salaries and have careers with above the average job growth. For example, actuaries have a 24 percent job growth till 2030. According to the Bureau of Labor Statistics, the average job growth rate for all occupations is 7.7 percent .

Earning a mathematics PhD is difficult but you will graduate with a wide range of job opportunities. People with a PhD in Math earn between $82,360 to $108,660 per year. Overall, people with PhDs in Mathematics have a good salary and job outlook.

What Can You Do With a PhD in Mathematics?

With a PhD in Mathematics, you can work in education or IT and for private, corporate, or government corporations. You can work as a postdoctoral research associate, a math professor in postsecondary or higher education, a director of analytics, a research scientist, a principal software engineer, or an asset manager.

Best Jobs with a PhD in Mathematics

• Data Scientist
• Mathematicians and Statistician
• Operations Research Analyst

What Is the Average Salary for a PhD in Mathematics?

The average salary for a PhD in Mathematics is $110,000 , according to PayScale. The salary range for doctorate-level degree mathematics jobs ranges from $48,690 to $167,040 per year. Lower-earning operations research analysts make an average of $48,690 , while top-earning data scientists earn $167,040 annually, according to the Bureau of Labor Statistics.

Highest-Paying Mathematics Jobs for PhD Grads

Best mathematics jobs with a doctorate.

There are many jobs you can find with a math PhD. The skills you will gain are applicable to almost any field. Find out more about the best PhD in Mathematics jobs below.

Data scientists are specialists who know how to extract and interpret data. They know how to use models and algorithms to analyze massive data repositories. They use various strategies to determine the optimal methods for developing a data model for a business. Data scientist is one of the most in-demand and highest-paid jobs in 2022. 

• Salary with a Mathematics PhD: $108,660
• Job Outlook: 22% job growth from 2020 to 2030
• Number of Jobs: 105,980
• Highest-Paying States: Washington, California, Delaware, New York, New Jersey

Actuaries are more concerned with the financial implications of risk and uncertainty. Actuaries are financial analysts who analyze past and present financial data and forecast future risks. They assess risk using financial theory, statistics, and math and develop plans that reduce the cost of risk.

• Salary with a Mathematics PhD: $105,900
• Job Outlook: 24% job growth from 2020 to 2030
• Number of Jobs: 27,700
• Highest-Paying States: Georgia, New Hampshire, New York, Connecticut, Vermont

Some of the main responsibilities economists have are to predict the customer demand for the firm's products and the firm's product sales. They deal extensively with microeconomic issues while researching trends, collecting, evaluating, and analyzing data. Economists also investigate how to efficiently allocate resources like raw materials, labor, land, or machines.

• Salary with a Mathematics PhD: $105,630
• Job Outlook: 13% job growth from 2020 to 2030
• Number of Jobs: 18,600
• Highest-Paying States: New York, District of Columbia California, New Hampshire, Illinois

In most cases mathematicians and statisticians work in academia and government. Usually, both of the positions require the use of analyzing data or applying statistical and mathematical techniques that help solve problems. 

Statisticians are increasingly involved in statistics and research methodology. Mathematicians are more involved in researching mathematical models or abstractly measuring values and creating results. Mathematics and statistics are the best duos that understand the principles of probability.

• Salary with a Mathematics PhD: $96,280
• Job Outlook: 33% job growth from 2020 to 2030
• Number of Jobs: 44,800
• Highest-Paying States: District of Columbia, New York, New Jersey, Virginia, Maryland

Operations research analysts utilize mathematics and logic to assist businesses in making informed decisions and solving complex problems. They are high-level problem solvers that use sophisticated approaches such as mathematical modeling and statistical analysis to help companies operate more economically.

• Salary with a Mathematics PhD: $82,360
• Job Outlook: 25% job growth from 2020 to 2030
• Number of Jobs: 104,100
• Highest-Paying States: Virginia, Alabama, Maryland, Hawaii, New York

Is a PhD in Mathematics Worth It?

Yes, a PhD in Mathematics is worth it if you are interested in solving math problems and analytical thinking. You also have to be willing to commit to the long educational journey and research required to achieve this level of degree.

Exploring the mathematical fields is challenging and demanding but with time it provides excellent career opportunities. Math positions are respected and well-paid with positive job outlooks. Other than its academic difficulty, there aren’t many downsides when it comes to doctoral math degrees because you can go on to work in many fields.

Additional Reading About Mathematics

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PhD in Mathematics FAQ

Yes, a math PhD is useful because it will help you acquire some transferable skills that will be useful in virtually any industry. It is also useful for those interested in mathematics research or academia. If you wonder what you can do with a math degree , a PhD will equip you with many valuable skills.

Yes, a PhD in Mathematics is difficult to learn. It is difficult to be admitted to a doctoral program in mathematics, and it is also difficult and too abstract for most people to grasp advanced mathematical principles taught in PhD studies. Doctoral math studies are objectively difficult, even for those who are naturally strong at math and have excelled at it their whole life.

Mathematicians need several skills like active learning, complex problem-solving, critical thinking, and analytical skills. A good mathematician also needs information ordering and inductive and deductive reasoning abilities.

Mathematicians mainly explore mathematical principles or models and create their own mathematical theories and concepts. Most of the work they do is in the theoretical realm, that is why they mainly want to work in IT, social science, engineering, or financial fields.

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PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the  Qualifying Examinations .  Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.

Current Course Requirements: To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry

• Math 216A, B, & C: Introduction to Algebraic Geometry
• Math 230A, B, & C: Theory of Probability
• 3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later: 

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. (The course sequence requirement is discontinued for students starting in Autumn 2023 and later.)

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination, which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

© Stanford University . Stanford , California 94305 .

PhD in Mathematical Sciences

When you pursue a PhD in Mathematical Sciences at WPI, you join a vibrant community of faculty members, postdoctoral researchers, and students who are creating new knowledge and applying their expertise to solve to complex, real-world problems.

Value Proposition Description

We accept about five new doctoral students in our PhD in mathematical sciences each year, all of whom are fully funded, and maintain a team of about 25 PhD candidates. You will be encouraged to collaborate with researchers in the department and across campus as you make important discoveries in an area of interest, from theoretical mathematics to applications in diverse areas like data science, electrical and computer engineering, bioinformatics and computational biology, and biomedical engineering.

Our flexible curriculum enables you to tailor programs of research and study to your professional goals. You will select courses in mathematical sciences and other disciplines and may choose to complete a PhD project with an external sponsor that allows you to connect your theoretical knowledge with relevant applications. We also offer professional development training to enhance your skills in teaching, grant writing, interviewing, and the job search process.

As you pursue your PhD in mathematical sciences, you will be expected to pass two general comprehensive exams by the end of your first year of study and a series of preliminary exams before registering for your dissertation research.

Research for PhD in Mathematical Sciences

Research in our PhD in mathematical sciences program at WPI plays a vital role in solving complex problems facing our world. You will work alongside faculty and student researchers who are involved in a wealth of diverse projects, both fundamental and applied, in these areas:

• Discrete mathematics, combinatorics, and graph theory
• Analysis and differential equations
• Computational mathematics
• Statistics and stochastic analysis

Our strong interdisciplinary culture also offers exciting possibilities to interact with researchers in other disciplines, including physics, engineering, and the life sciences.

In addition, as a PhD in mathematical sciences student, you will have access to a modern and diverse line-up of computing facilities and industry-standard software programs, including SAS, R, MATLAB, Python, and Turing, our high-performance computer cluster.

Faculty Profiles

The evolution of defects in materials present very interesting mathematical challenges.  My research focuses on improving mathematical models for material defects and advancing mathematical methods for studying them. Of particular interest are the growing lower-dimensional surfaces found in fracture mechanics.  There are many open questions here, and my projects involve postdocs, graduate students, and undergraduates, as well as other mathematicians and collaborators from other fields.

I am a mathematical physicist working on the development and application of mathematical methods to atmospheric research and satellites orbits. As part of this research, I am also developing new methods for the use of symmetry principles to solve differential equations. I have taught a broad spectrum of applied math courses on the undergraduate and graduate levels.

Research is a core part of the undergraduate experience at WPI. As Associate Dean of Undergraduate Studies, Prof. Suzanne Weekes increases the focus on the undergraduate research enterprise at the university to continue to advance WPI’s mission to create, to discover, and to convey knowledge at the frontiers of academic inquiry for the betterment of society.

Bill Martin's goal is to find mathematical research projects that lie between beautiful and powerful mathematical theory, on the one hand, and pressing technological applications, on the other. This effort requires one to keep abreast of both mathematical developments and applications in computer science and engineering. Professor Martin's mathematical research is in the area of algebraic combinatorics, where tools from linear and abstract algebra are applied to problems in discrete math.

Refer a Friend

Do you have a friend, colleague, or family member who might be interested in Worcester Polytechnic Institute’s (WPI) graduate programs? Click below to tell them about our programs.

Looking for More of a Statistics Focus? Earn a PhD in Statistics Instead.

Maybe you’re interested in specializing in a statistics PhD rather than mathematical sciences? Our PhD in statistics challenges students to use critical thinking and problem solving to identify patterns in big data. Choose from six statistics and mathematics courses ranging from time series analysis to theoretic probability theory when you pursue a PhD in statistics at WPI.

Do You Need Your Master’s First? Explore Our Mathematics MS Programs.

Whether you have a passion for a specific area of mathematics like finance or prefer a broader scope of study, our mathematics master’s programs can help you gain the knowledge you need to get ahead. If you’re looking for a broad background in mathematics, our master’s in applied mathematics may be a good fit for you. Maybe you’re interested in how to solve complex problems as it pertains to business and industry? A master’s in industrial mathematics is the way to go. This MS program provides students the business background needed to tackle real-world industry problems. Do you have a gift for working with big data and tackling challenges? Be sure to explore our master’s in applied statistics , which dives into crucial statistical methods with the flexibility to select courses that align with your career aspirations. Are you interested in becoming a financial analyst who assesses data findings to steer business decisions? Our master’s in financial mathematics will provide a solid understanding in computational methods and credit risk modeling.

Just Starting to Carve Out Your College Career? Explore a BS in Mathematical Sciences.

If you’re an incoming undergrad interested in mastering mathematical theory to solve real-world problems, our BS in mathematical sciences could be the degree for you. Our bachelor’s explores pure mathematics, applied mathematics, and statistics to give you a breadth of expertise. 

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

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PhD in Mathematics Course, Admission 2024, Eligibility, Syllabus, Fees, Career

PhD mathematics is a doctoral degree programme of a minimum of three years of duration and maximum of six years that deals with various mathematics concepts such as the study of space, structure, change, and quantity. The mathematics degree programme comes to its completion after the students submit their ‘thesis’ and get it approved by their supervisor.

Highlights - PhD Mathematics

Phd in mathematics eligibility criteria, phd mathematics admission process, top ph.d in mathematics entrance examinations, phd mathematics cutoff, skills required for ph.d in mathematics, syllabus of ph.d in mathematics, ph.d in mathematics fee structure, scope of ph.d mathematics, career options after ph.d in mathematics, benefits of studying phd mathematics, salary after phd in mathematics, list of top 10 ph.d. mathematics colleges in india with fees, top private ph.d mathematics colleges in india with fees, top government ph.d in mathematics colleges in india with fees.

The eligibility criteria to pursue a Phd in Mathematics depends on the institute, but generally candidates require a Bachelor’s degree in Mathematics or any other related discipline. Many career options are available after graduating in a Ph.D Mathematics course such as Mathematician, Statistician and Mathematics Lecturer.

Students applying for the Ph.D in Mathematics course must know the top colleges offering Ph.D in Mathematics including Acharya Institute of Technology, Aditanar College of Arts and Science, and Agra College. Admission depends on the institute, generally students need to appear for entrance exams such as UGC NET to pursue Ph.D in their desired field.

Generally, the minimum duration for this programme is three years but students can take up to a maximum of six years to complete the course. Candidates with a master’s degree in mathematics (MSc mathematics), physical sciences or M.Tech candidates can choose to pursue a PhD in mathematics. After its completion, candidates can find various options of employment in various sectors.

The eligibility criteria for PhD mathematics is quite subjective and depends on the chosen institute. Tier-1 institutes generally require students to have strong academic backgrounds as well as some work experience in teaching or research. Students are required to meet the eligibility criteria and ensure their admission. Some of the most common eligibility requirements for PhD mathematics are mentioned below:

• Candidates must have completed their Master’s degree in mathematics or physical sciences or a related field. Some of the popular master’s degree programs are MSc statistics, MSc mathematics, MSc chemistry, MA Economics, or MTech.
• Candidates must have obtained a minimum of 60 per cent aggregate score in class 12, bachelor’s, and master’s degree programmes.
• Candidates must appear for the relevant entrance exam such as UGC NET and score a valid cut-off.

The admission process for PhD mathematics is quite simple and follows certain steps that students need to complete. The PhD mathematics admission process is both merit-based as well as entrance based. Eligible candidates must carefully follow the complete admission process. Candidates can find the complete step-by-step information on admission procedure for PhD mathematics mentioned below:

Merit based admission:

• Many institutes offer admission to the Ph.D in Mathematics course, the admission to the programme is based on the score of the previous course of study. Some universities may also conduct personal interviews, group discussions or aptitude tests.
• Many institutes also offer admission to Ph.D. mathematics degree programmes based on their scores of previous courses of study. In addition to this, these universities might conduct a personal interview to screen the most deserving candidates.

Entrance Exam Based:

• Many institutes also offer the admission based on the entrance examination, one of the popular entrance exams for Ph.D degree is UGC NET, some universities may conduct their own entrance exams.
• The universities offering the Ph.D in Mathematics course provide admissions on the basis of entrance exams. The exam is conducted on the basis of mathematics subject and includes Multiple Choice Questions from different topics from Mathematics.
• Many institutes also offer mathematics degree programmes and generally provide admission based on entrance exams. The entrance examination is conducted on the mathematics subject and includes multiple choice questions from various chapters such as advanced algebra, discrete mathematics, analysis, and more.
• The universities offering Ph.D. mathematics degree programmes shortlist candidates based on their scores in the entrance examinations.
• One of the popular entrance examinations for admission to top PhD mathematics universities are UGC NET.

Various colleges in India provide admission to PhD mathematics degree programmes only through an entrance examination. Not many universities conduct their own entrance test and rely on central or state-level entrance tests. Mentioned below is the entrance examination accepted by most of the universities.

UGC NET : UGC-NET exam is conducted by the National Testing Agency (NTA) for admission to top Ph.D. degree programmes across the country. Candidates who qualify for the exam with high scores are offered junior fellowship awards (JFA) and assistant professorships across various universities in India. The relevant UGC-NET information is listed below:

• UGC NET Admit Card
• UGC NET Syllabus
• UGC NET Exam Pattern
• UGC NET Result
• UGC NET Cutoff
• UGC NET Preparation Tips
• UGC NET Eligibility
• UGC NET Application

The cutoff for PhD mathematics is different for every university since every university has a different number of seats available and different levels of popularity among students. The cutoff is defined for a course and a university and the minimum score that students need to obtain in their recent qualifying exam.

Candidates interested in pursuing Ph.D in Mathematics must have excellent research skills, and interest and aptitude for Mathematics and its application. Apart from these skills, candidates need many skills that will help the candidate perform well both academically and professionally. Mentioned below are the skills required for a Phd in Mathematics.

• Problem-Solving
• Good Communication
• Good Observation skills
• Quantitative Aptitude

The syllabus for PhD mathematics is subjective in nature and depends on the desired institute. PhD mathematics syllabus comprises both theoretical as well as practical subjects and a final thesis. Candidates can find the complete PhD mathematics syllabus according to the year and specialisations mentioned in the table below is the MDU Rohtak curriculum of Ph.D in Mathematics.

The fee structure for PhD mathematics is variable and depends on various factors such as on the type of institute, location of the company and the status of the institute.Candidates’ academic scores also play a huge role in deciding the fee. The average fees of a Ph.D Mathematics course ranges from Rs. 2,480 to Rs. 3.97 Lakhs.

The scope of PhD mathematics is quite huge and there are ample opportunities in both private as well as government sectors. After the completion of PhD mathematics degree programmes, candidates are offered with lucrative job opportunities in the academic sector as well as in corporate, depending on the experience of the graduate.

The employment opportunities after completing PhD mathematics are huge and various sectors are open for PhD graduates to choose from. In the case of academics, candidates can choose to work as an assistant professor or professor in a private or government college within their specialisation.

Economist : An economist is a professional who studies different economic equations and analyses the consumption and production of a particular state in order to decide their economic strengths and weaknesses. After a certain result is derived, an economist comes with better solutions and equations for how to develop better economic trades.

Statistician : A statistician is a professional who is responsible for analysing and studying large amounts of data such as bar graphs, histograms, and others to make economic, strategic, or operational decisions. A statistician derives the concepts from a huge amount of data and delivers it to the clients so that the final decision can be made.

Scientist : A scientist is a professional who is responsible for conducting various research and experiments around mathematics and related fields to derive new equations and technical solutions. He or she works under both theoretical and practical mathematics.

Top Recruiters:

• Ernst & Young
• Tiger Analytics
• TCS Innovation Lab
• Weizmann Institute

PhD mathematics is one of the highly regarded and sought after degree programmes when it comes to doctoral studies. The degree programme not only offers a thorough understanding of one of the most complex subjects but also a wide range of career options to choose from. Students pursuing PhD mathematics work in various mathematical fields such as mathematical physics, dynamical systems, and numerical analysis.

The employment opportunities are also strong in the case of PhD mathematics. Candidates can find senior profile employment in the banks, colleges, investment banking, Indian civil service, commerce industry, inventory management, business industry, research and development firms, insurance agencies, and inventory management.

The salary after completion of a Ph.D. in Mathematics depends on various factors, such as the location of the company, type of company, skills, and experience of the candidate, and the job profile applied by the candidates. Mentioned in the table below are the average salaries of some of the top career options in the field of Ph.D. in Mathematics.

Source: AmbitionBox

There are various PhD mathematics degree colleges in India and the top PhD mathematics colleges in India are the ones with quality education, research proposals, and good industrial exposure. Candidates applying to these colleges must meet the eligibility requirements and carefully follow the admission process. Some of the top PhD Mathematics colleges in India are mentioned below:

Private colleges in India offering admission to top PhD mathematics degree programmes are gaining a lot of popularity among students due to attractive fellowship awards, and research scope offered by them. The top private PhD Mathematics colleges in India are mentioned below:

The government colleges offering admission to PhD mathematics degree programmes are top in students’ list when it comes to PhD. The government colleges not only offer fellowships and scholarships but also offer a lot of research facilities in the PhD mathematics field. Some of the top government PhD mathematics colleges in India are mentioned below:

Ph.D in Mathematics offers the students with various career options and wide scope, students after completing their Ph.D Mathematics course work can join both private and government sectors and make a handsome salary. Some of the top career options include Statistician, Economist and Scientist.

Frequently Asked Question (FAQs)

PhD mathematics is a doctoral degree programme which deals with various mathematics concepts. 

The minimum duration of getting a PhD in mathematics is three years whereas the maximum is six years.

Yes, after the completion of PhD mathematics degree programmes, candidates are offered with lucrative job opportunities in the academic sector as well as in corporate roles. 

In the government sector, the average salary for a professor or scientist is around Rs. 80,000 to Rs. 95,000 per month. In the private sector, the salary bar ranges from Rs. 65,000 to Rs. 1.5 lakh per month and depends on the job profile.

Some of the popular job profiles are statistician, economist, demographer, scientist, research associate, and more.

How much does it cost to do a PhD mathematics?

The eligibility criteria for a PhD mathematics degree programme is that students must have completed a master’s degree in mathematics.

Ernst & Young, Tiger Analytics, TCS Innovation Lab, and Weizmann Institute are some of the companies that hire PhD in mathematics graduates.

UGC-NET, and GATE are some of the top entrance examinations for admission to top PhD mathematics degree programmes. 

The PhD in mathematics is generally considered a tough degree programme. Some of the core subjects of PhD in mathematics are mathematical physics, dynamical systems, biomathematics group, numerical analysis, fluid dynamics, and more.

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Remote Sensing Technician

Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive. 

Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.

Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

Finance Executive

Product manager.

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

Stock Analyst

Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.

A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.

Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

Conservation Architect

A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software. 

Highway Engineer

Highway Engineer Job Description:  A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials. 

Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

Veterinary Doctor

Speech therapist, gynaecologist.

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism , Advertising , Marketing Management . Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication) , B.M.M. (Bachelor of Mass Media) , or  MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.  

Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

Production Manager

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

ITSM Manager

Automation test engineer.

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process. 

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An Overview of a PhD in Mathematics

• May 12, 2022
• No Comments

A PhD in Mathematics is an academic degree for those who have completed a program studying the field of Mathematics . 

Mathematics is highly interdisciplinary and is the science of patterns. Therefore, this doctorate offers courses in both pure mathematics (mathematical analysis and algebraic systems). For example, on one hand, and computation methods, applied mathematics (computational mathematics), on the other hand. 

PhD in Mathematics study consists of patterns, abstracting them into a formal system, as well as formal systems to describe everyday problems. 

How to Choose the Right PhD Admission Program in Mathematics : 

The first thing you’ll need to do is decide what area of mathematics interests you the most. Your options for specific areas include: 

Pure mathematics: This involves topics like geometry, algebra, number theory, and topology. If this is your area of interest, your work will focus largely on theoretical concepts rather than applied work. 

Applied mathematics: This includes more specialized fields such as fluid dynamics and aerodynamics; as well as research areas like mathematical biology and mathematical physics. If you’re interested in applied math, you’ll be using theories from fields such as. Statistics , algebra, and calculus to solve practical problems in other disciplines. 

Mathematical statistics: Those who are interested in mathematical statistics apply statistical methods to problems in other areas of mathematics. You’ll need to have a firm grasp on probability in order to pursue a degree in this field. 

Probability theory: The goal of this field is to analyze random phenomena to understand any activity properly. It’s closely related to statistics, but with a more theoretical approach. 

Statistics: This involves probability theory and data collection for hypothesis testing. Statistical analysis can be both theoretical and applied. 

Other Options Include:

Discrete mathematics and combinatorial analysis, numerical analysis (by computer scientists), operations research (a mix of math and engineering) .

Why Get a PhD in Mathematics?  

There are many reasons to get a PhD in Mathematics. Math covers a broad set of interesting topics, and the ability to understand mathematics can lead to a higher starting salary than most careers.  

• The ability to do and understand mathematics is an asset in almost every field, and it opens doors that would otherwise remain closed.  
• In addition, mathematics is essential for any career in science, engineering, economics, or finance. 
• You can also work as an applied mathematician, developing mathematical models for businesses and companies throughout the country, including health care and industrial settings. 
• By earning your PhD in mathematics, you open up a world of career possibilities.  
• You may want to pursue a career in academia or teach courses while continuing to perform research or publish papers of your own creation.  
• Some universities offer positions that reward teachers for having strong research backgrounds, so if teaching is what you enjoy most about mathematics, this could be the perfect opportunity for you. 

What is the Difference Between an MA, MS, and PhD?  

• An MA stands for Master of Arts and an MS stands for Master of Science. These degrees are both generally just called Masters degrees.  
• The difference between an MA and MS degree is that one type of degree focuses on the arts, while the other focuses on science.  
• However, this distinction is not very important for most graduate math programs because most do not offer an MA at all and because there is no real difference between the courses one would take for either type of degree.  
• Therefore, when I talk about a Master’s degree below, I am referring to both types (i.e., both MA and MS). 
• A PhD stands for Doctor of Philosophy. This is often abbreviated as “PhD” but sometimes people say “Doctorate in Philosophy.”  
• A PhD in Mathematics typically requires two years of full-time study, which includes coursework, comprehensive exams, and dissertation research and writing.  
• A master’s program usually takes one year of full-time study (or two years part-time). 

Further, many jobs requiring a doctorate-level education in mathematics exist in academia or for government organizations. Successful careers and research careers in these areas require advanced knowledge of PhD in mathematics, with the specialization required for this profession vastly exceeding what most people learn in a lifetime.  

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Doctor of Philosophy (PhD) in Mathematics Admission, Top Colleges, Syllabus, Scope and Salary 2023

• PhD Programs

A Ph.D. in Mathematics is equivalent to a very advanced maths degree. You learn about shapes, numbers, and how things change while also attempting to figure out new things. When you finish, you must write a large document known as a 'thesis,' and then you will be awarded the special degree.

The programme requires at least three years and can take up to five or six years to complete. To participate, you must have a Master's degree in maths or science, or you can join if you have a different degree, such as engineering. Some places allow exceptionally bright candidates to join immediately after completing their Bachelor's degree. The programme combines study and research, and you must complete a large research report.

This programme is designed for people who are serious about becoming math experts. You learn new techniques to solve problems and gain a thorough understanding of maths. You can work on a wide range of maths issues, from the most abstract to the most practical. You will also learn how to teach and explain mathematics.

After completing the programme, you will be able to work in a variety of settings, including banks, enterprises, and colleges. Mathematician, statistician, banker, accountant, researcher, and more vocations are possible. The salary ranges from 3 to 9 lakhs depending on your knowledge and length of service.

PhD In Mathematics: Course Highlights

The following is a list of course highlights that candidates should consider before pursuing a PhD in Mathematics.

Ph.D. in Mathematics: What is it about?

Students who want to work in a mathematical research field should obtain a Ph.D. in mathematics.

• This course takes at least two years to complete, but you have up to 3-5 years if you need extra time.
• A PhD in mathematics is a full-time degree program.
• Students in the Ph.D. Mathematics program learns about statistics in fields such as inspection, design, and quality assurance.
• Students in the PhD in Mathematics program conduct research utilizing many methods of performing maths. They examine graphs, large intricate numbers, computer calculations, how things break into different courses, the likelihood of events occurring, and other factors.
• Students in this course learn about how numbers are related, how normal things are, how likely certain things are to happen, how to choose a group to research, how to figure out relationships between numbers, and how to be certain about outcomes. The course also teaches students how to use arithmetic in real-world circumstances, such as working with numbers and shapes, solving problems, and dealing with difficult topics.

Why study PhD Mathematics?

If you want to work in a research environment, there are many options at research organisations and universities. There are good-paying teaching jobs available at private engineering colleges if you wish to be a teacher. Many large corporations and financial institutions hire Indian mathematicians for their research centres.

Let us now discuss why pursuing a PhD in Mathematics is a good choice.

• This program keeps you up to date on fresh information and teaches you how to do research that is relevant to what our country needs right now.
• You will learn how to create an effective research paper and how to present data using graphics.
• You can pursue a career in accounting, business, banking, investment, insurance, government, or public administration after completing this program.
• If you enjoy teaching, you can work in schools or colleges. To teach in a college, you must pass the NET test and fulfil the UGC standards.

List of Top 10 Phd In Mathematics Colleges

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The following are the common Ph.D. (Mathematics) eligibility criteria for admission to a college providing this course:

• You can apply if you have an M.Sc. or Master's degree in Math or Physical Sciences. 
• You may also be eligible if you hold a B. Tech degree in any discipline, depending on the institute. 
• Some institutes may also allow you to attend if you performed exceptionally well in your undergraduate studies. 
• Keep in mind that each college has a minimum score requirement. In general, it is around 55%. If you are from the SC/ST group, 50% is also acceptable.

The eligibility criteria described above are the fundamental eligibility criteria. Each college will have its own set of criteria for evaluating prospective students.

How To Get Admission In PhD Mathematics

As a result, many schools and universities that teach extremely difficult maths, such as Ph.D. level maths, frequently allow applicants to attend if they performed well on previous university exams. However, certain places may have a unique test to assess how good you are. They admit candidates to their Ph.D. maths programmes in one of two ways: based on their previous university grades or through a particular test.

Merit-Based Admission:

So, when it comes to private universities like Lovely Professional and AMU, if students fared well in their previous master's or graduate studies, they usually allow them join their Ph.D. in Mathematics programmes. These colleges may also conduct a brief interview with the candidates or administer a short written test to learn more about them and their abilities.

Entrance Exam Based:

Large universities such as Chandigarh University, RKMVCC, and Stella Maris College provide unique programmes for people who desire to become math specialists. To gain admission, you must normally take a test containing multiple-choice questions regarding various arithmetic areas such as Algebra and Analysis.

They may contact those who performed well in interviews after they have finished marking the examinations. This allows them to determine whether the programme is a good fit for the individual and whether they have the necessary abilities. They may also examine some of the person's creations, such as art or projects, to gain a better understanding of who they are.

How to Prepare for the Mathematics Entrance Exam?

What you need to study for the entrance exams for a Ph.D. in Mathematics may fluctuate depending on the institute you're applying to. However, in general, these exams are designed to assess your maths knowledge and skills.

Let us now discuss the exam paper itself. It is broken into two sections.

• Part I: There will be ten questions here. Six of these questions must be answered. This section will be worth 40 points.
• Part II: There will also be ten questions, six of which must be answered. This section will be worth 60 points.

The following topics are often covered in the syllabus for Ph.D. Mathematics entrance exams:

• Abstract Algebra
• Complex Analysis
• Elements of Numerical Analysis
• Linear Algebra
• Ordinary Differential Equations
• Partial Differential Equations
• Real Analysis

It's a fantastic notion to purchase study and practise materials if you're preparing for Ph.D. Mathematics entrance exams. The exam is worth 100 points and you will have 3 hours to complete it. So gather those resources in order to properly prepare.

PhD in Mathematics Admission Process

If you want to get into the best Ph.D. programs for math, remember these things:

• Most institutions begin accepting applications in January of each year, and classes typically begin in August.
• To be admitted to these universities, you must often perform well on entrance examinations and then be interviewed.
• If you wish to do a PhD at a good college, you should take the CSIR-NET and UGC-NET tests. Some colleges also take your GATE score into account.
• For example, if you want to attend the Ph.D. In the mathematics program at ISI Kolkata, your GATE score will be considered. The NBHM Screening test is also used by several colleges to accept students and award scholarships.

PhD Mathematics Entrance Exams

Some colleges provide programmes leading to a PhD in Mathematics. Some colleges require you to take a particular test in order to get admitted to certain programmes. This test is worth 100 points and must be completed in 3 hours.

Here are several well-known tests for PhD programs in Mathematics.

• CSIR-UGC NET for JRF Entrance Exam: The CSIR UGC NET is similar to a large test that the National Testing Agency (NTA) organises for the Council of Scientific and Industrial Research (CSIR). This test identifies individuals who may be eligible for a Junior Research Fellowship (JRF) or to teach at Indian universities and colleges.
• UGC NET Entrance Exam: The UGC NET for JRF, also known as the National Eligibility exam or NTA-UGC-NET, is an exam that determines if you are eligible for a Junior Research Fellowship (JRF) or an Assistant Professor position at Indian universities and colleges.
• NBHM Entrance Exam: The National Board for Higher Mathematics is like a group in India that organizes a big test for people who really like math. They want to help math grow, make new math places, and give money to people doing math research. This is for students who are studying a lot of math and also for those who have finished their studies and want to do even more advanced math.

A few private colleges, such as Chandigarh University and LPU, hold their own entrance exams for this subject.

PhD in Mathematics Syllabus

So, when studying for a Ph.D. in Mathematics, the material you learn may differ depending on the college you attend. However, there are several fundamental classes that everyone must take. You can select these classes based on your interests.

The following are the typical subjects in the PhD. Mathematics programme:

PhD Mathematics: Books

Check out these Ph.D. Mathematics books to help you better grasp your course. These books will also help you pass your Ph.D. Mathematics exams. Take a look at the following list:

Ph.D. in Mathematics: Job Prospects and Career Options

Many students in India choose to pursue a Ph.D. in Mathematics, which is a high-level study of numbers and shapes. After completing this unique study, you will be able to find decent jobs in India and other countries.

• People with PhD degrees in math can work in different math areas like Numbers, Computer Analysis, Math in Biology, Complex Patterns, Systems, Moving Things, Fluid Movement, and more.
• If you're good with customers and know a bit about business, you can work at banks, whether they're private or government ones.
• You can also find jobs in places like studying markets, helping with money at companies, working in banks, planning budgets, giving advice, and working at big companies.
• Some of the top companies where these experts can get jobs are Aquis, Airtel , ITC Infotech, IBM Global Services, ABC Consultants, NEXT Techno Enterprises, and Brainfuse.

The table below depicts some of the most prevalent Ph.D. Mathematics job descriptions and career opportunities after completing the course:

PhD in Mathematics Scope

Mathematicians with a Ph.D. are playing an important role in education. According to UGC regulations, one of the Head of Department positions is allocated exclusively for persons having a Ph.D.

• More math experts are likely to find work in India because there is a high need for their skills in private companies that work with data.
• These private-sector enterprises pay well and have high growth prospects. Math specialists can earn considerably more if they learn additional abilities such as computer programming and statistics.

With Our Expert Guidance And Support You Can Easily Get Enrolled In The Best PhD University And Achieve Your Goals.

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Master of Philosophy in Mathematics Doctor of Philosophy in Mathematics

MPhil(MATH) PhD(MATH)

Both full- and part-time

Full-time: 2 years Part-time: 4 years  

Full-time: 3 years (with a relevant research master’s degree), 4 years (without a relevant research master’s degree) Part-time: 6 years

Department of Mathematics

https://www.math.ust.hk/pg/

[email protected]

The Master of Philosophy (MPhil) Program seeks to strengthen students’ general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. A candidate for an MPhil degree is expected to demonstrate knowledge in the discipline and to synthesize and create new knowledge, making a contribution to the field. It can be a terminal degree or a preliminary degree leading to the PhD.  

The Doctor of Philosophy (PhD) Program aims to prepare students to become research scholars in an academic or industrial environment and enable students to do independent and original research. It provides a broad background in mathematics and mathematical sciences. Students can choose to focus their research in one of the three areas: Pure Mathematics, Applied Mathematics, and Probability and Statistics. A candidate for a PhD degree is expected to demonstrate mastery of knowledge in the chosen discipline and to synthesize and create new knowledge, making an original and substantial contribution to the discipline.

On successful completion of the MPhil program, graduates will be able to:

• Conduct research in mathematics;
• Demonstrate knowledge in the chosen discipline of mathematics;
• Be able to synthesize and create new knowledge and to making contributions to the discipline of mathematics; and
• Demonstrate communication skills in presenting reporting findings in mathematics.

On successful completion of the PhD program, graduates will be able to:

• Be able to conduct independent and original research in mathematics;
• Demonstrate mastery of knowledge in the chosen discipline of mathematics;
• Be able to synthesize and create new knowledge and to make original and substantial contributions to the discipline of mathematics;
• Demonstrate a broad knowledge in mathematics and mathematical sciences; and
• Demonstrate effective communication skills in presenting and publishing findings in mathematics.

The programs are offered by the Department of Mathematics with the following research foci and state-of-the-art facilities, strengthening students’ knowledge in mathematics and training them to carry out original research independently and innovatively.  

Research Foci

Algebra and Number Theory

The theory of Lie groups, Lie algebras and their representations is an important branch in modern mathematics and it has interactions with many other branches in mathematics and physics. Our research includes representation theory of reductive groups, quantum groups, infinite dimensional Lie groups and Lie algebras and applications to mathematical physics. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms and applications of number theory.  

Geometry and Topology

Geometry and topology provide an essential language describing all kinds of structures in nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincare conjecture. Active research areas in the department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorics and combinatorial topology, and geometrical structures in mathematical physics.  

Analysis and Differential Equations

The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, harmonic analysis, wavelets analysis, nonlinear equations and dynamical systems, integrable systems, fluid dynamics, and inverse problems.  

Applied and Computational Mathematics

The research focuses on development of mathematical models and advance numerical algorithms, as well as applications of mathematics to interdisciplinary science and engineering areas. The research areas include: modeling and simulation in fluid dynamics and materials science, computational fluid dynamics, multiscale modeling, kinetic theory, atomistic simulations, image processing, computational harmonic analysis, inverse problems and wave propagation, graph theory, optimization, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, numerical PDEs and numerical linear algebra, parallel algorithms, and numerical software.  

Financial Mathematics

Traditionally, financial mathematics includes three areas: asset allocation/management, derivative modeling, pricing and hedging, and division or firm-wise risk management. The mathematical tools include probability, stability, stochastic calculus and numerical analysis. The recent trend of financial mathematics research, however, has been data driven, parallel to the development in the financial market where both sell-side and buy-side firms are trying to adopt the methodologies of big data and machine learning, in order to gain advantages in proprietary trading, market making, hedging and investments. Some faculties of the department working in related fields have embraced the changes and adopted the new technologies in their teaching and research.  

Probability and Statistics

Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.  

Data Science

Statistics and data science play a more and more important role in scientific research and applications, particularly in the era of big data. Some research interests include random matrix, survival analysis, financial statistics, econometrics, bioinformatics, statistical machine learning, statistical genetics and genomics, computational biology and bioinformatics, error in variables model, generalized linear models; biological and medical statistics, topological and geometric methods in data analysis.  

We also develop algorithms that provably and significantly improve the state-of-the-art for mathematical data analysis, in terms of accuracy, running time, memory efficiency, scalability, or other computational measures. This includes adapting existing algorithms or approaches to exploit contemporary computing architectures, new statistical paradigms, or heterogeneous information sources. We investigate the solution of specific practical data science problems that use novel methodology and are of broad interest. These problems include imaging, high dimensional data analysis, machine learning, social networks, genetics and genomics.  

The Department enjoys a range of up-to-date facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.  

To assist computations that require a large amount of processing power, a High Performance Computing (HPC) laboratory was setup in 2000. The high-speed computers in this laboratory in which InfiniBand technology and GPU technology are applied are capable of delivering a processing power of 150 TFLOPS practically. By making use of these powerful computing facilities, our faculty and postgraduate students are able to solve computationally intensive problems in their innovative research projects so that they can stay at the forefront of their fields.

Minimum Credit Requirement

MPhil: 24 credits PhD: 36 credits  

Credit Transfer

PhD students who have obtained an MSc or MPhil degree from other institutions may be granted credit transfer of up to 18 credits, subject to departmental approval.  

Required Courses

MPhil: 24 credits in mathematics or related fields, normally including at least 18 credits of mathematics courses at postgraduate level. PhD: 36 credits in mathematics or related fields, including at least 24 credits of mathematics courses at postgraduate level. PhD students can choose to focus their research in one of the three areas:

Pure Mathematics;

Applied Mathematics; and

Probability and Statistics.  

Students with a first degree in an area other than mathematics may be required to take additional courses.  

Graduate Teaching Assistant Training

All full-time RPg students are required to complete PDEV 6800. The course is composed of a 10-hour training offered by the Center for Education Innovation (CEI), and session(s) of instructional delivery to be assigned by the respective departments. Upon satisfactory completion of the training conducted by CEI, MPhil students are required to give at least one 30-minute session of instructional delivery in front of a group of students for one term. PhD students are required to give at least one such session each in two different terms. The instructional delivery will be formally assessed.  

Professional Development Course Requirement

Students are required to complete PDEV 6770. The 1 credit earned from PDEV 6770 cannot be counted toward the credit requirements. PhD students who are HKUST MPhil graduates and have completed PDEV 6770 or other professional development courses offered by the University before may be exempted from taking PDEV 6770, subject to prior approval of the School.

Students are required to complete MATH 6771. The 1 credit earned from MATH 6771 cannot be counted toward the credit requirements. PhD students who are HKUST MPhil graduates in Mathematics and have completed MATH 6771 before may be exempted from taking MATH 6771, subject to prior approval of the Department Head or Department PG Coordinator.  

English Language Requirement

Full-time RPg students are required to take an English Language Proficiency Assessment (ELPA) Speaking Test administered by the Center for Language Education before the start of their first term of study. Students whose ELPA Speaking Test score is below Level 4, or who failed to take the test in their first term of study, are required to take LANG 5000 until they pass the course by attaining at least Level 4 in the ELPA Speaking Test before graduation. The 1 credit earned from LANG 5000 cannot be counted toward the credit requirements.  

Students must complete and pass LANG 5010, which should be taken in the first year of study. The 1 credit earned from LANG 5010 cannot be counted toward the credit requirements. PhD students who are HKUST MPhil graduates may be considered for exemption from this requirement, subject to prior approval from the Department Head and PG Coordinator.  

Postgraduate Seminar

Full-time students are required to complete MATH 6900 in their first four regular terms of study. The maximum number of credits to be earned from this course is 4.  

PhD Qualifying Examination

PhD students are required to pass a qualifying examination. Pure Mathematics To become PhD candidates, students must first pass a written qualifying examination (normally at the end of the first year of study) on two of the three subject areas: analysis, algebra, and geometry. At a later date (normally no later than the end of the second year of study) an oral examination on a major area excluding the two areas covered in the written examination. Applied Mathematics To become PhD candidates, students must first pass a written preliminary examination (normally before the end of the first year of study) on two subjects: advanced calculus and linear algebra. Students must also submit a thesis proposal, and pass an oral examination on the thesis proposal and two minor subjects. The oral examination should normally take place before the end of the second year of study. Probability and Statistics To become PhD candidates, students must pass an oral qualifying examination on one major subject and two minor subjects (normally no later than the end of the second year of study). For Probability students, the major subject is Probability while the two minor subjects would be Statistics and an area in Mathematics or an appropriate area outside Mathematics. For Statistics students, the major subject is Statistics while the two minor subjects would be Probability and an area in Mathematics or an appropriate area outside Mathematics.  

Thesis Research

Registration in MATH 6990; and

Presentation and oral defense of the MPhil thesis.

Registration in MATH 7990; and

Presentation and oral defense of the PhD thesis.

Last update: 31 July 2019

Scientific Computation Concentration

In addition to the existing program requirements, students who opt for the Scientific Computation concentration are required to:  

MPhil: Complete a minimum of 7 credits from the following course lists. PhD: Complete a minimum of 10 credits from the following course lists. The credits earned under the concentration will be counted toward the total credit requirements of the programs. Core Courses MPhil: at least 3 credits PhD: at least 6 credits All students must take MATH 6915 and MATH 6916. Credits earned from MATH 6915 can be repeated for up to 2 credits.  

Elective Courses

Conduct research in the area of scientific computation.

Last update: 29 August 2023

To qualify for admission, applicants must meet all of the following requirements. Admission is selective and meeting these minimum requirements does not guarantee admission.

Applicants seeking admission to a master's degree program should have obtained a bachelor’s degree from a recognized institution, or an approved equivalent qualification;

Applicants seeking admission to a doctoral degree program should have obtained a bachelor’s degree with a proven record of outstanding performance from a recognized institution; or presented evidence of satisfactory work at the postgraduate level on a full-time basis for at least one year, or on a part-time basis for at least two years.

Applicants have to fulfill English Language requirements with one of the following proficiency attainments:

TOEFL-iBT: 80*

TOEFL-pBT: 550

TOEFL-Revised paper-delivered test: 60 (total scores for Reading, Listening and Writing sections)

IELTS (Academic Module): Overall score: 6.5  and All sub-score: 5.5

* refers to the total score in one single attempt

Applicants are not required to present TOEFL or IELTS score if

their first language is English, or

they obtained the bachelor's degree (or equivalent) from an institution where the medium of instruction was English.

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Join Our Journey of Excellence at K.R Mangalam University!

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Ph.D. in Mathematics

Duration: 3 Years

Fee Structure:

Total Fee Per Year

Rs.110000/-

Eligibility Criteria:

The candidate should have a postgraduate degree or its equivalent from a recognized University, in a respective discipline, with a minimum of 55% marks or a minimum CGPA of 5.5 on a 10 point scale. They are required to supply a brief statement of research interests (maximum 1 page) Research experience like project work or internships at the undergraduate or master’s level should be highlighted. Candidates who have qualified CSIR-NET or GATE examination will be preferred.

A Ph.D. in Mathematics at School of Basic and Applied Sciences (SBAS) is available to students who have shown mastery of the subject of Mathematics. It involves a training program that involves advanced courses, research on a specialized area, and thesis defense on completion of coursework. Students are required to take some classes in other disciplines to obtain a more comprehensive understanding of the topic at hand.

K.R. Mangalam University awards a Ph.D. degree in Mathematics from K.R. Mangalam University after a student has completed extensive coursework in the field of mathematics, submitted a dissertation that makes an original contribution to knowledge, and successfully defended it before examiners who are experts in their field. A Ph.D. program will take at least four years to complete, possibly longer depending on how much leave time the student takes or whether or not he or she attends full-time status.The Ph.D. programme caters to the following categories of students

Full-Time Scholars

Scholars are required to devote full time on campus for the Ph.D.programme. Some scholars may be offered a teaching/research/project assistantship. The selected scholars will be required to assist in teaching/laboratories and other developmental work under the guidance of a mentor.

Sponsored Scholars

Employees of organizations/industries having collaborations with the university can enroll under this category.

Part-Time Scholars

Scholars working in organizations situated in close vicinity of the university can enroll under this category.

Program Structure

Fundamentals, new age skills, specialization, live projects and internships.

• Introduction To Psychology(Life skill)
• Perspective in Social Psychology(Entrepreneurship)
• Introduction to Psychology Practicum/Lab
• Communication Skills(Life skill)
• Open Elective-1
• Statistical Method For Psychological Research-I
• Biopsychology
• Biopsychology Practicum/Lab
• Environmental Studies
• Open Elective-2
• Abnormal Psychology(Employability)
• Introduction To Personality(Life skill)
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• Introduction To Personality_Practicum/LAB
• Psychology of Relationships (Entrepreneurship)
• Inter Group Relations(Open Elective)
• Disaster Management
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• Counseling skill(Life Skill &Employability)
• Statistical Method for Psychological research-II
• Counseling skill_ Practicum/Lab
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Connecting Talent to Dream Careers

At KRMU, we are proud to collaborate with a prestigious array of Digit, Cutback Coach, Betterment, Ieso Digital Health, Medanta, and Ganga Ram Hospital. These esteemed partners actively engage in our campus recruitment initiatives and internships for the Ph.D. in Mathematics programmes.

Career Options

There are various areas in which you can build a good career after graduating from this course. Some of these paths are well-known, while others aren’t much of a common choice. Here is the list of some of the possible career sectors that you can take up after completing this degree:

• Lecturer/Professor/Academicians
• Mathematical Model Specialist
• Data Analyst
• Market Analyst
• Mathematicians and Statisticians
• Operations Research Analyst
• Decision Analytics Consultant
• Data Scientist
• Quant Research Analyst
• Principal Data Scientist
• R&D Advisor

Hear straight from our Students

When I completed my undergraduate degree, I was looking for an ideal college for my further studies that would enrich my knowledge of the mathematics field. I was slightly aware of K.R. Mangalam University and I had heard a lot of good things about this university. Hence, without wasting more time, I applied here and trust me it was the best decision I made.

Manoj Kumar

The study environment at K.R. Mangalam University is very calm and engaging. I always learn something new here. Mentors are genuinely very supportive here and encouraging at the same time.

Shivani Singh

The faculty's expertise and mentorship have shaped my approach to complex mathematical problems. The collaborative nature of research projects and the exposure to diverse mathematical disciplines make KRMU an ideal environment for fostering a deep appreciation for the vast landscape of mathematics.

Rajan Bhatia

"KRMU's Ph.D. in Mathematics program's emphasis on rigorous mathematical foundations, coupled with the mentorship from distinguished faculty, has honed my analytical skills.

Programme Outcomes

Becoming more employable.

One of the reasons why you should opt for a Ph.D. in Mathematics is that it will enhance your employability. After studying Mathematics, you will have a wide range of career options to choose from. Having knowledge in multiple avenues will also help you in getting a good starting salary package.

Gaining confidence in communication

Another reason why you should consider getting a Mathematics degree is that you will get the confidence to communicate with all sorts of people.

Global Communication

By opting for this course, you will be able to communicate different messages with people and enterprises all over the world. This will eliminate any barriers when it comes to global communication.

Programme Highlights

The Ph.D. in Mathematics Programme is based on the research carried out by the student under the guidance of the Supervisor/Co-supervisor(s) and the programme duration is dependent upon the completion of the chosen research by the student.

The research work is characterized either by the discovery of new facts or the proposition of a new theory/theories or by a fresh interpretation of known facts.

It should bear evidence of the candidate’s capacity for analysis and judgment as well as his/her ability to carry out independent investigation, design or development.

Ph.D. Admission Process

Candidates are required to download the Ph.D. admission form from the university website (click here) and submit it completely filled in all respects with copies of all the documents. Shortlisted candidates will be called for written examination and interview. They will be required to pay a Registration-cum-Processing fee of INR 5000 (Refundable).

Admission to Ph.D. in CSE programme will be based on the overall performance in Post Graduate degree, Entrance Examination, Personal Interview and positions available. Preference will be given to CSIR/UGC NET qualified candidates and those having sponsored projects.

Selection Process

WRITTEN ENTRANCE EXAMINATION It will broadly test the research aptitude and ability to comprehend. Candidates with NET, GATE, M Phil. or equivalent qualifications may be exempted from the entrance examination.

PERSONAL INTERVIEW Candidates who clear the written entrance examination will be selected for the personal interview. The interview will be conducted by the Interview Board of the University to comprehensively judge in-depth knowledge in the concerned subject/area and ability to do research.

Admitted candidates will be required to pay the first installment of the Ph.D.programme fee and security deposit within the specified time to confirm admission.

Who Should Pursue

Students who are willing to build a career that revolves around the futuristic principles of Mathematics should opt for this programme. After graduating from this course, you will have plentiful opportunities to create financial freedom in your life and live wherever you want to. This field is also for those people who are lifelong learners and want to develop their critical thinking skills. Mathematicians are the new-age problem solvers and this programme is best suited for such passionate individuals.

Frequently Asked Questions

What is the minimum qualification for phd admission 2024 at k.r. mangalam university, to apply for phd programs, is it mandatory that i have with me all mark sheet of the required degree/master’s program, till the final semester, can i apply to the phd program by personally visiting the campus and submitting a hard copy, when can i apply to a phd program , who are expected to submit an noc (no objection certificate) for phd admission in gurgaon, commence your journey in 6 simple steps.

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At admissions.krmangalam.edu.in

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Pay the required Application Fee

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K.R. Mangalam University Entrance Examination (KREE)

Appear for interaction

Attend our Faculty-Led Interview.

Get the admission offer

You will receive the offer letter after the successful interaction

Get Enrolled

Be prepared to embark on your journey

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Ph.D Mathematics Jobs, Scope, Salary in India

Updated on - Jan 4, 2023

PhD Mathematics graduates in India can work in government and international organizations. PhD Mathematics graduates work in areas such as Census Officers,  Researchers, and Professors. Graduates of the PhD Mathematics course will be able to pursue a variety of rewarding fellowships and opportunities.

Career Opportunities After PhD Mathematics

PhD Mathematics in India has a promising future both in India and worldwide. The availability of PhD Mathematics jobs in India is determined by specialization and demand. The salary is high due to the high demand for PhD Mathematics graduates. In India, there are numerous PhD Mathematics job opportunities. The PhD Mathematics program is intended to provide students with all of the knowledge required to begin a rewarding career.

The following are some of the jobs available to PhD Mathematics graduates:

• Mathematics Tutor
• Associate Professor
• Mathematics Instructor
• Assistant Professor
• Mathematics Teacher
• Subject Matter Expert
• Assessment Specialist
• Census Officer

Area of Recruitment For PhD Mathematics

The PhD Mathematics course specialization aims to prepare students for industry employment. There are numerous job opportunities in India for PhD Mathematics graduates. The PhD Mathematics program's scope is constantly expanding in the following areas:

• Academic Institutes
• Banking Sector
• Stock Exchanges
• Math Research Centers
• Military Schools
• Defense Services
• Trade & Transportation Center

Salary Packages for PhD Mathematics

According to PayScale, salaries for PhD Mathematics graduates in India range from INR 2.5 - 9 LPA. In India, the salary of a PhD Mathematics graduate is determined by their education, grades, and required skills. The table below contains the salary range of PhD Mathematics graduates in India:

The following are some of the job openings and salary packages for PhD Mathematics graduates:

Source: Payscale

Government Jobs After PhD Mathematics

PhD Mathematics jobs in the government are available in a variety of departments. PhD mathematics graduates' most common central government jobs are hospitals, universities, and nutritional planning programs. According to PayScale, PhD Mathematics government jobs in India pay between INR 9 LPA. Some government jobs with salaries are listed below:

Source: PayScale

Private Jobs for PhD Mathematics

Graduates of PhD Mathematics can find employment in international organizations. The average monthly salary for a PhD Mathematics in India is around INR 2.5 - 9 LPA, according to PayScale. Some of the job titles and PhD Mathematics salaries are as follows:

Job Opportunities Abroad for PhD Mathematics Graduates

PhD Mathematics graduates have a wide range of job options both in India and abroad. They can work in the private and public industries. The vast majority of them work in international firms and research institutes.

Top Companies

Check the list below for the top organizations that hire PhD Mathematics graduates:

• State Bank of India
• Government of India
• Xaviers University

Best Countries

Below is the list of top countries offering PhD Mathematics scope to graduates:

• United Kingdom
• New Zealand
• The United States of America

Various Career Designations Abroad for Graduates

Many interesting job profiles attract PhD Mathematics graduates to work abroad:

• Mathematics Professor
• Stock Broker
• Game Theory Expert

Famous Mathematicians

Many of the top graduates in the field of Mathematics are discovering new ways to apply science and technology to improve finding solutions in the field of Science, Technology, Commerce, and many more worldwide. Here are some of the few famous graduates in the field of PhD Mathematics:

• Reed Hastings, CEO of Netflix
• Sergey Brin, co-founder of Google
• Harvey Milk, pro-LGBTQ Icon
• Bal Gangadhar Tilak, Freedom Fighter

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Ph.D. in Mathematics: Overview, Course, Eligibility Criteria, Admission, Syllabus, Fees, Scope, Result and Cutoffs, & FAQs

Best Ph.D. in Mathematics Colleges in India 2023: Ph.D. in Mathematics stands for ‘Doctor of Philosophy in Mathematics.’ The doctoral degree deals with various concepts of mathematics like space, change, quantity, structure, etc. The Ph.D. in Mathematics program takes 3 to 6 years to complete. After successfully completing the program, the student receives a doctorate in mathematics. The ‘Thesis’ has to be submitted by the student & approved by the higher authorities to be eligible to take home this doctorate. They also become experts in theory, topology, formulating research methodologies, logical interpretation, analysis, formulation, and statistical concepts in mathematics.

During this degree, a student gets well-versed in the overall structure of mathematics giving birth to new laws and theories for the overall development of mathematics as a core subject. The candidate should hold an M.Tech degree, MSc in Mathematics, or physical science to proceed with their application for a Ph.D. in mathematics. After getting this degree, you will have many different career roles to choose from in the academic field and the research sector, such as lecturer, Math expert, or subject matter expert.

Course Highlights

Also Read:  Top Engineering Colleges in India

Eligibility Criteria

The eligibility criteria set for a Ph.D. in Mathematics in India vary according to the different terms and conditions set by Indian universities. Students need to conduct a thorough background check on their desired Ph.D. university to ensure that they meet its admission eligibility criteria. It will help them have a smooth onboarding process at the university. The best university for Ph.D. mathematics in India has preset protocols designed for the upcoming students, i.e, to have prior relevant experience as a lecturer, teacher, or in some research sector. On the other hand, other universities have direct admission criteria with no hard and fast rules. Let’s learn them from the below section –

• The student should have an aggregate score of at least 55% in his 12th standard class, graduation degree, and post-graduation degree. The score should be at least 50% for ST, SC, or OBCs.
• The student should score at least passing marks in the admission entrance exam set by the particular university.
• The student should have completed their master’s degree or postgraduate degree in mathematics, physical science, or any relevant field. The widely accepted degrees are MSC chemistry, MSc statistics, MSc Mathematics, Mtech, or MA economics.

Admission Process

The admission process for a Ph.D. in applied mathematics is straightforward and very simple. The students can apply for Ph.D. admission in 2023 either through their merit records or by clearing the entrance examination. Although in either of these two ways, a student has to follow the stringent step-by-step process to be accepted by their dream university. If your desired university has a policy for entrance examination then you should have clarity on the starting & ending date of filling out forms for the entrance examination and what all syllabus is going to be included in the exam. It will help you achieve good scores and make your admission process very easy. Now let’s understand the two ways of obtaining a Ph.D. in Mathematics admission in 2023 in detail below –

• Merit-Based Admission: The universities that follow the merit-based admission process don’t conduct any entrance examination but require solid marks, say at least 55% aggregate marks in their previous years of education. Various universities in India provide direct admission to students based on their previous year’s degree and school marks. Apart from this, most of these universities, like AMU and Lovely Professional University, prefer to conduct personal interview rounds with the Ph.D. candidates. Such interview rounds are solely based on understanding the mindset of a candidate, his plans, the level of interest he has in research, and how he is going to make a change in this field.
• Entrance Exam-based admission: Certain top-tier universities follow the entrance-based examination process to filter out eligible & non-eligible students. Here, a candidate needs to clear the entrance examination conducted by the university and score a preset passing mark to be eligible to be a student for the doctorate in mathematics. Such entrance exams have a core mathematics subject that includes topics from various chapters of math like discrete mathematics, advanced algebra, theorems, analysis, etc. The questionnaire you get is in the form of multiple-choice questions where you have to select the right option from the given choices.

Candidates appearing for the Ph.D. in Mathematics admission 2023 are shortlisted based on their entrance examination scores. The process of taking admission to top math Ph.D. programs based on the entrance examination starts in January every year. Further to this, the classes commence in August. Most of the best universities for Ph.D. in Mathematics in India accept GATE and CSIR-Net examinations.

Syllabus for Ph.D. in Mathematics

The syllabus stated by the top universities after taking admission to a Ph.D. in Mathematics is subjective, and some of the subject topics might vary based on the university. Even the specialization chosen by the candidate plays a major role in deciding the syllabus. All the candidates are going to learn about the practical aspects of mathematics, and its theoretical nature, followed by a thesis covered in the Ph.D. in Mathematics syllabus. Based on your current year and the specialization you have chosen, you can find the in-depth Ph.D. in Mathematics syllabus in the beneath section –

1st Year Syllabus

2nd Year Syllabus 

3rd Year Syllabus

Fee Structure for Ph.D. in Mathematics

In India, a Ph.D. in Mathematics is very reasonably priced. Depending on the university they want to enroll in, students may have to pay a fee structure that ranges from INR 50,000 to INR 1.5 lakh annually. Your overall costs for completing the Ph.D. in Mathematics degree program could reach Rs. 4 lakhs. The costs associated with earning a math Ph.D. at a public university will probably be considerably less than at a private university. If the student has been a meritorious student or has made an international achievement, he may also be eligible for a reduction in his overall tuition and use the scholarship. But once more, this will depend on the requirements set by the university. A candidate who performs well on the entrance exam for the Ph.D. in Mathematics program is eligible to receive a fellowship title.

Top Entrance Examinations for Ph.D. in Mathematics

Students need to clear the entrance examination to be admitted to the top math Ph.D. programs. Some of the most commonly accepted entrance examinations are the NBHM, CSIR-UGC NET, and GATE.

The GATE entrance examination is held by the Indian Institute of Technology for a candidate to take admission to the Ph.D. degree & M-Tech programs. Candidates can also get a job in the government sector by qualifying for the GATE entrance exam & personal interview sessions.

Syllabus for Entrance Exam

This exam is conducted by the UGC to offer assistant professorship and junior fellowship awards to the candidates who qualify for it with high scores. The syllabus for this examination is mentioned in the below table.

The National Board for Higher Mathematics (NBHM) is accepting applications for the entrance exam of Ph.D. program. Candidates must take the Joint Screening Test for Admission and Scholarship for Ph.D./Integrated Ph.D. Programs in order to be considered for admission and financial aid. Students pursuing a Mathematics Ph.D. are eligible for scholarships from the NBHM.

Apart from these, there are several universities conducting entrance examinations on their main campuses. Most universities accept candidates based on state or central-level entrance exams. The declaration of the final merit list is often based only on these entrance examinations. These entrance examinations act as a direct gateway to the best university for a Ph.D. in Mathematics in the world. Students need to meet the cutoff requirements by obtaining good scores in the university entrance examinations. All such details can be easily found on the official website of your desired university. The total time taken by the entrance examination to get completed is approximately 3 hours. The candidate needs to appear for such examinations in offline mode. The questions asked in such examinations are multiple choice questions (MCQs). The exam is held to assess qualitative ability, logical reasoning, data interpretation, and math subject-related knowledge.

Scholarship and Fellowship

The candidates wishing to pursue a Ph.D. in Mathematics have a great opportunity to support their finances through scholarships and fellowships. as the government takes care of the upcoming scientists and values their research papers by sponsoring them with financial support. The candidates can avail of the fellowship scheme by appearing in the CSIR-UGC NET exam, and some of the top students are provided with financial support as mentioned below.

For the first two years, a JRF (Junior Research Fellowship) selected via the CSIR-UGC National Eligibility Test (NET) will receive a stipend of Rs 31,000 per month. Additionally, a yearly contingency grant of Rs. 20,000 will be given to the university or institution for each fellow. After two years, the candidate is eligible to apply for the SRF (Senior Research Fellowship) program, in which the stipend amount is increased to Rs 35,000 per month.

Result and Cutoffs

Cut-off scores are the minimum marks that a candidate must have earned on his or her previous years of graduation, education, and entrance exams in order to be considered for admission to the university and course of their choice. Each Indian university has a different cutoff score for mathematics Ph.D. candidates. Such cut-off points are established in accordance with the number of seats available at the university in question and the popularity of that institution among its students.

Future Scope and Career Options after Ph.D. in Mathematics

The future is bright for Ph.D. in Mathematics degree holders, especially after 2023. These students mostly get roles in the educational industry as lecturers, teachers, or heads of departments. Furthermore, they have the choice to work in the government sector, the private sector, or research-based sectors. Some of the career options mentioned below can be pursued by students after completing Ph.D. in mathematics.

Employment Sectors 

Top recruiters, advantages of studying ph.d. in mathematics.

Whether you opt for a Ph.D. in Mathematics online or offline, it can turn out to be a very rewarding career for you. After getting a doctorate in mathematics degree from the best university for Ph.D. in Mathematics in India, you can become an affiliate researcher. Henceforth, your role will be to find the answer to the current mathematical problems. If not the exact solution, then at least the precise solution that is acceptable to the existing mathematical question. The best part is that you can go for the Ph.D. in Mathematics distance learning programs without disturbing your current work if you are lacking time to go ahead with the offline programs. Here is the list of advantages of taking admission to the top math Ph.D. programs –

• Pursuit of excellence: The subject of math is known as the pursuit of excellence. The researchers working in the field of mathematics are more inclined towards understanding all types of complications faced in this mathematical field and providing solutions to them. The Solutions can be formed after designing the appropriate theorems and patterns by conducting thorough research on the problem statement.
• Research-oriented skills: The Math Ph.D. program helps an individual to get incredible knowledge about the subject of mathematics. Moreover, the course curriculum supports refining the research-related skills of the student. The students this way can go ahead and perform better in real time based on complex research-related tasks. Not only this the students can also contribute to accomplishing the social and economical goals of our country.
• Part-time opportunities: The Ph.D. in Mathematics students not only get good opportunities in full-time jobs but they can also work part-time from the comfort of their homes and make a good amount of money. You can try freelancing or take part in skill-based jobs where you need to solve mathematical problems by devoting 2 to 3 hours or less every day without leaving your home.
• Work with different industries: Being a Ph.D. in Mathematics degree holder your career pathways are open to various industries & sectors with no limitations. Once you successfully become a Ph.D. mathematician, you can successfully take roles & responsibilities in various industries like stock exchange, academics, banking, defense, etc.

Salary Package After Completing Ph.D. in Mathematics

The Ph.D. in Mathematics graduate salary ranges between 2.5 lakhs to 10 lakhs per annum. The fresher in this field can expect to have a salary of 2.5 lakhs to 3 lakhs per annum based on his knowledge. Moreover, your salary gradually increases every year as soon as you gain expertise in real-time scenarios & can go up to 9 to 10 lakhs yearly. It comes down to INR 21,000 to 84,000 per month. Although, in private sector companies, you can even expect a monthly package between INR 65,000 to INR 1,50,000 per month. Your home takes in hand salary and upgrades in it solely depend on your expertise, education, grades, graduation from university, performance, and various other factors. On average, the salary of a Ph.D. mathematics graduate is INR 3.84 LPA in the Indian market. Your pay scale is also heavily affected by the role that you are applying for, whether it’s as a stock broker, professor, subject matter expert, etc.

Top Cities for Ph.D. in Mathematics

Candidates can find numerous top universities in India for a Ph.D. in Mathematics. Different universities are popular for different offerings. Although some of the universities in India are more popular than others, this is due to their location, research centers, and practical exposure to mathematical details. Most of these cities are tier-1 and tier-2 but they are number one in facilitating all the resources for Ph.D. in Mathematics candidates. The exposure you will get in these cities is hard to find in other parts of the nation due to the top-notch research-equipped curriculum and well-experienced facilities. Here is the list of top cities that offer Ph.D. in Mathematics in India –

Top university for Ph.D. in Mathematics in India

India is a country that is well known for top-notch math Ph.D. universities that are popular not only among Indian candidates but also foreign applicants. The best university for Ph.D. mathematics in India is recognized for its offerings, such as research proposals, experienced faculty, real-time-based industry exposure, quality education, and decent infrastructure. Candidates can apply to private universities or government universities for admission to the Ph.D. mathematics programs.

1. Private Ph.D. in Mathematics Universities in India

Ph.D. in Mathematics programs at private universities in India have gained immense attention from candidates who wish to pursue Ph.D. in Mathematics in the future. These universities are well known for providing research scope, hands-on experience with live projects, and fellowship rewards. Even they help students through placement assistance & the best pay scale in the industry. That’s one of the motivating factors for pursuing doctorate degrees from private universities. Here is the list of Ph.D. in Mathematics private universities in India –

2. Government Ph.D. in Mathematics Universities in India

Government colleges often get popular among students due to their minimal fee structure and the bright minds that take admission there. The admission criteria to government colleges for Ph.D. math might be quite difficult as compared to private colleges in India, but once you clear the entrance exam, they prove to be the best colleges in terms of gaining subject-relevant knowledge. They also provide the best scholarships, fellowships, and research facilities for their Ph.D. students. Whether you wish to go for Ph.D. in Mathematics distance learning or from the best university for Ph.D. in Mathematics in India in the offline mode, these top-tier government universities never fail to make you satisfied. Here is the list of top-notch Ph.D. in Mathematics government universities in India –

3. Top University for Ph.D. in Mathematics in World

If money isn’t the issue, then the sky’s the limit when it comes to choosing Ph.D. in Mathematics universities. Although, many universities across the world provide scholarships to make the fees minimum for a student having excellent scores in his previous years of education. Candidates wish to opt for Ph.D. programs outside their country to explore more about a particular subject. Undoubtedly, there are so many Ph.D. mathematics universities in the world that provide top-notch research facilities and well-equipped knowledge from highly experienced faculties. Apart from this, a student with a Ph.D. in mathematics from a renowned university across the world is eligible to get incredible salary packages across multiple MNCs in the world. Here is the list of the best university for Ph.D. in mathematics in the world –

FAQ’s Related to Ph.D. in Mathematics

Q. What entrance exams are conducted for admission to Ph.D. mathematics 2023? Ans. The candidate needs to clear GATE and UGC NET entrance examinations for admission to the best university for a Ph.D. in Mathematics in the world.

Q. What all job roles are available for the best mathematics graduate? Ans. The Ph.D. in applied mathematics graduate can take up the job role of a scientist, statistician, research associate, lecturer, demographer, economist, etc.

Q. How much time does it take to complete a Ph.D. in mathematics in India? Ans. The overall time to complete the Ph.D. mathematics syllabus is at least 3 years. Whereas, a student is allowed to take up to 6 years to complete his math Ph.D. degree.

Q. Do big MNCs hire Ph.D. mathematics graduates? Ans. Yes, several top-notch companies hire Ph.D. mathematics graduates. Some of these companies are TCS Innovation Lab, Ernst & Young, the Weizmann Institute, and Tiger Analytics.

Q. What is the monthly salary of a Ph.D. mathematics graduate degree holder? Ans. If you have been a student at the best university for Ph.D. mathematics in India and successfully cleared all the examinations, then you can expect your monthly take-home between INR 65,000 and INR 1,50,000.

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• Mathematics /

MA Mathematics

• Updated on  
• Aug 16, 2022

“Perfect numbers like perfect men are very rare.” Rene Descartes . Slightly different from the choicest MSc Mathematics course, MA Mathematics is a 2-year postgraduate course that aims to study mathematical theorems, formulas and concepts from a theoretical, philosophical and holistic point of view. Read this blog to know all about MA Mathematics, its syllabus, general eligibility criteria, the perks of pursuing MA Mathematics, top universities and colleges abroad and in India, and much more.

Also read: Career after BSc Maths [Study and Work Opportunities]

This Blog Includes:

Ma mathematics , ma in mathematics eligibility , ma mathematics subjects, gate mathematics ma books, best universities to study ma mathematics abroad , best countries to pursue ma mathematics , ma mathematics correspondence, scope of ma mathematics.

A Master of Arts or MA in Mathematics ventures into the study of Mathematics in a unique and different manner as it delves deeper into the art of proving mathematical theorems not just from a quantitative perspective but also from a philosophical and aesthetic point of view. The course incorporates non-Euclidean geometries, prime numbers, abstract groups, and uncountable sets as the methods for elaborating on mathematical formulas and theorems. If you have been interested in understanding Maths from a philosophical point of view, then this course is the best one to opt for. It also includes surveys of important results and unsolved problems that encourage research in mathematics and can help you further build a strong foundation for a career in research .

Also read: 6 Most Famous Indian Mathematicians

Here are the major eligibility requirements to apply for MA Mathematics:

• You must have a bachelor’s degree in mathematics or its related subjects.
• Some universities also conduct entrance exams for admission to their MA Mathematics degree PG program. 
• In some universities, the final merit, i.e. the total marks aggregated in the graduation final examinations and the entrance exam, is used to determine admission to the colleges’ MA Mathematics degree program.
• If you are aiming to pursue this master’s course abroad, you might be asked to provide GRE scores along with English proficiency scores of IELTS / TOEFL / PTE . A Statement of Purpose (SOP) and LORs are also required.

Check Out: MA in USA

Though the course syllabus often differs as per the university, here are the major subjects and syllabus overview of MA Mathematics:

• Functional Analysis
• Real Analysis
• Linear Algebra
• Modern Algebra
• Principle of Mechanics
• Elements of General Topology
• Complex Analysis
• Ordinary Differential Equations & Special Functions
• Operations Research
• Numerical Analysis
• Partial Differential Equations
• Differential Geometry
• Computer-Aided Numerical Practical
• Computer Programming
• Continuum Mechanics
• Graph Theory
• General Topology

Must Read: MA Economics: Eligibility, Subjects, Universities & Scope

MA Mathematics Colleges in India 

Here is a list of some of the best colleges in India:

• St. Stephens College, Delhi
• Mahatma Gandhi University – Kerala, Kottayam
• Arya Vidyapeeth College, Guwahati
• Miranda House College, Delhi
• Sai Nath University, Ranchi
• Guru Gobind Singh Indraprastha University, Delhi 
• SS Jain Subodh PG College, Jaipur
• Hindu College, Delhi
• Lady Shri Ram College for Women, New Delhi
• Sri Venkateswara College, Chennai
• Jamia Millia Islamia University, Delhi
• Indian Statistical Institute – ISI Hyderabad
• Dr. B.R. Ambedkar Open University – BRAOU, Telangana 
• Banaras Hindu University, Banaras 
• Central University of Kashmir, Kashmir 

Given below is a list of top destinations overseas that consists of a plethora of renowned and recognised universities that offer a degree in MA Mathematics. 

There are many distance education colleges in India that offer the MA Mathematics through distance learning. Here is a list of colleges to choose from that offer distance education in the course.

MA Mathematics has immense scope for students aiming to pursue a career in research, statistics, accountancy and much more. Let’s take a look at the career scope of MA Mathematics in further detail:

• It will serve as a foundation for higher education and study in mathematics, such as PhD in Mathematics and M.Phil degrees. 
• After completing this degree, a student may apply for the UGC-NET or JRF exam. It is said that success in these examinations qualifies a student for teaching, research and study and open a plethora of valuable and good options for the candidates as well. 
• The MA Mathematics degree is very useful in obtaining other accounting and statistics degrees, such as the ICWA, and so on.
• Many job opportunities in statistics, actuarial sciences, mathematical modelling, cryptography, computer sciences, and other fields open up after successfully completing the degree course.

Here are the major jobs you can pursue after MA Mathematics:

• Loan Officer
• Mathematician
• Statistician
• Technical Writer
• Treasury Management Specialist
• Computer Programmer
• Demographer
• Aerodynamics Specialist
• Quantitative Analyst
• Mathematics Teacher

The key employment areas for masters in Mathematics graduates are:

• Engineering Firms
• Research and Development Firms
• Insurance Agencies
• Banks and Investment Firms
• Central/State Government Departments
• Business and Industry
• Colleges/Universities

Take a look at the most popular international recruiters for MA Mathematics:

• Boston Consulting Group 
• Edward Jones
• Accenture 
• Adobe Systems
• American Express India
• Goldman Sachs
• Amazon India Development Center
• Axtria India Pvt. Ltd.
• Cisco systems
• Dunnhumby IT Services India Pvt. Ltd.
• Cognizant Technology Solutions
• Innoplexus Consulting Services Pvt. Lmt.
• JPMorgan Chase & Co.
• Oracle India Pvt. Ltd.

If You Can Pass This Simple Math Quiz, You’re a Genius!

We have always been told that Maths is not everyone’s cup of tea or forte. Not everyone likes to be constantly surrounded by numbers and numerals. MA Mathematics is a perfect combination of the art of mathematical science and the philosophy behind it. Want to pursue a course in Mathematics abroad? Reach out to our Leverage Edu counsellors and we will help you find the best course and university as per your interests and preferences! Sign up for a free session now!

Ankita Mishra

A writer with more than 10 years of experience, including 5 years in a newsroom, Ankita takes great pleasure in helping students via study abroad news updates about universities and visa policies. When not busy working you can find her creating memes and discussing social issues with her colleagues.

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Master of Science in Mathematics and Applied Statistics

At California State University Long Beach

The Department of Mathematics & Statistics at CSULB offers four Master of Science programs .

Teaching & Graduate Assistantships provide students with funding and with college teaching experience.

Graduates have found employment in both technical and academic workplaces. Many have obtained tenure-track community college professorships. Others have gone on to PhD programs.

MS in Mathematics, General Option

Study and explore concepts in areas including analysis, algebra, topology, and geometry, as well as the   deep connections between and among these subjects.

MS in Mathematics, Option in Applied Mathematics

Study applied math methods with an emphasis on computational skills.

MS in Mathematics, Option in Mathematics Education for Secondary School Teachers

A flexible program that includes coursework in mathematics and in mathematics education research & theory.

MS in Applied Statistics

Using conceptual foundations and statistical software packages ( SAS , R , and Python ), students are trained to analyze real world data appropriately and communicate their findings effectively. The tools learnt here will open the door for careers in data science and analytics, or prepare you for a PhD in a variety of related fields.

More Information & Application Instructions

Apply for Teaching and Graduate Assistantships

Contact Us with Questions

Dr. John Brevik, Pure Mathematics Graduate Advisor, [email protected]

Dr. Paul Sun, Applied Math Graduate Advisor, [email protected]

Dr. Xuhui Li, Mathematics Education Graduate Advisor, [email protected]

Dr. Kagba Suaray, Statistics Graduate Advisor, [email protected]