phd in mathematics and computer science

Mathematical Sciences

Mellon college of science, ph.d. programs, doctor of philosophy in mathematical sciences.

Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The most important requirement for the Ph.D. degree is timely completion and public defense of an original Ph.D. thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

Doctor of Arts in Mathematical Sciences

The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.

Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is administered jointly by the Department of Mathematical Sciences, the Department of Computer Science, and the Tepper School of Business. It focuses on discrete mathematics and algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The participating units evaluate applicants separately. The requirements for this degree and information on participating faculty are available at the ACO page .

Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the Department of Mathematical Sciences, the Department of Philosophy, and the School of Computer Science. The participating units evaluate applicants separately and set their own program requirements. Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

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Ph.D. programme in Mathematics and Computer Science

Course information, topics of interest.

• Artificial Intelligence, Knowledge Representation and Reasoning, Answer Set Programming, Logic Programming, Constraint Satisfaction Problems.
• Databases, Data and Knowledge Integration, Database Theory, Data and Text-Mining, Knowledge Management.
• Theoretical Computer Science, Game theory, Decidability and Complexity Theory.
• Grid Computing, Computational Science, Cellular Automata.
• Bioinformatics and biomedical informatics.
• Optimization Models and Methods for solving problems in Transport and Logistics.
• Combinatorics
• Study of canonical models of surfaces of general type. Algebraic curves and their moduli spaces, Groups and Graphs.
• Relationships between algebra and geometry, and geometry and mathematical physics in modern and contemporary art. Historical developments of the theory of decisions. History of mathematics in education. Mathematics Education with particular reference to the role and use of technology in teaching and learning
• "Calculus of variations, Variationals methods in Nonlinear Analysis, Critical points Theory and applications to nonlinear partial differential equations, Geometry of Banach spaces. Ordinary differential equations, Differential problems with local and non-local conditions, Implicit and explicit approximation methods, Minimum point problems and projections, Equilibrium problems of mixed or generalized type, Uniform distribution and discrepancy, Almost Monte Carlo integration methods."
• Random processes and fields, namely: percolation, statistical mechanics, interacting particle systems, dynamical systems, quantitative finance, stochastic simulation and mathematical statistics.
• Problems of Quantum Theory. Group-theoretic approach to the theory of the interaction. Semiclassical models and quantum for the transport of current and heat in semiconductors. Problems coupling devices-electrical networks.
• Sequences of Sheffer polynomials and approximation of operators involved. Numerical approximation of solutions of partial differential equations of high order and with boundary conditions that initial. Approximations for Scattered Data Interpolation and rational. Applications of mathematics to engineering problems and statistics.

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Research activities, possibilities, employment 3 years after ph.d.

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Computer Science, Ph.D.

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We have a thriving Ph.D. program with approximately 80 full-time Ph.D. students hailing from all corners of the world. Most full-time Ph.D. students have scholarships that cover tuition and provide a monthly stipend. Admission is highly competitive. We seek creative, articulate students with undergraduate and master's degrees from top universities worldwide. Our  current research strengths  include data management and analysis, cybersecurity, computer games, visualization, web search, graphics, vision and image processing, and theoretical computer science.

This degree program offers interested students opportunities to do their research abroad, under the supervision of faculty at NYU Shanghai or  NYU Abu Dhabi .

• View the Computer Science Ph.D. program flyer
• Admissions requirements for the Ph.D. Program.
• Find out more about general  Admission Requirements .

To receive a Ph.D. in Computer Science at the NYU Tandon School of Engineering, a student must:

• satisfy a breadth course requirement, intended to ensure broad knowledge of computer science,
• satisfy a depth requirement, consisting of an oral qualifying exam presentation with a written report, to ensure the student's ability to do research,
• submit a written thesis proposal and make an oral presentation about the proposal,
• write a Ph.D. thesis that must be approved by a dissertation guidance committee and present an oral thesis defense, and
• satisfy all School of Engineering requirements for the Ph.D. degree, as described in the NYU Tandon School of Engineering bulletin, including graduate study duration, credit points, GPA, and time-to-degree requirements.

Upon entering the program, each student will be assigned an advisor who will guide them in formulating an individual study plan directing their course choice for the first two years. The department will hold an annual Ph.D. Student Assessment Meeting, in which all Ph.D. students will be formally reviewed.

Note: for pre-fall 2015 Ph.D. students, please see the pre-fall 2015 Ph.D. Curriculum.

Program Requirements

Details about Breadth and Depth Requirements, Thesis Proposal and Presentation, and Thesis Defense can be found in the NYU Bulletin.

Program Details

Each incoming Ph.D. student will be assigned to a research advisor, or to an interim advisor, who will provide academic advising until the student has a research advisor. The advisor will meet with the student when the student enters the program to guide the student in formulating an Individual Study Plan. The purpose of the plan is to guide the student’s course choice for the first two years in the program and to ensure that the student meets the breadth requirements. The plan may also specify additional courses to be taken by the student in order to acquire necessary background and expertise. Subsequent changes to the plan must be approved by the advisor.

Sample Plan of Study

In order to obtain a Ph.D. degree, a student must complete a minimum of 75 credits of graduate work beyond the BS degree, including at least 21 credits of dissertation. A Master of Science in Computer Science may be transferred as 30 credits without taking individual courses into consideration. Other graduate coursework in Computer Science may be transferred on a course-by-course basis. Graduate coursework in areas other than Computer Science can be transferred on a course-by-course basis with approval of the Ph.D. Committee (PHDC). The School of Engineering places some limits on the number and types of transfer credits that are available. Applications for transfer credits must be submitted for consideration before the end of the first semester of matriculation. 

All Ph.D. students will be formally reviewed each year in a Ph.D. Student Assessment Meeting. The review is conducted by the entire CSE faculty and includes at least the following items (in no particular order):

• All courses taken, grades received, and GPAs.
• Research productivity: publications, talks, software, systems, etc.
• Faculty input, especially from advisors and committee members.
• Student’s own input.
• Cumulative history of the student's progress.

As a result of the review, each student will be placed in one of the following two categories, by vote of the faculty:

• In Good Standing: The student has performed well in the previous semester and may continue in the Ph.D. program for one more year, assuming satisfactory academic progress is maintained.
• Not in Good Standing: The student has not performed sufficiently well in the previous year. The consequences of not being in good standing will vary, and may include being placed on probation, losing RA/GA/TA funding, or not being allowed to continue in the Ph.D. program.

Following the review, students will receive formal letters which will inform them of their standing. The letters may also make specific recommendations to the student as to what will be expected of them in the following year. A copy of each student’s letter will be placed in the student’s file.

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Program Admissions Chair

Justin Cappos

Program director.

Rachel Greenstadt

Periwinkle Doerfler

Nektarios Tsoutsos

Ph.D. Program

The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is conferred in recognition of marked ability and high attainment in advanced applied and computational mathematics, including the successful completion of a significant original research project. The program typically takes four to five years to complete, although this length may vary depending on the student. Below, we describe the requirements and expectations of the program. All graduate students require a 3.0 GPA to graduate (no exceptions).

Written Preliminary Exam

Upon entry into the Ph.D. program, students are required to take the Written Preliminary Exam, typically scheduled the week before classes start in the Fall semester. The coverage of the exam is in Linear Algebra, Advanced Calculus, Complex Variables, and Probability at the undergraduate level. Details of the exam can be found here: Preliminary Exam Details

The student must pass the exam to continue as a Ph.D. student. The Written Exam is offered in April and August. If the student fails on the first attempt, two more attempts are granted (three attempts total).

Course Requirements

The student must take the following six core courses:

• Analysis: AMCS 6081/6091 (MATH 6080/6090)
• Numerical Analysis: AMCS 6025/6035
• Probability and Stochastic Processes: AMCS 6481/6491 (MATH 6480/6490)

These six core courses are to be completed in the first and second years of graduate studies.

Ten elective courses (a total of 14 courses) are required for graduation. These elective courses should be chosen according to the interests and/or research program of the student and must contain significant mathematical content. Whether a given course can be counted toward AMCS elective course credit will be decided in consultation with the Graduate Chair. Recent courses approved for elective credit can be discussed with your advisor and the Graduate Group Chair.

Deviations from the above may be necessary or recommended depending on the individual student; such decisions are made with the approval of the graduate chair.

Choosing an Advisor

In the first two years of graduate studies, students must choose their thesis advisor. Some students already have an advisor to whom they have committed upon entry to the program. Other students will typically start working with their prospective advisors in the latter half of the first year or the summer between the first and second year.

The purpose of the oral exam is to assess a student’s readiness to transition into full-time research and eventually write his or her dissertation. This exam will be taken by the end of the third year of graduate study.

First, an oral exam committee must be formed, consisting of three faculty members, two of whom must belong to the AMCS graduate faculty. The student must then produce a document of up to about 20 pages describing the research proposal and background material, which is then approved by the oral exam committee before the exam. In the exam, the student will give an oral presentation to the committee. A discussion with the committee follows this. In the oral exam, the committee may ask the student about the presentation as well as about necessary background material as seen fit by the committee. If the student fails this exam, the student will have one more attempt.

Dissertation and Defense

The dissertation must be a substantial original investigation in the field of applied mathematics and computational science, done under the supervision of a faculty advisor. A Ph.D. Thesis Committee consists of at least three faculty members, including the thesis advisor. When the dissertation is complete, it must be defended in a Dissertation Exam, at which the student will be expected to give a short public exposition of the results of the thesis and to satisfactorily answer questions about the thesis and related areas.

Teaching Assistant

Full-time students admitted to our Ph.D. program who are offered a financial support package for four years of study are required to be teaching assistants during the second year. Students for whom English is not their native language are required to pass a test the “Speak Test” (IELTS) demonstrating proficiency in English. More information can be found on the English Language Programs  web page.

https://www.elp.upenn.edu/institute-academic-studies/requirements

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Dept of Math, Stat, & Comp Sci

College of liberal arts and sciences.

Doctor of Philosophy in Mathematics

The PhD in Mathematics is designed to provide the highest level of training for independent research. Students may apply with or without a Masters degree. For those with a previous Masters degree in mathematics (or related field) the PhD is typically 5 years in duration, whereas for those without a previous Masters degree it is typically 6 years.

To earn the PhD, the student must fulfill the Graduate College requirements specified in the Graduate College catalogue as well as departmental requirements detailed in the MSCS Graduate Handbook , which includes:

• Provide proof of an equivalent MS degree or earn a high pass on the Department's written Master's Examination.
• Fulfill the doctoral preliminary examinations and minor sequence requirement.
• Pass the doctoral oral examination (Probability and Statistics students only).
• Produce and defend a thesis that makes a contribution to original research.
• Earn 96 semester hours of graduate credit including:
• 32 credit hours for a previously earned master's degree (requires DGS approval), or earn a high pass on the Department's Master's Exam
• 40 credit hours of departmental 500-level courses which may include 500-level courses taken from the MS degree earned in residence but may NOT include thesis research (MATH 599, STAT 599, or MCS 599)
• 32 hours of thesis research (MATH 599, STAT 599, or MCS 599)

Theoretical Computer Science

This field comprises two sub-fields: the theory of algorithms, which involves the design and analysis of computational procedures; and complexity theory, which involves efforts to prove that no efficient algorithms exist in certain cases, and which investigates the classification system for computational tasks. Time, memory, randomness and parallelism are typical measures of computational effort.

Theoretical computer science is a natural bridge between mathematics and computer science, and both fields have benefited from the connection. The field is very active, with exciting breakthroughs and intriguing challenges. The P =? NP problem is one of the seven of the Clay Millennium Problems. The recent polynomial time primality algorithm received a Clay Math research award.

MIT has been the leading center for theoretical computer science for several decades. A strong group of EECS Department faculty also works in this field and runs joint activities with the Mathematics faculty through CSAIL. The RSA cryptosystem and Akamai Technologies are two important success stories that were developed by Mathematics and EECS Department faculty.

Our group investigates active areas such as quantum computation, approximation algorithms, algorithms in number theory, distributed computing and complexity theory.

Department Members in This Field

• Michel Goemans Algorithms, Combinatorics & Optimization
• Jonathan Kelner Theoretical Computer Science
• Tom Leighton Theoretical Computer Science, Combinatorics
• Ankur Moitra Theoretical Computer Science, Machine Learning
• Elchanan Mossel Probability, Algorithms and Inference
• Peter Shor Quantum Computation, Quantum Information
• Michael Sipser Algorithms, Complexity Theory

Instructors & Postdocs

• Mitali Bafna Theoretical Computer Science
• Manik Dhar Combinatorics, Theoretical Computer Science
• Jason Gaitonde Algorithms, Learning Theory, Probability Theory, Networks
• Alexander Poremba Quantum computation, cryptography
• Yihui Quek Quantum Computing, Complexity Theory, Quantum Noise and Error Correction
• Michael Simkin Probabilistic combinatorics, random graphs, and random processes
• Anirudh Sridhar Statistical inference, network cascades, graph algorithms, graph matching

Graduate Students*

• Anna Brandenberger
• Andrey Khesin Quantum Computing
• Jonathan Lu
• Yuchong Pan
• Jonathan Rodriguez Figueroa
• Xinyu (Norah) Tan Quantum computing, quantum information, coding theory
• Neekon Vafa
• Lichen Zhang Theoretical computer science, machine learning and data science
• Kai Zhe Zheng

*Only a partial list of graduate students

Academic Programs

• CSE PhD Overview
• Dept-CSE PhD Overview
• CSE Doctoral Theses
• Program Overview and Curriculum
• For New CCSE Students
• Terms of Reference

MIT Doctoral Programs in Computational Science and Engineering

The Center for Computational Science and Engineering (CCSE) offers two doctoral programs in computational science and engineering (CSE) – one leading to a standalone PhD degree in CSE offered entirely by CCSE (CSE PhD) and the other leading to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science (Dept-CSE PhD).

While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree in Computational Science and Engineering is awarded by CCSE via the the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation within the chosen engineering or science discipline.

For more information about CCSE’s doctoral programs, please explore the links on the left. Information about our application and admission process is available via the ‘ Admissions ‘ tab in our menu. MIT Registrar’s Office provides graduate tuition and fee rates as set by the MIT Corporation and the Graduate Admissions section of MIT’s Office of Graduate Education (OGE) website contains additional information about costs of attendance and funding .

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UMass Boston

• Computational Sciences PhD

Reach the highest level of academic achievement in mathematical modeling, machine learning, and theoretical computer science.

Computational Science is concerned with the construction of mathematical models to solve problems in science, technology, engineering and mathematics. This is accomplished through the design and implementation of numerical, probabilistic and statistical models, machine learning and theoretical computer science. The methods and applications are necessarily cross disciplinary.

A typical example is the use of topological data analysis—which has roots in algebraic topology in pure mathematics—to analyze protein data or large data clouds. Other examples include environmental modeling via image processing, risk management and forecasting in finance via stochastic simulations, which in turn can be used in computational biology to understand the roles of non-coding RNA in cancer.

The Computational Sciences PhD Program at UMass Boston coordinates and promotes multidisciplinary exchange of ideas among researchers and graduate students. The program involves faculty and graduate students in various departments at the College of Sciences and Mathematics. Departments currently participating in the program include: Biology, Chemistry, Computer Science, Engineering, Physics and Mathematics. The program is built on the existing strong scientific collaborations among faculty and industry partners. Graduates from the program are expected to be competitive for securing positions in academia or at companies seeking expertise in data analytics and high-end implementation of computational modeling.

You can select from the following tracks:

• Data Analytics
• Bioinformatics
• Computational Physics

Start Your Application

Plan Your Education

How to apply.

Applicants must also meet general graduate admission requirements in addition to the following program-specific requirements:

• Applicants will be required to determine the track they are interested in pursuing (Data Analytics, Bioinformatics, or Computational Physics) and demonstrate adequate preparation at the undergraduate level in the form of relevant coursework and research experience.
• Given the multi-disciplinary nature of the Computational Science program, we expect that our applicants will be undergraduates with bachelor of science degrees in computer science, mathematics, biology, chemistry, physics, or graduates with master’s degrees in these areas.
• Applicants are required to take the general GRE test.
• The program requires three letters of recommendation submitted with the application.

Transfer Requirements

Students who transfer to the Computational Science program will receive transfer credit or advanced standing for their previous work if they can demonstrate course equivalency. Credits for previous work will be given at the discretion of the Program Committee. Transfer students will still be required to pass written and oral qualifying exams and fulfill all other candidacy requirements.

Deadlines & Cost

Deadlines: February 15 for fall; October 1 (priority deadline) or December 1 (final deadline) for spring

Application Fee: The nonrefundable application fee is $75. UMass Boston alumni and current students that plan to complete degree requirements prior to graduate enrollment can submit the application without paying the application fee.

Program Cost Information: Bursar's website

Core Courses (16 Credits)

• MATH 625 - Numerical Analysis 4 Credit(s)
• MATH 626 - Numerical Linear Algebra& 4 Credit(s)
• MATH 647 - Probability Models 4 Credit(s)
• MATH 648 - Computational Statistics 4 Credit(s)

Track Courses (15 to 18 Credits)

Complete five courses. Three courses from your declared track and one course from each of the other two tracks.

Data Analytics Courses:

• CS 624 - Analysis of Algorithms 3 Credit(s)
• CS 670 - Artificial Intelligence 3 Credit(s)
• CS 671 - Machine Learning 3 Credit(s)
• CS 724 - Topics in Algorithm Theory and Design 3 Credit(s)

Computational Physics Courses:

• PHYSIC 610 - Topics in Medical Imaging 4 Credit(s)
• PHYSIC 611 - Theory of Classical Mechanics and Fluid Mechanics 4 Credit(s)
• PHYSIC 616 - Mathematical Methods for Physicists 4 Credit(s)
• PHYSIC 638 - Quantum Measurement Theory 4 Credit(s)
• BIOL 370 Molecular Biology (see Undergraduate Catalog)
• BIOL 625 - Genomics and Biotechnology 3 Credit(s)
• BIOL 664 - Bioinformatics for Molecular Biologists 3 Credit(s)
• BIOL 674 - Cell Signaling 3 Credit(s)
• CS 612 - Algorithms in Bioinformatics 3 Credit(s)

Bioinformatics Courses:

Electives (9 to 12 Credits)

Complete three courses from below. Additional track courses from above may be applied toward this requirement with permission of the graduate program director.

• BIOL 615 - Immunology 3 Credit(s)
• BIOL 677 - Advanced Eukaryotic Genetics 3 Credit(s)
• BIOL 681 - Network Biology 3 Credit(s)
• CHEM 601 - Thermodynamics & Kinetics 4 Credit(s)
• CHEM 602 - Quantum Mechanics & Spectroscopy 4 Credit(s)
• CS 630 - Database Management Systems 3 Credit(s)
• CS 636 - Database Application Development 3 Credit(s)
• CS 680 - Object-Oriented Design and Programming 3 Credit(s)
• CS 681 - Object-Oriented Software Development 3 Credit(s)
• CS 682 - Software Development Laboratory I 3 Credit(s)

Research Seminars (4 Credits)

Consult with you advisor for course options.

Dissertation (20 Credits)

Complete 20 credits of dissertation research by registering for a science dissertation course to be approved by your faculty advisor.

Graduation Criteria

Complete 64 to 70 credits from at least 15 courses including 40 credits of course work from four core courses, five track courses, three electives, and four credits of research seminar; and 20 credits of dissertation research.

Track: Students must choose a track in data analytics, bioinformatics, or computational physics. Doctoral candidacy: Pass a comprehensive examination after completion of 30 credits of course work. This examination consists of two parts: written and oral. Passing the written examination is a prerequisite to enter the oral examination. Dissertation: Compose and defend a dissertation based on original research.

Minimum grade: No course with a grade below B may be applied toward program requirements. Statute of limitations: Seven years.

Graduate Program Director Kourosh Zarringhalam kourosh.zarringhalam [at] umb.edu (617) 287-7486

Student Success Program Coordinator Velina Batchvarov velina.batchvarov [at] umb.edu (617) 287-3283

Computer Science

Learn more about UMass Boston's Computer Science department, our research, and our faculty.

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• Mathematics with Computer Science (Course 18-​C)
• Physics (Course 8)
• Department of Electrical Engineering and Computer Science
• Institute for Data, Systems, and Society
• Chemistry and Biology
• Climate System Science and Engineering
• Computation and Cognition
• Computer Science and Molecular Biology
• Computer Science, Economics, and Data Science
• Humanities and Engineering
• Humanities and Science
• Urban Science and Planning with Computer Science
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• Biomedical Engineering
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• Latin American and Latino/​a Studies
• Middle Eastern Studies
• Polymers and Soft Matter
• Public Policy
• Russian and Eurasian Studies
• Statistics and Data Science
• Women's and Gender Studies
• Advanced Urbanism
• Computational and Systems Biology

Computational Science and Engineering

• Design and Management (IDM &​ SDM)
• Joint Program with Woods Hole Oceanographic Institution
• Leaders for Global Operations
• Microbiology
• Music Technology and Computation
• Operations Research
• Real Estate Development
• Social and Engineering Systems
• Supply Chain Management
• Technology and Policy
• Transportation
• School of Architecture and Planning
• School of Engineering
• Aeronautics and Astronautics Fields (PhD)
• Artificial Intelligence and Decision Making (Course 6-​4)
• Biological Engineering (PhD)
• Nuclear Science and Engineering (PhD)
• School of Humanities, Arts, and Social Sciences
• Humanities (Course 21)
• Humanities and Engineering (Course 21E)
• Humanities and Science (Course 21S)
• Sloan School of Management
• School of Science
• Brain and Cognitive Sciences (PhD)
• Earth, Atmospheric and Planetary Sciences Fields (PhD)
• Interdisciplinary Programs (SB)
• Climate System Science and Engineering (Course 1-​12)
• Computer Science, Economics, and Data Science (Course 6-​14)
• Interdisciplinary Programs (Graduate)
• Computation and Cognition (MEng)
• Computational Science and Engineering (SM)
• Computer Science, Economics, and Data Science (MEng)
• Leaders for Global Operations (MBA/​SM and SM)
• Music Technology and Computation (SM and MASc)
• Real Estate Development (SM)
• Statistics (PhD)
• Supply Chain Management (MEng and MASc)
• Technology and Policy (SM)
• Transportation (SM)
• Aeronautics and Astronautics (Course 16)
• Aerospace Studies (AS)
• Civil and Environmental Engineering (Course 1)
• Comparative Media Studies /​ Writing (CMS)
• Comparative Media Studies /​ Writing (Course 21W)
• Computational and Systems Biology (CSB)
• Computational Science and Engineering (CSE)
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• Data, Systems, and Society (IDS)
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Doctoral Programs in Computational Science and Engineering

Doctor of philosophy in computational science and engineering, program requirements, programs offered by ccse in conjunction with select departments in the schools of engineering and science.

The interdisciplinary doctoral program in Computational Science and Engineering ( PhD in CSE + Engineering or Science ) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering.

Doctoral thesis fields associated with each department are as follows:

• Aerospace Engineering and Computational Science
• Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier)
• Chemical Engineering and Computation
• Civil Engineering and Computation
• Environmental Engineering and Computation
• Computational Materials Science and Engineering
• Mechanical Engineering and Computation
• Computational Nuclear Science and Engineering
• Nuclear Engineering and Computation
• Computational Earth, Science and Planetary Sciences
• Mathematics and Computational Science

As with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department.

The interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the application process, requirements, and relevant deadlines .

Once admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the CSE website . The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below).

Computational Concentration Subjects

Note: Students may not use more than 12 units of credit from a "meets with undergraduate" subject to fulfill the CSE curriculum requirements

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The PDF includes all information on this page and its related tabs. Subject (course) information includes any changes approved for the current academic year.

Engineering & Computational Mathematics

PhD in Engineering & Computational Mathematics

Whether you’re well into your engineering career or just beginning, the joint PhD in Engineering & Computational Mathematics broadens your understanding of the mathematical principles that underlie all engineering sub-disciplines and increases your professional value.

Program Highlights

Thanks to its flexible scheduling, this career-oriented program attracts students from well-known engineering and research firms, including Boeing, Northrup Grumman, and Raytheon.

With a joint degree from the CSULB/CGU program, you’ll be prepared to build a career in the growing fields of:

• Operations research
• Computer science
• Computational sciences
• Biomechanics
• Energy sustainability

Program Details

• Degree Requirements
• Mathematics Resources
• Mathematics Faculty

Program At-a-glance

required units

degree awarded

Spring, Fall

program start

7 years | full time*

estimated completion time

Where You Can Find Our Alumni

ReResearch Nanotechnology

RAND Corporation

Jet Propulsion Laboratory

Hess Corporation

New Jersey Institute of Technology

U.S. Patent & Trademark Office

Professor of Mathematics Director, Institute of Mathematical Sciences

Research Interests

Probability, Statistics, Computing, Algorithms, Navigation, Systems Engineering, Mathematical Finance

Marina Chugunova

Ellis Cumberbatch Professor of Mathematics Program Director, PhD in Engineering & Computational Mathematics

Surfactant-driven thin film flows in biomedical applications; Nonlinear parabolic equations; Stability problems in fluid dynamics; Scientific computations; Applied operator theory; Sturm-Liouville problems

Hrushikesh Mhaskar

Research Professor of Mathematics

Approximation theory, Computational harmonic analysis, Machine learning, Signal processing

Professor of Mathematics

Fluid Dynamics, Mathematical Modeling, Scientific Computing

Andrew Nguyen

Adjunct Professor of Mathematics

Stochastic processes, Statistics, Risk management, Financial derivatives, Actuarial sciences, Statistical software

Research Associate Professor of Mathematics

Statistical inferences, Stochastic differential equations, Stochastic modeling, Simulation, Machine learning, Approximation theory, Graph theory

Allon Percus

Joseph H. Pengilly Professor of Mathematics

Discrete optimization; Network models; Statistical physics; Random combinatorial structures

Claudia Rangel-Escareño

Probabilistic methods in computational biology, Statistical inference of genetic networks, Bioinformatics

Henry Schellhorn

Professor of Mathematics Academic Director, Financial Engineering Program

Financial engineering, Credit risk, Stochastic analysis, Traffic models

Extended Faculty

Pitzer College

Geometric topology, differential geometry

Konrad Aguilar

Pomona College

Noncommutative/quantum metric geometry, functional analysis, operator algebras

Asuman G. Aksoy

Claremont McKenna College

David Bachman

Low-dimensional topology

Arthur Benjamin

Harvey Mudd College

Combinatorics, game theory, operations research

Andrew Bernoff

Applied dynamical systems, fluid mechanics, self-similarity and scaling

Sarah Cannon

Randomized algorithms, Markov chains, stochastic processes, discrete geometry, statistical physics

Alfonso Castro

Partial differential equations, variational methods, inverse-function theorems, water waves (solitons)

Anie Chaderjian

Scripps College

Combinatorics

Gabriel Chandler

Lisette g. de pillis.

Computational fluid dynamics, numerical linear algebra, mathematical biology

Vin de Silva

Computational topology, manifold learning

Christina Edholm

Mathematical biology, epidemiological modeling

Lenny Fukshansky

Number theory, discrete geometry

Stephan Garcia

Complex symmetric operators, operator theory, complex function theory

Edray Goins

Algebraic geometry, number theory, representation theory

Differential geometry, Grassman manifolds

Jamie Haddock

Mathematical data science, optimization, applied convex geometry

Johanna Hardin

Model-based clustering, outlier detection, robust clustering, analysis of microarray data

Computational probability

Mike Izbicki

Machine learning, high-dimensional probability, computational geometry

Jon Jacobsen

Nonlinear elliptic partial differential equations, fluid dynamics

Chiu-Yen Kao

Numerical analysis and scientific computing

Gizem Karaali

Lie & Hopf algebras, quantum groups, Poisson-Lie structures, combinatorial representation theory

Algebraic geometry

Adam Landsberg

Joint Science

Scientific modeling of complex systems

Ran Libeskind-Hadas

Computational biology, cophylogenetics, design and analysis of algorithms

Haydee Lindo

Commutative algebra, homological algebra, representation theory

Jemma Lorenat

History of mathematics, geometry

Susan Martonosi

Operations research, applied probability, aviation security

John Milton

Computational neuroscience

Algebraic topology, knot theory

Mohamed Omar

Combinatorial optimization, graph theory, algebraic geometry

Mike O’Neill

Complex analysis and harmonic analysis

Michael Orrison

Harmonic analysis on finite groups, algebraic voting theory

Harmonic analysis

High-performance computing, data science

Ami Radunskaya

Dynamical Systems, stochastic processes, applications of dynamical systems to instrument modeling, sound generation, and interactive composition

Animesh Ray

Keck Graduate Institute

Genomics, computational and systems biology

Adolfo Rumbos

Nonlinear analysis, differential equations

Ghassan Sarkis

Number theory and commutative algebra, p-adic formal group

Shahriar Shahriari

Combinatorics, representation theory of finite groups

James Sterling

Bioengineering, microfluidics

Geometric and topological combinatorics, game theory, mathematical economics

Chris Towse

Arithmetic geometry, algebraic number theory, combinatorics

Talithia Williams

Spatial-temporal modeling of rainfall data

Low-dimensional topology, applications to molecular biology, data analysis, and quantum computation

Darryl Yong

Mathematics education, applied mathematics, perturbation theory, partial differential equations

Heather Zinn Brooks

Applied mathematics, mathematical modeling, complex systems, nonlinear dynamics, network theory, social systems, mathematical biology

Affiliated Faculty

Robert o. abad.

Adjunct Faculty, Financial Engineering

Kenneth Abbott

Adjunct Faculty

Peter Bergevin

Degree Requirements A minimum of 72 units of course work, independent study, and research (including transfer credit) must be completed.

• Transfer credits of up to 24 units of related courses at the master’s level is permissible on approval of the program committee; this course work must have been completed with at least a grade of B or its equivalent at an accredited institution and must be directly related to the joint program and to the student’s PhD goals.
• Of the 72 units, a minimum of 24 units must normally be completed in the graduate engineering program at CSULB and a minimum of 24 in the graduate mathematics program at CGU. Both sets of 24 units must conform to the area requirements of the relevant institution and must be approved by the Program Committee.
• All degree requirements must be completed within seven years (or six with the transfer of 24 units according to CGU regulations) from the time a student begins graduate study.

Residency Requirement The residency requirements for the PhD degree may be met either by two semesters of full-time study in a 24-month period or by the completion of 48 units of course work within a 48-month period, including work in the summer session, on either or both campuses.

Research Tool A student in the joint PhD program must demonstrate proficiency in problem-solving ability using computer programs. This demonstration may take different forms depending on the student’s engineering sub-discipline, but it must include evidence that the student has used an appropriate computer language and an algorithmic method to solve a problem from an engineering discipline.

Preliminary Examinations The student is required to pass written preliminary examinations. These examinations consist of two examination areas: one in engineering and one in mathematics.

Research Preparation On completion of at least 48 units of course work (including transfer units) and completion of the preliminary examinations and research tool test, a student embarks on the research phase of the joint doctoral program. In preparation for the research phase, the student is expected to spend at least a semester in advanced graduate courses, seminars, or directed reading courses, where exposure to research material is emphasized.

Research Proposal and Qualifying Examination The student will define an area of proposed research and prepare a written dissertation proposal containing an outline of the research to be undertaken and references to relevant source materials. The dissertation proposal is presented to the doctoral committee at least two weeks prior to the qualifying examination. The qualifying examination is an oral presentation to the doctoral committee by the student describing the research planned. The student is expected to present evidence both as to the mathematical content and to the engineering application of the proposed research, supporting such evidence with references to previous research work in both areas.

Advancement to Candidacy After successful completion of the qualifying examination and certification that all other requirements are fulfilled, the student is advanced to candidacy.

Dissertation and Final Oral Examination On completion of the research, the student will prepare the Dissertation in accordance with CGU regulations. A final draft of the dissertation will be presented to each member of the doctoral committee at least three weeks prior to the final oral examination. The oral defense will be held on the campus of the dissertation supervisor.

Engineering & Computational Mathematics Clinic CGU’s internationally recognized Engineering & Computational Mathematics Clinic offers first-hand experience solving significant mathematical problems for industry and government clients.

Recent projects include:

• Optimizing Transmission of Renewable Energy–Southern California Edison
• Hardware-Software Codesign–Los Alamos National Laboratory
• Data Cohort Analysis–Fair Isaac
• Optimizing Smart Power Grids–Los Alamos National Laboratory
• Credit Risk in a Network Economy–Fitch Rating
• Isogeometric Analysis–Boeing
• Gate to Base Capacitance Modeling for Nanoscale MOSFETs–USC Information Sciences Institute
• Practical Semi-Analytic Model for the Substrate Current of Short Channel MOSFETs with LDDs–USC Information Sciences Institute

Claremont Center for the Mathematical Sciences Through the Claremont Center for the Mathematical Sciences (CCMS), you’ll have access to one of the largest mathematical science communities in California, as well as to workshops, conferences, and seminars, including:

• Southern California Analysis Seminar
• Math-in-Industry Workshop
• Michael E. Moody Lecture Series
• History and Philosophy of Mathematics Seminar
• Claremont Mathematics Weekend
• CCMS Software Lab

Application Guidelines

Please see the application checklist for more details.  

In order to be considered for admission, applicants must submit separate and complete applications to both  Cal State Long Beach  and  Claremont Graduate University .

You can also visit the Cal State Long Beach  program page  for program information and faculty listings.

CGU operates on a priority deadline cycle. Applicants are strongly encouraged to submit complete applications by the priority dates in order to assure maximum consideration for both admission and fellowships.

Spring 2024 Priority Deadline – November 1, 2023 Final Deadline (International) – November 15, 2023 Final Deadline (Domestic) – December 1, 2023 Classes begin – January 16, 2024

Fall 2024 Priority Deadline – February 1, 2024 Final Deadline (International) – July 5, 2024 Final Deadline (Domestic) – August 1, 2024 Classes begin – August 26, 2024

Application Checklist

The Claremont Graduate University online application is hosted online by Slate Technolutions via a secure web server. You will create a username and password so that you can return to continue your application over several sessions and check your status after submission. After you submit your application, it is made available for review by our faculty and staff.

Begin your application

The application fee is non-refundable.

Applicants must submit a sealed, official transcript from every undergraduate and graduate institution that has granted the applicant a degree. Electronic transcripts sent to [email protected] are also accepted. For undergraduate coursework, applicants are required to submit proof of a completed bachelor’s degree from a regionally accredited college or university. Unofficial copies of transcripts are accepted for review purposes, but official copies will be required upon admission.

Applicants currently earning a degree that will be completed prior to attending CGU are required to submit a transcript showing work in progress for evaluation purposes. Once the degree has been granted, a final official transcript documenting the degree conferred must be submitted to CGU.

International applicants are advised to review the International Transcript Guidelines for additional information on submitting international transcripts.

Applicants must submit an up-to-date copy of their resume.

A valid score on one of the following examinations TOEFL, IELTS, Pearson PTE scores is required of all non-native English-speaking applicants. The examination is not required for the following applicants:

• Citizens or permanent residents of countries where English is the sole official language of instruction, e.g., Australia, Bahamas, Barbados, Canada (except Quebec), England, Ghana, Ireland, Jamaica, Kenya, New Zealand, Nigeria, Scotland, St. Vincent and the Grenadines, Trinidad, Tobago, Uganda, and Wales (see the CGU Bulletin for a complete list of accepted countries).
• Applicants who hold an undergraduate or advanced degree, or will have earned such a degree prior to enrolling at CGU, from an institution in the US or in countries where English is the sole official language of instruction (see above).
• Applicants who have successfully completed an academic English pre-master’s or intensive graduate bridge program from a nationally recognized, regionally accredited four-year college or university in the United States in the last two years, with submitted evidence of successful completion, and subject to curriculum approval.

CGU’s school code for the TOEFL exam is 4053 .

International applicants are encouraged to visit our International Applicants page for more information, including score requirements.

When filling out the online application, please enter references acquainted with your potential for success who will submit a written recommendation on your behalf. In most academic departments, references from faculty members who can speak to your academic ability are preferred; applicants with substantial work experience may request professional references. Please do not enter family members as references.

You will be required to input information for your recommenders (whether they are submitting online or not) in the “Recommendations” section of the online application. Please follow the directions in this section carefully before clicking on “Recommendation Provider List” to input the names and contact information for each recommender. You will have an opportunity to indicate if the reference writer will be submitting online. These reference writers will receive an email from CGU with instructions on submitting an online recommendation.

Recommenders who are indicated as offline will not receive an email from CGU with instructions to submit. These reference writers can submit via traditional mail and should use the supplemental New Student Recommendation Form. Recommenders can also email their letter of recommendation to the Office of Admissions at [email protected] .

Download the Recommendation Form

Please submit a 2-3 page statement of purpose that details your academic and/or professional achievements, your specific areas of research interest within your desired field of study, why you are a strong candidate for graduate studies at CGU, and your career goals.

GMAT or GRE examination scores must be dated within the past five years. Request that an official GMAT or GRE score be sent to admissions directly from Educational Testing Service (ETS).

Scores must be sent directly to CGU by the testing agency.

CGU’s school codes: GMAT DZK-QS-08 ETS (GRE and TOEFL) 4053

ESTIMATED TUITION (CALIFORNIA RESIDENTS, NON-RESIDENTS, INTERNATIONAL)

*Based on 2023-2024 tuition rates.

STUDENT FEES (PER SEMESTER)

For estimates of room & board, books, etc., please download CGU’s  Cost of Attendance 2022-2023  .

Review General Costs

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Request More Info

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Department of Computer Science

Joint phd program in mathematics and computer science.

• Maps and Directions
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• Masters Program in Computer Science (MPCS)
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In Winter 2018, the Department of Mathematics and the Department of Computer Science launched a joint program through which participating students can earn the degree

The basic structure is that students must gain admission to both PhD programs and satisfy both sets of course requirements. They write a single dissertation that satisfies both programs.

While the program is open to all eligible students, we expect that at least initially it will be most popular among students working in CS Theory, Discrete Mathematics, and Mathematical Logic.

Each student in this program will have a primary program (either Mathematics or Computer Science). Throughout the course of studies, the primary program will provide administrative support to the student, including in matters regarding financial support.

To be admitted to the joint program, students will have to be admitted by both departments as follows.

Application before entering the PhD program

The applicant must apply to the primary program indicating in the application that he/she wishes to be considered for the joint program. If admitted to the primary program, the application will be automatically forwarded to the Graduate Admissions Committee of the secondary program. To be assisted in making the decision, the Graduate Admissions Committee of the secondary program may request from the applicant additional materials in accordance with customs and rules of its department.

Application after entering the PhD program

Students enrolled in either the Mathematics or the Computer Science PhD program may apply to the joint program during the first four years in their current program. If admitted to the joint program, their current program will be primary.

Such an applicant must submit the following material to the Director of Graduate Studies/Graduate Committee Chair of the intended secondary program, while notifying the Director of Graduate Studies/Graduate Committee Chair of the primary program:

• statement of purpose, explaining why the joint program is the right program for the applicant
• statement of coursework and research done so far
• statement of a schedule how the applicant proposes to satisfy the secondary program's requirements
• advisor's recommendation, including endorsement of the applicant's statements (items 2, 3, 4 above)
• if the application occurs during the first year of the primary program, the applicant needs to provide two additional letters of recommendation and his/her undergraduate transcript. It is permitted to reuse material from the application to the primary program.

Requirements, monitoring

Course requirements.

Students enrolling in the joint program will need to satisfy the course requirements of both departments. They will have to satisfy the course requirements of their primary program on the schedule of that program, and satisfy the course requirements of their secondary program by the end of their fifth year in the primary program.

According to current rules, two of the CS electives can be courses offered by the Mathematics department. These courses are permitted to overlap with the Mathematics course requirements.

Exam Requirements

Students in the joint program shall fulfill the examination requirements of the primary program; the current list of requirements can be found at

• Computer Science Requirements
• Mathematics Requirements

For students participating in the joint program, the deadlines for these exams can be relaxed by petitioning the Director of Graduate Studies/Graduate Committee Chair of the primary program.

Monitoring student progress

Students' annual progress reports go to both departments' Director of Graduate Studies/Graduate Committee Chair in accordance with each department's format.

PhD dissertation and defense

Subject of the dissertation.

The dissertation is expected to be in an area relevant to both fields.

PhD thesis defense

The scheduling of the PhD Thesis defense follows the Mathematics Department's custom as follows.

• A nearly final draft of the thesis is made accessible to faculty at least two weeks prior to the defense, either in hard copy in the departmental office or, preferably, by posting on the internet.
• The dissertation is reviewed in writing by two readers, one of whom is typically the thesis advisor.
• The reports by the first and the second readers are circulated among faculty of both departments, along with the Thesis abstract and the following information: the location (physical or virtual) where the thesis can be viewed, the planned time and location of the defense, and the names and affiliations of the thesis committee members.
• There is a two-week period for comments by faculty before the admission of the thesis for defense.

The thesis defense itself consist of a 50-minute public presentation of the main results and methods of the dissertation, followed by a public question-answer period, followed by a closed-session question-answer period.

Oversight, committees

The program proceeds under joint Math-CS oversight, exercised by the Director of Graduate Studies/Graduate Committee Chair of each department.

Examination committees

The following rules apply to all examination committees (Qualifying/Topic Exam, Master's, Candidacy, and PhD). The committee will consist of at least three members, including the student's advisor(s). It will include at least one member of each department, and will either be chaired by a joint appointee of the two departments or co-chaired by a member of each department. Each department shall publicize these exams in accordance with its established customs.

Chennai Mathematical Institute

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Ph.D in Computer Science and Mathematics of Computation

University of Insubria

Welcome! Here you can find information about the Ph.D. program in Computer Science and Mathematics of Computation , offered by Università Degli Studi dell’Insubria

The goal of this program is to prepare students with a sound cultural background, providing them with a high level of flexibility, open-minded and in-depth cutting-edge competencies in specific fields. These students will be able to carry out, manage and disseminate independent theoretical and/or applied research activities at an international level. They will be able to design mathematical models aimed at defining and building complex Information Technology (IT) systems, develop innovative IT applications and transfer their knowledge to the private sector, thereby also contributing to strengthening the role played by Italian industrial organizations in the global economic scenario. Our Ph.D. program stresses an interdisciplinary approach that nowadays characterizes most of the advanced researches worldwide.

The deadline for the next call (italian XXXIX cycle) is

August 2, 2023 at 12 (GMT + `2) 

The application is online; further information available in ENGLISH and  ITALIAN