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Applied Mathematics

Prospective ph.d. students, applied mathematics ph.d. program.

The Division of Applied Mathematics is devoted to research, education and scholarship. Our faculty engages in research in a range of areas from applied and algorithmic problems to the study of fundamental mathematical questions. By its nature, our work is and always has been inter– and multidisciplinary. Among the research areas represented in the division are dynamical systems and partial differential equations, control theory, probability and stochastic processes, numerical analysis and scientific computing, fluid mechanics, computational biology, statistics, and pattern theory. Our graduate program in applied mathematics includes around 50 Ph.D. students, with many of them working on interdisciplinary projects. Joint research projects exist with faculty in various biology and life sciences departments and the departments of Chemistry, Computer Science, Cognitive and Linguistic Sciences, Earth, Environmental, and Planetary Sciences, Engineering, Mathematics, Physics and Neuroscience, as well as with faculty in the Warren Alpert Medical School of Brown University.

Prospective PhD applicants who are interested in visiting the campus and meeting with a faculty member to discuss graduate and research programs are encouraged to contact Candida Hall , Student Affairs Manager (401.863.2463).

Get to know us: Virtual workshop

Attend talks by faculty and graduate students. Ask questions at the Q&A panel with faculty and students.

Saturday, December 2, 2023

How to Apply

Please visit our webpage on the Graduate School for information and guidance on the application process, all relevant deadlines, and required materials. 

Inquire or Apply to our Ph.D. Program

• Applied Math code for GRE:  3094, GREs are not required for the Academic Year,  2023-2024
• Applied Math code for TOEFL:  3094
• Brown University code for ETS:  3094

Ph.D. Program in Computational Biology

The Division of Applied Mathematics is one of four Brown academic units that contribute to the doctoral program administered by the Center for Computational Molecular Biology. Graduate students in this program who choose applied mathematics as their home department will receive a PhD in Applied Mathematics (with Computational Biology Annotation). For further information about this program, including the application process, please visit the  CCMB Graduate Program page .

Frequently Asked Questions

Applications which are missing materials will be considered, but may be at a disadvantage in regards to admission decisions.    

Admission to our programs depends on many factors. We cannot assess your chances of admission prior to reviewing your entire application. 

The Admission Committee reviews all aspects of your application, including personal statement, recommendation letters, grades, GRE scores, research experience and related original publications, etc. There is no precise formula followed to make an admission decision, but a strong showing in the above components is likely to increase your chances of admission. 

The Admission Committee reviews all aspects of your application when making decisions. The fact that a candidate attended a particular University X (whether X is Brown or any other institution) does not mean that an application will be treated any differently from other applications.

We expect to send the results to you before March 1. Our Student Affairs Manager, Candida Hall , can be contacted if you need information prior to that date.

Yes, we will organize a common Visiting Day for all admitted students sometime in March, and make arrangements for a visit on another day, if needed, to accommodate any schedule conflicts.  

Students are admitted to the Division of Applied Mathematics as a whole, and not to a particular professor or group. 

Over recent years, the incoming PhD class has averaged about 12-15 students per year. The target and actual enrollment for our program varies each year based on a number of factors.  For the academic year 2023-2024, the GRE scores are not required, and the deadline of application is December 9, 2023.

Each year, roughly half of the intake consists of international students. However, we do not have set quotas and decisions are made depending on the quality of the applicant. We are strongly committed to maintaining a fair and equitable admission process and to cultivating diversity in our student body. 

Your chances of admission depend on many factors including test scores (both the TOEFL score and the regular and subject GRE scores), transcripts, recommendation letters, research experience, statement of purpose and research interests, as well as the general background of the students. Improving any or all of these would improve your chances of admission.  For the academic year 2023-2024, the GRE scores are not required.  

Information about the research conducted in the Division can be found on the Division's webpages. If you have specific questions regarding a particular professor's research, you may e-mail that professor directly. 

If you have any technical difficulties with your applications or any other administrative questions related to your application, contact our Student Affairs Manager, [email protected] .

A Bachelors' degree is required, but the area does not have to be in mathematics.  Applicants are expected to have a strong background in mathematics. 

No, you only need to have a Bachelors' degree to apply for the PhD degree. However, you may also apply for a PhD degree after having completed the Masters' degree. 

A $75 application fee must be paid when an application is submitted. Applicants who want to be evaluated by more than one graduate program must submit a separate application and a separate fee for each additional program.

Applicants who are U.S. citizens or permanent residents may be eligible for fee waivers. (Please note that your completed application must be submitted 14 days in advance of the program’s application deadline in order to be considered for a fee waiver. Please choose the “Request a fee waiver” option as your method of payment on the payment information page.) Application fee waivers are not available for international applicants. 

Admission to our PhD program includes at least five years of guaranteed funding, including stipend, tuition, health services fee, and health insurance, for students who maintain good standing in the program.  

For the PhD program, the GRE general test is required and the GRE (mathematics) subject test is highly recommended.  Please note that although the subject test is not required, the absence of a subject score makes determining the quality of your application more challenging.  Nevertheless, it is possible that other portions of your application, such as general GRE scores, grades, letters of recommendation, etc. may provide enough information for a decision to be made.  For the academic year 2023-2024, the GRE scores are not required.

Yes, it is in your own interests to provide as much information as you can.  The more information we have, the more likely that we will be able to assess your application accurately.

Yes. The TOEFL cannot be waived unless you have completed an undergraduate or Masters degree at an accredited institution in which the medium of instruction is English in a predominantly English-speaking country (e.g., the United States, United Kingdom, Australia, New Zealand). The IELTS exam can be substituted for TOEFL. 

The minimum score for admission consideration is 577 on the paper-based test and 90 on the Internet-based test. For IELTS, the recommended minimum overall band score is 7. These exams should be taken early enough to allow the scores to reach the Graduate School by your program's deadline. Performance on the tests is one of many factors considered in making admission decisions. 

Admissions decisions are based on many factors of which test scores are just one (see Q11).  It is your overall performance which will be considered, so your performance in any particular area need not preclude your application being successful.  

We do not track and share average GRE or TOEFL scores. 

Brown University requires official and original test scores sent by ETS.  You may self-report your test scores and upload copies of your score report(s) into your application, prior to the reception of original test scores. 

All international applicants whose native language is not English must submit an official Test of English as a Foreign Language (TOEFL) or International English Language Testing System (IELTS) score.  Language proficiency exams are not required of those students who have earned a degree from a non-U.S. university where the primary language of instruction is English, or from a college or university in the United States, or in any of a number of countries.

We really cannot advise you on this or similar matters since we are not familiar with you or your history, and suggest that you contact an advisor at University X for advice about what choice of courses would be best for your specific circumstances. 

Transferring to the PhD program from the PhD program at another university happens only in very rare circumstances, and depends on many factors. It is unusual for a student's mathematical preparation to be sufficient to merit a transfer and in most cases, the student would need to start the program afresh as a new student. This is best accomplished by applying to the program as a regular applicant for admission in the following Fall.

Applied Mathematics

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Applied Mathematics is an area of study within the Harvard John A. Paulson School of Engineering and Applied Sciences. Prospective students apply through Harvard Griffin GSAS; in the online application, select  “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Graduates of the program have gone on to a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA.

Standardized Tests

GRE General:  Not accepted

APPLICATION DEADLINE

Questions about the program.

Graduate Programs

Applied mathematics.

The graduate program provides training and research activities in a broad spectrum of applied mathematics. The breadth is one of the great strengths of the program and is further reflected in the courses we offer.

The Division of Applied Mathematics is devoted to research, education and scholarship. Our faculty engages in research in a range of areas from applied and algorithmic problems to the study of fundamental mathematical questions. By its nature, our work is and always has been inter– and multidisciplinary. Among the research areas represented in the division are dynamical systems and partial differential equations, control theory, probability and stochastic processes, numerical analysis and scientific computing, fluid mechanics, computational biology, statistics, and pattern theory. Our graduate program in applied mathematics includes around 50 Ph.D. students, with many of them working on interdisciplinary projects. Joint research projects exist with faculty in various biology and life sciences departments and the departments of Chemistry, Computer Science, Cognitive and Linguistic Sciences, Earth, Environmental, and Planetary Sciences, Engineering, Mathematics, Physics and Neuroscience, as well as with faculty in the Warren Alpert Medical School of Brown University.

Application Information

Application requirements, gre subject:.

Not Required

GRE General:

Dates/deadlines, application deadline, completion requirements.

Eight courses, of which at least six must be at the 2000 level, at least six must be applied mathematics courses, and at least six must be completed with a grade of B or better; preliminary oral examination; two semesters of teaching; dissertation and oral defense.

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Contact and Location

Division of applied mathematics, mailing address.

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Ph.D. in Mathematics, Specializing in Applied Math

Table of contents, overview of applied mathematics at the courant institute.

• PhD Study in Applied Mathematics
• Applied math courses

Applied mathematics has long had a central role at the Courant Institute, and roughly half of all our PhD's in Mathematics are in some applied field. There are a large number of applied fields that are the subject of research. These include:

• Atmosphere and Ocean Science
• Biology, including biophysics, biological fluid dynamics, theoretical neuroscience, physiology, cellular biomechanics
• Computational Science, including computational fluid dynamics, adaptive mesh algorithms, analysis-based fast methods, computational electromagnetics, optimization, methods for stochastic systems.
• Data Science
• Financial Mathematics
• Fluid Dynamics, including geophysical flows, biophysical flows, fluid-structure interactions, complex fluids.
• Materials Science, including micromagnetics, surface growth, variational methods,
• Stochastic Processes, including statistical mechanics, Monte-Carlo methods, rare events, molecular dynamics

PhD study in Applied Mathematics

PhD training in applied mathematics at Courant focuses on a broad and deep mathematical background, techniques of applied mathematics, computational methods, and specific application areas. Descriptions of several applied-math graduate courses are given below.

Numerical analysis is the foundation of applied mathematics, and all PhD students in the field should take the Numerical Methods I and II classes in their first year, unless they have taken an equivalent two-semester PhD-level graduate course in numerical computing/analysis at another institution. Afterwards, students can take a number of more advanced and specialized courses, some of which are detailed below. Important theoretical foundations for applied math are covered in the following courses: (1) Linear Algebra I and II, (2) Intro to PDEs, (3) Methods of Applied Math, and (4) Applied Stochastic Analysis. It is advised that students take these courses in their first year or two.

A list of the current research interests of individual faculty is available on the Math research page.

Courses in Applied Mathematics

The following list is for AY 2023/2024:

--------------------------------------

(MATH-GA.2701) Methods Of Applied Math

Fall 2023, Oliver Buhler

Description:  This is a first-year course for all incoming PhD and Masters students interested in pursuing research in applied mathematics. It provides a concise and self-contained introduction to advanced mathematical methods, especially in the asymptotic analysis of differential equations. Topics include scaling, perturbation methods, multi-scale asymptotics, transform methods, geometric wave theory, and calculus of variations.

Prerequisites : Elementary linear algebra, ordinary differential equations; at least an undergraduate course on partial differential equations is strongly recommended.

(MATH-GA.2704) Applied Stochastic Analysis

Spring 2024, Jonathan Weare

This is a graduate class that will introduce the major topics in stochastic analysis from an applied mathematics perspective.  Topics to be covered include Markov chains, stochastic processes, stochastic differential equations, numerical algorithms, and asymptotics. It will pay particular attention to the connection between stochastic processes and PDEs, as well as to physical principles and applications. The class will attempt to strike a balance between rigour and heuristic arguments: it will assume that students have some familiarity with measure theory and analysis and will make occasional reference to these, but many results will be derived through other arguments. The target audience is PhD students in applied mathematics, who need to become familiar with the tools or use them in their research.

Prerequisites: Basic Probability (or equivalent masters-level probability course), Linear Algebra (graduate course), and (beginning graduate-level) knowledge of ODEs, PDEs, and analysis.

(MATH-GA.2010/ CSCI-GA.2420) Numerical Methods I

• Fall 2023, Benjamin Peherstorfer

Description:   This course is part of a two-course series meant to introduce graduate students in mathematics to the fundamentals of numerical mathematics (but any Ph.D. student seriously interested in applied mathematics should take it). It will be a demanding course covering a broad range of topics. There will be extensive homework assignments involving a mix of theory and computational experiments, and an in-class final. Topics covered in the class include floating-point arithmetic, solving large linear systems, eigenvalue problems, interpolation and quadrature (approximation theory), nonlinear systems of equations, linear and nonlinear least squares, and nonlinear optimization, and iterative methods. This course will not cover differential equations, which form the core of the second part of this series, Numerical Methods II.

Prerequisites:   A good background in linear algebra, and some experience with writing computer programs (in MATLAB, Python or another language).

(MATH-GA.2020 / CSCI-GA.2421) Numerical Methods II

Spring 2024, Aleksandar Donev

This course (3pts) will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments in MATLAB/Python will form an essential part of the course. The course will introduce students to numerical methods for (approximately in this order):

• The Fast Fourier Transform and pseudo-spectral methods for PDEs in periodic domains
• Ordinary differential equations, explicit and implicit Runge-Kutta and multistep methods, IMEX methods, exponential integrators, convergence and stability
• Finite difference/element, spectral, and integral equation methods for elliptic BVPs (Poisson)
• Finite difference/element methods for parabolic (diffusion/heat eq.) PDEs (diffusion/heat)
• Finite difference/volume methods for hyperbolic (advection and wave eqs.) PDEs (advection, wave if time permits).

Prerequisites

This course requires Numerical Methods I or equivalent graduate course in numerical analysis (as approved by instructor), preferably with a grade of B+ or higher.

( MATH-GA.2011 / CSCI-GA 2945) Computational Methods For PDE

Fall 2023, Aleksandar Donev & Georg Stadler

This course follows on Numerical Methods II and covers theoretical and practical aspects of advanced computational methods for the numerical solution of partial differential equations. The first part will focus on finite element methods (FEMs), and the second part on finite volume methods (FVMs) including discontinuous Galerkin (FE+FV) methods. In addition to setting up the numerical and functional analysis theory behind these methods, the course will also illustrate how these methods can be implemented and used in practice for solving partial differential equations in two and three dimensions. Example PDEs will include the Poisson equation, linear elasticity, advection-diffusion(-reaction) equations, the shallow-water equations, the incompressible Navier-Stokes equation, and others if time permits. Students will complete a final project that includes using, developing, and/or implementing state-of-the-art solvers.

In the Fall of 2023, Georg Stadler will teach the first half of this course and cover FEMs, and Aleks Donev will teach in the second half of the course and cover FVMs.

A graduate-level PDE course, Numerical Methods II (or equivalent, with approval of syllabus by instructor(s)), and programming experience.

• Elman, Silvester, and Wathen: Finite Elements and Fast Iterative Solvers , Oxford University Press, 2014.
• Farrell: Finite Element Methods for PDEs , lecture notes, 2021.
• Hundsdorfer & Verwer: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations , Springer-Verlag, 2003.
• Leveque: Finite Volume Methods for Hyperbolic Problems , Cambridge Press, 2002.

-------------------------------------

( MATH-GA.2012 ) Immersed Boundary Method For Fluid-Structure Interaction

Not offered AY 23/24.

The immersed boundary (IB) method is a general framework for the computer simulation of flows with immersed elastic boundaries and/or complicated geometry.  It was originally developed to study the fluid dynamics of heart valves, and it has since been applied to a wide variety of problems in biofluid dynamics, such as wave propagation in the inner ear, blood clotting, swimming of creatures large and small, and the flight of insects.  Non-biological applications include sails, parachutes, flows of suspensions, and two-fluid or multifluid problems. Topics to be covered include: mathematical formulation of fluid-structure interaction in Eulerian and Lagrangian variables, with interaction equations involving the Dirac delta function; discretization of the structure, fluid, and interaction equations, including energy-based discretization of the structure equations, finite-difference discretization of the fluid equations, and IB delta functions with specified mathematical properties; a simple but effective method for adding mass to an immersed boundary; numerical simulation of rigid immersed structures or immersed structures with rigid parts; IB methods for immersed filaments with bend and twist; and a stochastic IB method for thermally fluctuating hydrodynamics within biological cells.  Some recent developments to be discussed include stability analysis of the IB method and a Fourier-Spectral IB method with improved boundary resolution.

Course requirements include homework assignments and a computing project, but no exam.  Students may collaborate on the homework and on the computing project, and are encouraged to present the results of their computing projects to the class.

Prerequisite:   Familiarity with numerical methods and fluid dynamics.

(MATH-GA.2012 / CSCI-GA.2945) :  High Performance Computing

Not offered AY 23/24

This class will be an introduction to the fundamentals of parallel scientific computing. We will establish a basic understanding of modern computer architectures (CPUs and accelerators, memory hierarchies, interconnects) and of parallel approaches to programming these machines (distributed vs. shared memory parallelism: MPI, OpenMP, OpenCL/CUDA). Issues such as load balancing, communication, and synchronization will be covered and illustrated in the context of parallel numerical algorithms. Since a prerequisite for good parallel performance is good serial performance, this aspect will also be addressed. Along the way you will be exposed to important tools for high performance computing such as debuggers, schedulers, visualization, and version control systems. This will be a hands-on class, with several parallel (and serial) computing assignments, in which you will explore material by yourself and try things out. There will be a larger final project at the end. You will learn some Unix in this course, if you don't know it already.

Prerequisites for the course are (serial) programming experience with C/C++ (I will use C in class) or Fortran, and some familiarity with numerical methods.

(MATH-GA.2011) Monte Carlo Methods

Fall 2023, Jonathan Weare and Jonathan Goodman

Topics : The theory and practice of Monte Carlo methods. Random number generators and direct sampling methods, visualization and error bars. Variance reduction methods, including multi-level methods and importance sampling. Markov chain Monte Carlo (MCMC), detailed balance, non-degeneracy and convergence theorems. Advanced MCMC, including Langevin and MALA, Hamiltonian, and affine invariant ensemble samplers. Theory and estimation of auto-correlation functions for MCMC error bars. Rare event methods including nested sampling, milestoning, and transition path sampling. Multi-step methods for integration including Wang Landau and related thermodynamic integration methods. Application to sampling problems in physical chemistry and statistical physics and to Bayesian statistics.

Required prerequisites:

• A good probability course at the level of Theory of Probability (undergrad) or Fundamentals of Probability (masters)
• Linear algebra: Factorizations (especially Cholesky), subspaces, solvability conditions, symmetric and non-symmetric eigenvalue problem and applications
• Working knowledge of a programming language such as Python, Matlab, C++, Fortran, etc.
• Familiarity with numerical computing at the level of Scientific Computing (masters)

Desirable/suggested prerequisites:

• Numerical methods for ODE
• Applied Stochastic Analysis
• Familiarity with an application area, either basic statistical mechanics (Gibbs Boltzmann distribution), or Bayesian statistics

(MATH-GA.2012 / CSCI-GA.2945) Convex & Non Smooth Optimization

Spring 2024, Michael Overton

Convex optimization problems have many important properties, including a powerful duality theory and the property that any local minimum is also a global minimum. Nonsmooth optimization refers to minimization of functions that are not necessarily convex, usually locally Lipschitz, and typically not differentiable at their minimizers. Topics in convex optimization that will be covered include duality, CVX ("disciplined convex programming"), gradient and Newton methods, Nesterov's optimal gradient method, the alternating direction method of multipliers, the primal barrier method, primal-dual interior-point methods for linear and semidefinite programs. Topics in nonsmooth optimization that will be covered include subgradients and subdifferentials, Clarke regularity, and algorithms, including gradient sampling and BFGS, for nonsmooth, nonconvex optimization. Homework will be assigned, both mathematical and computational. Students may submit a final project on a pre-approved topic or take a written final exam.

Prerequisites: Undergraduate linear algebra and multivariable calculus

Q1: What is the difference between the Scientific Computing class and the Numerical Methods two-semester sequence?

The Scientific Computing class (MATH-GA.2043, fall) is a one-semester masters-level graduate class meant for graduate or advanced undergraduate students that wish to learn the basics of computational mathematics. This class requires a working knowledge of (abstract) linear algebra (at least at the masters level), some prior programming experience in Matlab, python+numpy, Julia, or a compiled programming language such as C++ or Fortran, and working knowledge of ODEs (e.g., an undergrad class in ODEs). It only briefly mentions numerical methods for PDEs at the very end, if time allows.

The Numerical Methods I (fall) and Numerical Methods II (spring) two-semester sequence is a Ph.D.-level advanced class on numerical methods, meant for PhD students in the field of applied math, masters students in the SciComp program , or other masters or advanced undergraduate students that have already taken at least one class in numerical analysis/methods. It is intended that these two courses be taken one after the other, not in isolation . While it is possible to take just Numerical Methods I, it is instead strongly recommended to take the Scientific Computing class (fall) instead. Numerical Methods II requires part I, and at least an undergraduate class in ODEs, and also in PDEs. Students without a background in PDEs should not take Numerical Methods II; for exceptions contact Aleks Donev with a detailed justification.

The advanced topics class on Computational Methods for PDEs follows on and requires having taken NumMeth II or an equivalent graduate-level course at another institution (contact Aleks Donev with a syllabus from that course for an evaluation), and can be thought of as Numerical Methods III.

Q2: How should I choose a first graduate course in numerical analysis/methods?

• If you are an undergraduate student interested in applied math graduate classes, you should take the undergraduate Numerical Analysis course (MATH-UA.0252) first, or email the syllabus for the equivalent of a full-semester equivalent class taken elsewhere to Aleks Donev for an evaluation.
• Take the Scientific Computing class (fall), or
• Take both Numerical Methods I (fall) and II (spring), see Q1 for details. This is required of masters students in the SciComp program .

Applied Mathematics

Applied Mathematics at Harvard School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities.

Working individually and as part of teams collaborating across the University and beyond, faculty and students in Applied Mathematics seek to quantitatively describe, predict, design and control phenomena in a range of fields. This involves the study of relations between models and observations, while examining the mathematical foundations and limitations of these models and techniques.

Research and educational activities have particularly close links to Harvard's efforts in  Mathematics ,  Economics ,  Computer Science , and  Statistics . 

Applied Math Programs

Undergraduate

Bachelor of Arts (AB)

Bachelor of Arts (AB) / Master of Science (SM)

• Secondary Field

Applied Mathematics Leadership

In applied mathematics.

• First-Year Exploration
• Areas of Application
• AM & Economics
• How to Declare
• Who are my Advisors?
• Senior Thesis
• Research for Course Credit (AM 91R & AM 99R)
• AB/SM Information
• Peer Concentration Advisors (PCA) Program
• Student Organizations
• How to Apply
• PhD Timeline
• PhD Model Program (Course Guidelines)
• Oral Qualifying Examination
• Committee Meetings
• Committee on Higher Degrees
• Research Interest Comparison
• Collaborations
• Cross-Harvard Engagement
• Clubs & Organizations
• Centers & Initiatives
• Alumni Stories

Research Areas

• Active Matter
• Applied Algebra and Geometry
• Computational Neuroscience
• Computational Science and Engineering
• Control Theory and Stochastic Systems
• Data Science
• Economics and Computation
• Fluid Mechanics
• Machine Learning
• Modeling Physical/Biological Phenomena and Systems
• Numerical Analysis
• Theory of Computation

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College of Arts & Sciences

PhD Program in Applied Mathematics

Phd program.

Applying to PhD Program

PhD Degree Requirements

PhD Coursework

PhD Institutional Funding

Applied Mathematics Graduate Seminar

Program Contact

The PhD program in Applied Mathematics prepares students for careers in academia, industry, or government. Students will receive expert guidance in research and a foundation in teaching pedagogy.

Applied Mathematics

In the Cornell Department of Mathematics, the “applied” group includes mathematicians working in dynamical systems theory, PDEs, calculus of variations, computational algebra, applied probability theory, statistics, numerical analysis, and scientific computing. The group’s activities are often coordinated with the Center for Applied Mathematics and the graduate field of applied mathematics.

Many great mathematicians of the past would be hard pressed to identify themselves as either pure or applied, and many of us at Cornell share this philosophy. Applied mathematics is regarded as an interdisciplinary activity that results from the interaction of mathematics with other sciences and engineering. Whether new mathematics is inspired by questions arising in other fields or new applications are discovered for pre-existing mathematics, the results should stand on their own within a single discipline. In addition to applied talks in departmental seminars, the group members participate in seminars and colloquia outside the department, including the interdisciplinary CAM Colloquium and the SCAN seminar.

Faculty Members

Emeritus and other faculty  , activities and resources:.

• CAM Colloquium
• Scientific Computing and Numerics (SCAN) Seminar
• Center for Applied Mathematics
• Graduate field of applied mathematics

Related people

Professor Emeritus

Michler Scholar

NSF Postdoctoral Associate (Visiting Assistant Professor)

Ph.D. Candidate

Abram R. Bullis Professor Emeritus of Mathematics

Senior Lecturer

H.C. Wang Assistant Professor

Associate Professor

Tisch University Professor of Computer Science and Information Science and Interim Dean of Computing and Information Science

Joseph Newton Pew, Jr. Professor in Engineering

Ph.D. Student

Distinguished Professor of Arts and Sciences in Mathematics

Abram R. Bullis Professor of Mathematics

Professor, Stephen H. Weiss Presidential Fellow

Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics, Stephen H. Weiss Presidential Fellow

Jacob Gould Schurman Professor

Associate Professor, Stephen H. Weiss Junior Fellow

Goenka Family Assistant Professor in Mathematics

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Ph.D. Program

Introduction.

These guidelines are intended to help familiarize graduate students with the policies governing the graduate program leading to the degrees of Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the graduate school requirements found on the  Graduate Student Resources  page and the  Doctoral Degree Policies  of the graduate school. Students are expected to be familiar with these procedures and regulations.

The Doctor of Philosophy program

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions that are relevant to a significant area of application.

Course requirements for the Ph.D. program

• AMATH 561, 562, 563
• AMATH 567, 568, 569
• AMATH 584, 585, 586
• AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year.
• Students must take a minimum of 15 numerically graded courses. At most two of these can be at the 400 level or be cross listed with courses at the 400 level. Graduate level courses previously taken at UW (e.g., during a Master's program) count toward this requirement. Graduate level courses taken outside of UW may count toward the requirement for 15 numerically graded courses with the approval of the Graduate Program Coordinator. The entire course of study of a student and all exceptions to this list must be approved by the Graduate Program Coordinator and the student’s advisor or faculty mentors.

For students who entered the doctoral program autumn 2017 or autumn 2018, please see these degree requirements. For students who entered the doctoral program prior to autumn 2017, please see these degree requirements.  

Faculty mentoring

Upon arrival, incoming students will be assigned two faculty mentors. Until a student settles on an advisor, the faculty mentors aid the student in selecting courses, and they each guide the student through a 2-credit independent reading course on material related to the student’s research interest. The faculty mentors are not necessarily faculty in the Department of Applied Mathematics.

Faculty advisor

By the end of a student’s first summer quarter, an advisor must be determined.  T he advisor provides guidance in designing a course of study appropriate for the student’s research interests, and in formulating a dissertation topic.

A full Supervisory Committee should be formed four months prior to the student’s General Exam. The full Supervisory Committee should have a minimum of three regular members plus the Graduate School Representative , and will consist of at least two faculty members from Applied Mathematics, one of whom is to be the Chair of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chair. The dissertation advisor may be from another department,  or may have an  affiliate  (assistant, associate, full) professor appointment with the Applied Mathematics department  and is then also a member of the Supervisory Committee.

The Dissertation Reading Committee , formed after the General Exam,  is a subset of  at least   three members from the Supervisory Committee   who are appointed to read and approve the dissertation.  Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty. At least one of the committee members must be a member of the core  Applied Mathematics faculty. It is required that this member is present for both the general and final examination, and is included on the reading committee.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of the Supervisory Committee. It is suggested that the student meet with the Supervisory Committee at least once a year to discuss their progress until the doctoral thesis is completed.

Examination requirements for the Ph.D. program

Students in the Ph.D. program must pass the following exams:

• The  qualifying exam
• The  general exam
• The  final exam  (defense)

Satisfactory performance and progress

At all times, students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.4/4.0 or better. Satisfactory progress on the examination requirements consists of passing the different exams in a timely manner. Departmental funding is contingent on satisfactory progress.   The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress .   The Department of Applied Mathematics follows these recommended guidelines of the Graduate School including an initial warning, followed by a maximum of three quarters of probation and one quarter of final probation, then ultimately being dropped from the program.    We encourage all students to explore and utilize the many available  resources  across campus.

Expected academic workload

A first-year, full-time student is expected to register for a full course load, at least three numerically graded courses, typically totaling 12-18 credits. All other students are expected to consult with their advisor and register for at least 10-18 credits per quarter.  Students who do not intend to register for a quarter must seek approved  academic leave  in order to maintain a student status.   Students who do not maintain active student status through course registration or an approved leave request need to request reinstatement to rejoin the program. Reinstatement is at the discretion of the department. Students approved for reinstatement are required to follow degree requirements active at time of reinstatement. 

Annual Progress Report

Students are required to submit an Annual Progress Report to the Graduate Program Coordinator by the second week of Spring Quarter each year. The annual progress report should contain the professional information related to the student’s progress since the previous annual report. It should contain information on courses taken, presentations given, publications, thesis progress, etc., and should be discussed with the student's advisor prior to submission. Students should regard the Annual Progress Report as an opportunity to self-evaluate their progress towards completing the PhD. The content of the Annual Progress Report is used to ensure the student is making satisfactory progress towards the PhD degree.

Financial assistance

Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student’s thesis supervisor, to the Graduate Program Coordinator.

Master of Science program

Students in the Ph.D. program obtain an M.Sc. Degree while working towards their Ph.D. degree by satisfying the  requirements for the M.Sc. degree.  

Additional Ph.D. Degree Options and Certificates

Students in the Applied Mathematics Ph.D. program are eligible to pursue additional degree options or certificates, such as the  Advanced Data Science Option  or the  Computational Molecular Biology Certificate .  Students must be admitted and matriculated to the PhD program prior to applying for these options. Option or certificate requirements are in addition to the Applied Mathematics degree requirements. Successful completion of the requirements for the option or the certificate leads to official recognition of this fact on the UW transcript.

Career resources, as well as a look at student pathways after graduation, may be found   here.

FAQs |  Contact the Graduate Program  |  Apply Now

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The range of possibilities for graduate study encompasses the areas of specialization of all of the faculty members in the field, who current number more than one hundred. The faculty members are drawn from fourteen departments in the College of Engineering, the College of Arts and Sciences, the College of Agriculture and Life Sciences and the Samuel Curtis Johnson Graduate School of Management. There is opportunity for further diversification on the choice of minor subjects.

Graduate students are admitted to the Field of Applied Mathematics from a variety of educational backgrounds that have a strong mathematics component. Generally, only students who wish to become candidates for the Doctor of Philosophy Degree are considered. About forty students are enrolled in the program, which usually requires four to five years to complete.  

A normal course load for a beginning graduate student is three courses per term. Please see field requirements for details on courses. The Director of Graduate Studies in conjunction with the student's temporary committee chair will assist first-year students in determining the appropriate courses to meet individual needs. The program allows great flexibility in the selection of courses. Most students design their own course sequences, subject to requirements, to meet their own interests. Courses are typically chosen from the math department and many applications departments. The course requirements in detail can be found under Requirements .  

Minor Subjects and Special Committee

Incoming students are assigned a temporary committee chair. Students are expected to select a permanent full committee by the end of the third semester. Students submit a "Special Committee Change and Selection Form" to the Graduate School to indicate their selection. Students may change committee members at any time by submitting a new form to the Graduate School. However, if they are post A-exam or three months within Ph.D. exam (B-exam), they must petition.

The Special Committee consists of a Chair/thesis advisor and at least one member for each of two minor subjects. One of the minor subjects must be mathematics. The other minor field can be from any area chosen by the student that is relevant to their doctoral research.  

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. The admission to candidacy examination is given to determine if the student is "ready to begin work on a thesis." The content and methods of examination are agreed on by the student and his/her committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the standard first-year graduate courses.  

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the Special Committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes four to five years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.  

Thesis/B Exam

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the Special Committee. When the thesis is completed, the student presents his/her results at the thesis defense or B exam.  

Graduate Handbook

For further details on the program, see the  Graduate Handbook .

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2024 Best Applied Mathematics Doctor's Degree Schools

For its 2024 ranking, College Factual looked at 44 schools in the United States to determine which ones were the best for applied mathematics students pursuing a doctor's degree. When you put them all together, these colleges and universities awarded 315 doctor's degrees in applied mathematics during the 2020-2021 academic year.

What's on this page: * Our Methodology

• Best Doctor’s Degree Schools List

Choosing a Great Applied Mathematics School for Your Doctor's Degree

A Great Overall School

A school that excels in educating for a particular major and degree level must be a great school overall as well. To take this into account we consider a school's overall Best Colleges for a Doctor's Degree ranking which itself looks at a collection of different factors like degree completion, educational resources, student body caliber and post-graduation earnings for the school as a whole.

Early-Career Earnings

One measure we use to determine the quality of a school is to look at the average salary of doctorate graduates during the early years of their career. This is because one of the main reasons people pursue their doctor's degree is to enable themselves to find better-paying positions.

Other Factors We Consider

The metrics below are just some of the other metrics that we use to determine our rankings.

• Major Focus - How many resources a school devotes to applied mathematics students as compared to other majors.
• Major Demand - How many other applied mathematics students want to attend this school to pursue a doctor's degree.
• Educational Resources - How many resources are allocated to students. These resources may include educational expenditures per student, number of students per instructor, and graduation rate among other things.
• Student Debt - How easy is it for applied mathematics to pay back their student loans after receiving their doctor's degree.
• Accreditation - Whether a school is regionally accredited and/or accredited by a recognized applied mathematics related body.

Our full ranking methodology documents in more detail how we consider these factors to identify the best colleges for applied mathematics students working on their doctor's degree.

One Size Does Not Fit All

When choosing the right school for you, it's important to arm yourself with all the facts you can. To that end, we've created a number of major-specific rankings , including this Best Applied Mathematics Doctor's Degree Schools list to help you make the college decision.

Featured Applied Mathematics Programs

Learn about start dates, transferring credits, availability of financial aid, and more by contacting the universities below.

BA in Mathematics

If you have a knack for mathematics and an interest in learning more, study online to achieve your career goals at Southern New Hampshire University. Our mathematics degree can help you enhance your mathematical abilities, including reasoning and problem-solving in three areas: analysis, algebra and statistics.

BA in Mathematics - Applied Mathematics

Put mathematical concepts to work to solve today's most complex real-world problems by studying applied mathematics with this specialized online bachelor's from Southern New Hampshire University.

Best Schools for Doctorate Students to Study Applied Mathematics in the United States

Explore the top ranked colleges and universities for applied mathematics students seeking a a doctor's degree.

10 Top Schools for a Doctorate in Applied Math

It's hard to beat Brown University if you want to pursue a doctor's degree in applied mathematics. Brown is a fairly large private not-for-profit university located in the city of Providence. More information about a doctorate in applied mathematics from Brown University

Harvard University is a wonderful decision for individuals interested in a doctor's degree in applied mathematics. Located in the midsize city of Cambridge, Harvard is a private not-for-profit university with a very large student population. More information about a doctorate in applied mathematics from Harvard University

Any student pursuing a degree in a doctor's degree in applied mathematics needs to look into Northwestern University. Located in the small city of Evanston, Northwestern is a private not-for-profit university with a very large student population. More information about a doctorate in applied mathematics from Northwestern University

University of Southern California is a good option for students interested in a doctor's degree in applied mathematics. Located in the city of Los Angeles, USC is a private not-for-profit university with a fairly large student population. More information about a doctorate in applied mathematics from University of Southern California

UChicago is a fairly large private not-for-profit university located in the city of Chicago. More information about a doctorate in applied mathematics from University of Chicago

Carnegie Mellon is a fairly large private not-for-profit university located in the large city of Pittsburgh. More information about a doctorate in applied mathematics from Carnegie Mellon University

Located in the city of Ithaca, Cornell is a private not-for-profit university with a very large student population. More information about a doctorate in applied mathematics from Cornell University

Located in the city of Baltimore, Johns Hopkins is a private not-for-profit university with a fairly large student population. More information about a doctorate in applied mathematics from Johns Hopkins University

UW Seattle is a fairly large public university located in the large city of Seattle. More information about a doctorate in applied mathematics from University of Washington - Seattle Campus

Located in the suburb of College Park, UMCP is a public university with a fairly large student population. More information about a doctorate in applied mathematics from University of Maryland - College Park

Related Programs

Learn about other programs related to Applied Mathematics that might interest you.

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Applied Mathematics by Region

View the Best Applied Mathematics Doctor's Degree Schools for a specific region near you.

Other Rankings

Best bachelor's degrees in applied mathematics, best overall in applied mathematics, highest paid grads in applied mathematics, best for veterans in applied mathematics, most popular in applied mathematics, most focused in applied mathematics, best master's degrees in applied mathematics, best value in applied mathematics, best for non-traditional students in applied mathematics, best online in applied mathematics, most popular online in applied mathematics.

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Rankings in Majors Related to Applied Math

One of 4 majors within the Mathematics & Statistics area of study, Applied Mathematics has other similar majors worth exploring.

Applied Math Focus Areas

Most popular related majors, notes and references.

• The bars on the spread charts above show the distribution of the schools on this list +/- one standard deviation from the mean.
• The Integrated Postsecondary Education Data System ( IPEDS ) from the National Center for Education Statistics (NCES), a branch of the U.S. Department of Education (DOE) serves as the core of the rest of our data about colleges.
• Some other college data, including much of the graduate earnings data, comes from the U.S. Department of Education’s ( College Scorecard ).
• Credit for the banner image above goes to Steven G. Johnson . More about our data sources and methodologies .

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Ph.D. in Applied Mathematics

See the catalog copy of the description of the Ph.D. in Applied Mathematics program.

1. Overview

A student in the Ph.D. in Applied Mathematics degree program must maintain satisfactory academic progress towards completion of the degree. Student satisfactory academic progress is primarily assessed by: (a) satisfactory coursework performance, (b) the Qualifying Examination, (c) the Dissertation Topic Approval Defense, and (d) the Dissertation Defense. Courses and the Qualifying Examination are used to ensure that the student has the breadth as well as the depth of knowledge needed for research success. The Dissertation Topic Approval Defense is used to ensure that the scope of dissertation research is important, that the plan is well thought out, and that the student has sufficient skills and thoughtfulness needed for success. The Dissertation Defense is used to assess the outcomes of the dissertation research, and whether or not the plan agreed upon by the Dissertation Committee has been appropriately followed.

The key requirements and milestones for the Ph.D. in Applied Mathematics degree are provided below. Failure to satisfy the requirements can result in suspension or dismissal from the program.

• Minimum Hours
• Interdisciplinary Minor
• Core Courses
• Additional “Core” Courses
• Qualifying Examination
• Dissertation Committee
• Dissertation Topic Approval Defense
• Dissertation Defense

2. Minimum Hours

To earn a Ph.D. in Applied Mathematics degree, a student must complete at least 56 approved post baccalaureate credit hours. This includes 2 hours of Responsible Conduct of Research (GRAD 8302), at least 18 hours of dissertation research and reading (MATH 8994), and the hours for the interdisciplinary minor. Graduation requirements mandate that students must achieve a minimum grade point average of 3.0 to graduate. Receiving more than two grades of C or a single grade of U in any graduate course will result in a suspension from the program.

A limited amount of transfer credit is allowed. In accordance with rules of the UNC Charlotte Graduate School, students are allowed to transfer up to 30 semester hours of graduate credit earned at UNC Charlotte or other recognized graduate programs. Only courses with grades A or B may be accepted for transfer credit. To receive transfer credit, students must file an online request (and submit all necessary documents including copies of transcripts and course syllabi if requesting to transfer non-UNC Charlotte courses).

File an online request to transfer post-Baccalaureate credits at http://gpetition.uncc.edu .

3. Interdisciplinary Minor

The interdisciplinary minor may be satisfied by 9 hours of graduate work outside the mathematics department, by 6 credit hours for a directed project in an area of application (MATH 8691/8692), or by a combination of external coursework and a directed project in an area of application totaling 9 credit hours.

It is expected that interdisciplinary minor courses shall in general be in STEM disciplines, but if there are applications in the student’s dissertation work towards the social sciences, courses in those fields are allowed too. The following is a non-exhaustive list of interdisciplinary minor courses allowed for several fields.

Physics: PHYS 5222, 5232, 5242, 5271, 6101 through 6201, 6203 through 6211, 6221 through 6271. A common example is PHYS 6210, but 5242 and 5271 would also be along the same lines.

Optics: OPTI 8101, 8102, 8104, 8105, 8211 with 8102, 8104, and 8211 being particularly relevant.

Molecular Biophysics: PHYS 6108/OPTI 8000, PHYS 6204, PHYS 6610 ( https://mbp.charlotte.edu/ )

Mechanical Engineering: MEGR 6116, 7113, 7164 for students who have specialized in math of fluids, while 6141, 6125, 7102, 7142, and 7143 for those specializing in continuum mechanics and elasticity.

Computer Science: ITCS 6111, 6114, 6150, 6153, 6155, 6165, 6170, 6171, 6220, 6226 with 6114 commonly taken.

Finance and Economics: Any of FINN or ECON courses listed under the MS Mathematical Finance program. Common examples include FINN 6203, 6210, 6211, and ECON 6206, 6113, 6219.

Mathematics Education: Any graduate level MAED courses such as MAED 6122, 6123, 6124.

4. Core Courses

All students in the Ph.D. in Applied Mathematics degree program must take the following courses, regardless of their intended area of study:

• GRAD 8302 Responsible Conduct of Research (2 hours, usually required to take within the first year in the program)
• MATH 8143 Real Analysis I (3 hours)
• MATH 8144 Real Analysis II (3 hours)
• MATH 8994 Doctoral Research and Reading (at least 18 hours)

Students whose intended area of study is statistics or mathematical finance are also required to take

• MATH 8120 Theory of Probability I (3 hours)

5. Additional “Core” Courses

The following courses, though not explicitly required, are strongly recommended for each area of study.

Statistics: STAT 5123, 5124, 5126, 5127, 6115, 8127, 8133, 8135, 8137, 8139, 8122, 8123, 8027 (at least once)

Computational Math: MATH 5165, 5171, 5172, 5173, 5174, 5176, 8172, 8176

PDE and Mathematical Physics: MATH 5173, 5174, 8172

Probability: MATH 5128, 5129, 8120, 8125

Dynamical Systems: MATH 5173, 5174, 7275, 7276, 7277

Topology: MATH 5181, 8171, 8172 and independent study

Algebra: MATH 5163, 5164, 8163, 8164, and 8065 and/or independent study

Mathematical Finance: MATH 6202, 6203, 6204, 6205, 6206

6. Qualifying Examination

After being admitted to the Ph.D. program, a student is expected to take the qualifying examination within three semesters. This time limit may be extended up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination consists of two parts: the first part is a written examination based on Real Analysis I and II (MATH 8143/8144) or Theory of Probability I and Real Analysis I (MATH 8120/8143), the latter intended for a student with intended area of study in statistics or mathematical finance . The second part is a written examination based on two other courses chosen by the student to be specifically related to the student’s intended area of study and approved by the Graduate Coordinator. Typical choices for Part II are STAT 5126/5127, MATH 5173/5174, MATH 5172/5176, MATH 5163/5164, MATH 6205/6206, etc. The student may be allowed to retake a portion of the qualifying examination a second time if the student does not pass that portion on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. A student who does not complete the qualifying examination as per the regulations of the Graduate School will be terminated from the Ph.D. program.

Complete and submit the following form after taking the Qualifying Examination. (Qualifying Exam Report Form) -> Graduate School form.

7. Dissertation Committee

After passing the Qualifying Examination, the student must set up a Dissertation Committee of at least four graduate faculty members, which must include at least three graduate faculty members from the Department of Mathematics and Statistics and one member appointed by the Graduate School. The committee is chaired by the student’s dissertation advisor. If the dissertation advisor is a graduate faculty member from an outside department or institution, a graduate faculty member from the Department of Mathematics and Statistics must be a co-chair of the committee. The Dissertation Committee must be approved by the Graduate Coordinator. After identifying and obtaining the signatures of the Dissertation Committee faculty, the Appointment of Doctoral Dissertation Committee Form must be sent to the Graduate School for the appointment of the Graduate Faculty Representative.

The Dissertation Committee should be appointed as soon as it is feasible, usually within a year after passing the Qualifying Examination.

Complete and submit the following form within a year of passing the Qualifying Examination. (Appointment of Doctoral Dissertation Committee Form) -> Graduate School form.

8. Dissertation Topic Approval Defense

Each student must present and orally defend a Ph.D. dissertation proposal after passing the Qualifying Examination and within ten semesters of entering the Program. The Dissertation Topic Approval Defense will be conducted by the student’s Dissertation Committee, and will be open to faculty and students. The dissertation proposal must address a significant, original and substantive piece of research. The proposal must include sufficient preliminary data and a timeline such that the Dissertation Committee can assess its feasibility.

The student should provide copies of the written dissertation proposal to the Dissertation Committee at least two weeks prior to the oral defense. At the discretion of the Dissertation Committee, the defense may include questions that cover the student’s program of study and background knowledge and techniques in the research area. The Dissertation Committee will unanimously grade the Dissertation Topic Approval Defense as pass/fail according to the corresponding rubrics. A student may retake the Dissertation Topic Approval Defense if he/she fails the first time. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program. It is expected that the student first take the proposal defense by the ninth semester after enrollment to provide time for a second try should the first one fail. A doctoral student advances to Ph.D. candidacy after the dissertation proposal has been successfully defended. Candidacy must be achieved at least six months before the degree is conferred (so if you plan to graduate in a spring semester with the commencement on May 14, then you would need to successfully defend your dissertation topic by November 13 the prior year.)

The student must follow the following procedure in order to defend the dissertation proposal.

• Communicate with the Dissertation Committee to set up a date/time for the oral defense, and reserve a defense room for at least two hours .
• Send an electronic or written copy of the dissertation proposal to each member of the Dissertation Committee at least two weeks prior to the oral defense.
• Inform the Graduate Coordinator the schedule at least one week prior to the oral defense.

Complete and submit the following form only after successfully passing the Dissertation Topic Approval Defense. (Petition for Topic Approval Form) -> Graduate School Form.

9. Dissertation

Each student must complete and defend a dissertation based on a research program approved by the student’s dissertation advisor which results in a high quality, original and substantial piece of research. The student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. The Dissertation will be unanimously graded as pass/fail based on the corresponding rubrics by the Dissertation Committee and must be approved by the Dean of the Graduate School. Two attempts of the Dissertation Defense are permitted. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program.

The student must follow the following procedure in order to defend the dissertation.

• Communicate with the Dissertation Committee to set up a date/time for the public defense, and reserve a defense room for at least two hours with the help of the Graduate Coordinator.
• Send an electronic or written copy of the dissertation to each member of the Dissertation Committee at least three weeks prior to the public defense.
• Send an electronic copy of the dissertation in PDF as well as an abstract in a separate word file to the Graduate Coordinator at least two weeks prior to the public defense. The abstract is limited to 200 words, and does not have to be the same as the abstract included in the dissertation.
• Prepare a presentation that should be at least 45 minutes long.

Complete and submit the following forms after defending your Dissertation. (Dissertation Report for Doctoral Candidates Form) -> Graduate School Form.

Also, submit the Dissertation Title Page with Original Committee Signatures.

In addition, submit ETD Signature Form with original committee and student signatures to the Graduate School within 24 hours after defense.

10. Graduation

Detailed information about graduation including the dissertation manual can be found on the Graduate School’s Graduation website . The Graduation process consists of the following steps and all three are required to complete the graduation process.

• Complete the online graduation application – directions below – deadlines in the academic calendar.
• Submit an approved candidacy application to the Graduate School – directions below – deadlines in the academic calendar.
• Register for the term of graduation – deadlines in the academic calendar.

How to Apply for Graduation: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Online Graduation Application. Read the directions. Click “Continue” if this is the first time you have applied for graduation or “Create a New Application” if you have applied previously. After you complete all sections, remember to click the “Submit” button.

How to Access the Electronic Candidacy Application: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Apply for Candidacy for Graduate Students. Carefully read and follow all directions for each section. The total number of credit hours selected must be at least the minimum required for your degree or certificate. After you complete all sections, click the “Print” button. Do not change the page layout or formatting in any way. Take the printed document to your department for the Graduate Coordinator’s approval signature and then submit it to the Graduate School. Electronically submitted forms are not accepted.

Pay attention to the various deadlines in the official UNC Charlotte academic calendar , in particular, the following deadlines if you are planning to graduate.

• Deadline for graduate students to file candidacy form
• Deadline for graduate students to apply for graduation
• Doctoral dissertation pre-defense formatting consultation deadline
• Doctoral dissertation defense deadline
• Doctoral dissertation post-defense formatting consultation deadline
• Last day to submit doctoral dissertations to Graduate School

In addition, complete and submit the following forms to the graduate school.

• Complete Survey of Earned Doctorates at https://sed.norc.org/doctorate . Print the Certificate of Completion and submit to the Graduate School within 24 hours after defense.
• Contact Information Form
• Copyright and Open Access Publishing Payment Form (optional)

Finally, a sample graduation checklist for doctotal graduates can be found here . Make sure

• All courses with In Progress grades have been assigned grades; check with your advisor to ensure this happens. This must be completed 10 days prior to the commencement.
• All courses in the current term have been assigned grades; check with your advisor or instructor to ensure this happens. This must be completed 10 days prior to the commencement.

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Exploring the history of data-driven arguments in public life

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Political debates today may not always be exceptionally rational, but they are often infused with numbers. If people are discussing the economy or health care or climate change, sooner or later they will invoke statistics.

It was not always thus. Our habit of using numbers to make political arguments has a history, and William Deringer is a leading historian of it. Indeed, in recent years Deringer, an associate professor in MIT’s Program in Science, Technology, and Society (STS), has carved out a distinctive niche through his scholarship showing how quantitative reasoning has become part of public life.

In his prize-winning 2018 book “ Calculated Values ” (Harvard University Press), Deringer identified a time in British public life from the 1680s to the 1720s as a key moment when the practice of making numerical arguments took hold — a trend deeply connected with the rise of parliamentary power and political parties. Crucially, freedom of the press also expanded, allowing greater scope for politicians and the public to have frank discussions about the world as it was, backed by empirical evidence.

Deringer’s second book project, in progress and under contract to Yale University Press, digs further into a concept from the first book — the idea of financial discounting. This is a calculation to estimate what money (or other things) in the future is worth today, to assign those future objects a “present value.” Some skilled mathematicians understood discounting in medieval times; its use expanded in the 1600s; today it is very common in finance and is the subject of debate in relation to climate change, as experts try to estimate ideal spending levels on climate matters.

“The book is about how this particular technique came to have the power to weigh in on profound social questions,” Deringer says. “It’s basically about compound interest, and it’s at the center of the most important global question we have to confront.”

Numbers alone do not make a debate rational or informative; they can be false, misleading, used to entrench interests, and so on. Indeed, a key theme in Deringer’s work is that when quantitative reasoning gains more ground, the question is why, and to whose benefit. In this sense his work aligns with the long-running and always-relevant approach of the Institute’s STS faculty, in thinking carefully about how technology and knowledge is applied to the world.

“The broader culture more has become attuned to STS, whether it’s conversations about AI or algorithmic fairness or climate change or energy, these are simultaneously technical and social issues,” Deringer says. “Teaching undergraduates, I’ve found the awareness of that at MIT has only increased.” For both his research and teaching, Deringer received tenure from MIT earlier this year.

Dig in, work outward

Deringer has been focused on these topics since he was an undergraduate at Harvard University.

“I found myself becoming really interested in the history of economics, the history of practical mathematics, data, statistics, and how it came to be that so much of our world is organized quantitatively,” he says.

Deringer wrote a college thesis about how England measured the land it was seizing from Ireland in the 1600s, and then, after graduating, went to work in the finance sector, which gave him a further chance to think about the application of quantification to modern life.

“That was not what I wanted to do forever, but for some of the conceptual questions I was interested in, the societal life of calculations, I found it to be a really interesting space,” Deringer says.

He returned to academia by pursuing his PhD in the history of science at Princeton University. There, in his first year of graduate school, in the archives, Deringer found 18th-century pamphlets about financial calculations concering the value of stock involved in the infamous episode of speculation known as the South Sea Bubble. That became part of his dissertation; skeptics of the South Sea Bubble were among the prominent early voices bringing data into public debates. It has also helped inform his second book.

First, though, Deringer earned his doctorate from Princeton in 2012, then spent three years as a Mellon Postdoctoral Research Fellow at Columbia University. He joined the MIT faculty in 2015. At the Institute, he finished turning his dissertation into the “Calculated Values” book — which won the 2019 Oscar Kenshur Prize for the best book from the Center for Eighteenth-Century Studies at Indiana University, and was co-winner of the 2021 Joseph J. Spengler Prize for best book from the History of Economics Society.

“My method as a scholar is to dig into the technical details, then work outward historically from them,” Deringer says.

A long historical chain

Even as Deringer was writing his first book, the idea for the second one was taking root in his mind. Those South Sea Bubble pamphets he had found while at Princeton incorporated discounting, which was intermittently present in “Calculated Values.” Deringer was intrigued by how adept 18th-century figures were at discounting.

“Something that I thought of as a very modern technique seemed to be really well-known by a lot of people in the 1720s,” he says.

At the same time, a conversation with an academic colleague in philosophy made it clear to Deringer how different conclusions about discounting had become debated in climate change policy. He soon resolved to write the “biography of a calculation” about financial discounting.

“I knew my next book had to be about this,” Deringer says. “I was very interested in the deep historical roots of discounting, and it has a lot of present urgency.”

Deringer says the book will incorporate material about the financing of English cathedrals, the heavy use of discounting in the mining industry during the Industrial Revolution, a revival of discounting in 1960s policy circles, and climate change, among other things. In each case, he is carefully looking at the interests and historical dynamics behind the use of discounting.

“For people who use discounting regularly, it’s like gravity: It’s very obvious that to be rational is to discount the future according to this formula,” Deringer says. “But if you look at history, what is thought of as rational is part of a very long historical chain of people applying this calculation in various ways, and over time that’s just how things are done. I’m really interested in pulling apart that idea that this is a sort of timeless rational calculation, as opposed to a product of this interesting history.”

Working in STS, Deringer notes, has helped encourage him to link together numerous historical time periods into one book about the numerous ways discounting has been used.

“I’m not sure that pursuing a book that stretches from the 17th century to the 21st century is something I would have done in other contexts,” Deringer says. He is also quick to credit his colleagues in STS and in other programs for helping create the scholarly environment in which he is thriving.

“I came in with a really amazing cohort of other scholars in SHASS,” Deringer notes, referring to the MIT School of Humanities, Arts, and Social Sciences. He cites others receiving tenure in the last year such as his STS colleague Robin Scheffler, historian Megan Black, and historian Caley Horan, with whom Deringer has taught graduate classes on the concept of risk in history. In all, Deringer says, the Institute has been an excellent place for him to pursue interdisciplinary work on technical thought in history.

“I work on very old things and very technical things,” Deringer says. “But I’ve found a wonderful welcoming at MIT from people in different fields who light up when they hear what I’m interested in.”

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