Deadlines

MATH 

Applications for the MATH Ph.D. program are only processed once a year for admission for the fall semester.

DECEMBER 10, 2024: Deadline for all applicants (Domestic & International) PASSED

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

STAT & STAT-BB

Applications for the STAT Ph.D. program are only processed once a year for admission for the fall semester. Applications for the STAT M.A. program are encouraged for the fall semester. A limited amount of M.A. applications may be considered for the spring semester. Please contact the department prior to applying.

SEPTEMBER 10, 2024: M.A. Applications for International students entering Spring 2025 PASSED

DECEMBER 10, 2024: M.A. Applications for Domestics students entering Spring 2025 PASSED

JANUARY 10, 2025: Applications for all students entering Fall 2025

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

About Us

If you are considering applying to our Mathematics graduate program, here are some links you may want to read. See general information for an introduction to our graduate programs. If you are interested in the interdisciplinary program in Applied Mathematics and Scientific Computation, please visit the AMSC website. If you are interested in the Statistics Program, visit the STAT website. The official graduate catalog descriptions of our three programs, including a list of faculty and admission requirements and deadlines, are given in sites for the three programs MATH, AMSC, and STAT. For more information, you may contact us at .

Financial Aid

Our PhD students receive some form of financial aid, through fellowships, Teaching Assistantships, and Research Assistantships. The University also posts available graduate assistant positions, but most of our student support is administered by the mathematics department. Competition for this support is strong and we are able to fund only the best applicants. Students applying only for a master's degree will not qualify for financial aid and will have lower priority for admission. For information about financial aid administered by the Mathematics Department, send e-mail to  with your questions or requests. Some financial aid administered through the department comes from Federal grants and is restricted to US citizens and permanent residents. 

How to Apply - University of Maryland's Graduate Application Process

The University of Maryland's Graduate School accepts applications through its TerpEngage Graduate Admission Application system. Before completing the application, applicants are asked to check the Admissions Requirements site for specific instructions and additional requirements (select your program of interest).

As required by the Graduate School, all application materials are to be submitted electronically:

• Graduate application
• Transcripts (Unofficial transcripts are accepted)
• Statement of purpose
• Letters of recommendation (3)
• Graduate Record Examination (GRE) (optional)
• Math GRE Subject Tests (optional, but strongly recommended)
• TOEFL/IELTS (International students only)
• Program/Department supporting documents (as applicable)
• Non-refundable application fee ($75) for each program to which an applicant applies*
• Please check the Admissions Requirements site for additional requirements

* Fee waivers may be available to international students who meet requirements. Waivers are limited. Please email . Domestic students are encouraged to use FreeApp Waiver Request. 

 
The electronic submission of application materials helps expedite the review of an application. Completed applications are reviewed by an admissions committee in each graduate degree program. The recommendations of the committees are submitted to the Dean of the Graduate School, who will make the final admission decision. Students seeking to complete graduate work at the University of Maryland for degree purposes must be formally admitted to the Graduate School by the Dean.

Information for International Graduate Students

The University of Maryland is dedicated to maintaining a vibrant international graduate student community. The office of International Students and Scholars Services (ISSS) is a valuable resource of information and assistance for prospective and current international students. International applicants are encouraged to explore the services they offer, and contact them with related questions.

The University of Maryland Graduate School offers admission to international students based on academic information; it is not a guarantee of attendance. Admitted international students will then receive instructions about obtaining the appropriate visa to study at the University of Maryland which will require submission of additional documents.

Please see the Graduate Admissions Process for International Applicants for more information.

TOEFL Information for International Graduate Students

It is required that all applicants from non- English speaking countries submit a TOEFL for admittance into the Graduate Math and Statistics program.  Because our graduate students are supported by Teaching Assistantships, it is required that their English skills are higher than the minimum required to attend courses. This is a requirement for our Graduate Math Program, separate from the Graduate School Requirements. Unfortunately, there are no exceptions to this Graduate Math Program requirement.  

*A list of English-Speaking Countries that are exempt from the TOEFL/IELTS/PTE can be found visiting this link: https://gradschool.umd.edu/admissions/english-language-proficiency-requirements

Please note the following SPEAKING scores. 

Students will be exempt from speaking English support classes in one of two ways

• A speaking sub-score of 24 (iBT TOEFL), 7.5 (IELTS), or 76 (PTE) on their admission English proficiency exam. 

• Exempt from submitting English proficiency exams for admission, based on Graduate School guidelines.

Speaking scores below 24 on TOEFL or below 7.5 on IELTS will require Teaching Assistants to enroll in an English Language course their first semester. 

Please note the following WRITING scores:

Students will be exempt from writing English support classes if they score 24 or above on TOEFL or 7 or above on IELTS. 

Writing scores below 24 on TOEFL or below 7 on IELTS will require all students (whether they are a TA or not) to enroll in an English Writing course (UMEI 007)  that will not be covered by the department. As of 2023, the cost of this course is $3,083. More info on costs: https://marylandenglishinstitute.com/english-programs/umd-students/

Please note the following READING/LISTENING scores:

You will not be admitted to the program unless you have the reading score of 26 (TOEFL) or 7 (IELTS).

You will not be admitted to the program unless you have the listening score of 24 (TOEFL) or 7(IELTS).

Contact

Applicants are encouraged to contact for any technical issues. For questions related to the admissions process, prospective students may contact the Graduate School.

GENERAL STATEMENT

There are three graduate programs closely affiliated with the Department of Mathematics, namely Mathematics MATH, Applied Mathematics & Statistics and Scientific Computation AMSC, and Mathematical Statistics STAT. The Office of Graduate Studies provides administrative support for all three programs and the Associate Chair for Graduate Studies makes all decisions concerning the awarding and renewal of teaching assistantships. The Graduate Committee of the Department of Mathematics sets broad policies to achieve the basic goals of assuring an effective program providing students the maximum opportunity to earn advanced degrees and maintaining the standards of the degrees. The Committee also serves as an advisory body on admissions, curricula, and eligibility for graduate degrees.

Admission and degree requirements for the AMSC and STAT programs are set by independent committees and differ in some details from those for the MATH program. During the first year, a graduate student has the privilege of changing between MATH, AMSC, and STAT. After the first year an application must be submitted to the Graduate School.

Some general regulations of the Graduate School are listed on this webpage, as well as specific policies of the Department.

For more information, consult the following resources:

• Graduate School Policies
• Graduate Student Life Handbook
• Graduate Assistant Handbook
• Schedule of Classes

EXPECTATIONS FOR DOCTORAL STUDENTS

Most full-time doctoral students (entering with a bachelor's degree) are expected to graduate in six years or less, according to the following timetable. However, students are urged to aim to graduate in less than 6 years; financial support is not guaranteed in the sixth year.

• Become involved in research activity within the first two years.
• Identify field of specialty and advisor and advance to candidacy within three and one-half years.
• Identify a dissertation topic during the fourth year.
• Submit at least one paper for publication before graduation.
• Complete all requirements and graduate within six years.

For a detailed timetable regarding qualifying examinations, and candidacy, see Progress to Degree

Graduate students in CMNS doctoral programs normally may expect:

• A wide selection of courses.
• Advice and mentoring by faculty in their program prior to the selection of an adviser.

From their adviser (or, in some instances the program):

• Regular access and advice during the research and thesis writing process.
• Training in the preparation of oral and written scholarly presentations; in particular, advice and support for the writing of at least one paper for publication.
• Introductions, for example at conferences, to other members of the field.
• Assistance and advice with job searches.

Department of Mathematics (AMSC/MATH/STAT) Statement of Expectations for Graduate Student Mentoring can be found here.

General Information

The purpose of the written qualifying exams, as endorsed by the Policy Committee in Spring 1990, is to indicate that the student has the basic knowledge and mathematical ability to begin advanced study.

The Department Written Examination for the Ph.D and M.A. is administered in January and August of each year during the month preceding the first week of classes and is given in the following fields:

• algebra
• analysis
• probability
• statistics
• applied statistics:
  • (PhD level)
  • (MA level)
  and
• geometry/topology.

NOTE: MATH students do not take the Applied Stat exam, which is for STAT students. See the requirements for the PhD and MA.

M.A. students take the Ph.D. examination and are required to receive an "M.A. pass".

Each examination will last four hours and no two will be scheduled on consecutive days.

Each MATH student will be required to take two examinations.

Each STAT student must take probability, statistics, and one other part. Students taking the M.A. or Ph.D. in applied statistics may take the following three exams: applied statistics, mathematical statistics, and probability.

Each AMSC student takes  examinations, chosen in consultation with the study advisory committee but only one or two are chosen from the list above; the others are in areas of application.

The syllabi below are current and reflect the latest thinking of the respective field committees.

ALGEBRA

MATH 600

GROUPS

Review of elementary group theory including Lagrange's theorem: symmetric groups and Cayley's theorem: normal subgroups, quotient groups and the homomorphism and isomorphism theorems; abelian and cyclic groups (one week).

Groups with operators, normal series, Jordan-Hölder theorem, solvable groups; unsolvability of S_n for n > 4.

Group actions; class formula; Sylow's theorems; solvability of p-groups.

Language of categories: objects, maps and functors; Hom; universal mapping properties used to define quotients, products, coproducts (direct sums) and free objects in categories of groups and abelian groups. Constructive existence proofs of the above objects, especially generators and relations in category of groups. Internal direct sums in abelian groups; primary decomposition of abelian torsion groups.

RINGS

Definitions and examples; left, right and two-sided ideals; quotients, homomorphism and isomorphism theorems; products; examples should include matrix rings, group rings, and real quaternions. Simple rings: proof that a matrix ring over a division ring is simple. Definition and a few words about Artinian and Noetherian rings. Statement (no proof) of Wedderburn's theorem for simple Artinian rings. Hilbert Basis theorem.

Integral domains and fields; prime and maximal ideals-Zorn's lemma; operations on ideals; Chinese remainder theorems.

Localization: multiplicative sets; rings of quotients and quotient fields; local rings.

Factorization: P.I.D.'s UFD's; Euclidean rings; polynomial rings; Gauss's lemma. Proof that polynomial rings over UFD's are UFD's.

MODULES

Definitions and example; exact sequences; exactness properties of HOM; quotients, products, direct sums (internal and external), examples of modules over matrix rings and group rings.

Free modules; invariance of rank over a commutative ring; non-invariance in general.

Finitely generated modules over P.I.D.; applications to canonical forms of matrices and to abelian groups.

MATH 601

MODULES

Tensor product; localization; algebras and base change; exactness properties of tensor products.

Exterior algebra.

Projective and injective modules. Homology including the snake lemma. Statements (not proofs) of facts on derived functors including Tor and Ext.

FIELD THEORY

Extensions, algebraic and transcendental; characteristic; finite fields; algebraic closure; transcendence basis.

Galois theory: The Galois correspondence; Galois groups of polynomials as permutation groups; cyclic extensions; roots of unity; ruler and compass constructions; solvability by radicals; norms and traces; computations of Galois groups.

Introduction to representations of finite groups over the complex numbers (as in Serre Part 1 Chapters 1,2,3, and the part of 5 dealing with finite groups).

MATH 405

The contents of Linear Algebra by K. Hoffman and R. Kunze, probably the most comprehensive and readable book on the subject.

References

As references for MATH 600-601, we recommend the following general treatises on algebra:

• Algebra by S. Lang
• Algebra by van der Waerden (2 volumes)
• Algebra by J.K. Goldhaber and G. Ehrlich
• Commutative Algebra by M. Atiyah and I.G. MacDonald
• Basic Algebra by N. Jacobson (2 volumes)
• Topics in Algebra by I. Herstein
• Algebra by T. Hungerford
• Linear Representations of Finite Groups by J-P. Serre

ANALYSIS

The written examination in Analysis consists of six questions roughly based on the material of MATH 630 and MATH 660 (three questions from each course).

Students are responsible for all the material on the exam syllabus, even if it was not covered in a particular semester's course. Much of the material on the exam syllabus is often covered in undergraduate analysis courses.

Syllabus for both the MA and PhD Written Exams in Analysis:

Review from Advanced Calculus

1. Real and complex numbers. Continuity, sequences and series, compactness on the real line. Vector spaces (over R and C), linear maps.  ([F])

Real Analysis

1. Lebesgue measure and integration on the real line, differentiation and monotone functions, absolute continuity, functions of bounded variation, the Fundamental Theorem of Calculus. ([BeCz], Ch. 2, 3, 4; [FiRo], Ch. 2, 3 ,4, 6)
2. L^p spaces on the real line, including the Hölder and Minkowksi inequalities, the Riesz-Fischer Theorem, bounded linear functionals on L^p(R). ([BeCz] Ch. 3, 5; [FiRo] Ch. 7)
3. Convergence theorems: Fatou's Lemma, monotone convergence theorem, dominated convergence theorem, Egoroff's theorem, Vitali's convergence theorem, convergence in measure, convergence in L^p. ([BeCz] Ch. 3; [FiRo], Ch. 3, 4, 5, 7)

References

[BeCz] J. Benedetto and W. Czaja, "Integration and Modern Analysis," Birkhauser, Boston, MA, 2009.

[F] P. M. Fitzpatrick, "Advanced Calculus," 2nd edition, American Math. Soc., 2009.

[FiRo] P. M. Fitzpatrick and H. Royden, "Real Analysis," 4th edition, Pearson, 2010.

General references

W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, 1991

R. Wheeden and A. Zygmund, Measure and Integral: An introduction to Real Analysis, Marcel Dekker, 1977

Complex Analysis

Syllabus for Complex ExamSyllabus for Complex Exam with suggestions for study in a pdf file.

PROBABILITY

Master's Level Requirements (STAT 410, 650)

Foundations: Probability spaces, axioms, conditional probability and independence, Bayes' Theorem.

Discrete random variables: combinatorial probability, discrete densities, Bernoulli trials, expectations and moments, Poisson Limit Theorem.

General Random Variables and Vectors: definitions, distribution functions, densities, moments, change-of-variable formulas, joint distributions, conditional distributions, mixed distributions, moment generating functions, and characteristic functions.

Limit Theorems of Probability: convolutions, concepts of convergence, laws of large numbers, Central Limit theorem.

Discrete-time discrete-state Markov chains: definitions, transition probabilities, classification of states, periodicity, ergodicity, limiting and stationary behavior, absorption probabilities, recurrence.

Continuous-time Markov chains: definitions, birth-and death processes, Kolmogorov forward and backward equations, compound Poisson process.

Branching processes; extinction probabilities.

References

• Hoel, Port, Stone; Introduction to Probability Theory, Houghton-Mifflin (1971). All chapters.
• Karlin & Taylor: A First Course in Stochastic Processes, Academic Press (1975) (2nd edition) ch. 1-5, 8-9.
• Ross: A First Course in Probability, (3rd edition) Macmillan (1988). All chapters, except chapter 10.

Doctoral Level Requirements (STAT 600, 601) Revised June, 2010

PhD exam requirements:

1. Probability space, distribution functions and densities for random variables and vectors; particular distribution functions, Poisson limit theorem, de Moivre-Laplace theorem.
2. Measure-theoretic definition of expectation, Borel sigma-algebra, measure induced by a random variable, classification of measures on the real line, different types of convergence of random variables and their properties, Radon-Nikodym theorem (without proof), L^p spaces.
3. Conditional probabilities, independence of events, sigma-algebras and random variables, Bayes' theorem, pi-systems and Dynkin systems.
4. Markov chains with discrete phase space, law of large numbers, ergodic Markov chains, recurrence and transience, random walks, gambler's ruin problem.
5. Poisson Process, definition of a Markov chain on a general phase space.
6. Borel-Cantelli lemmas, Kolmogorov inequality, three series theorem, laws of large numbers; equivalent sequences and truncation.
7. Weak convergence of measures, Prokhorov theorem (in Euclidean space), Characteristic functions, Gaussian random variables, CLT with the Lindeberg condition.
8. Definition of a random process, Kolmogorov consistency theorem. Conditional expectations and martingales (proofs in the discrete time only), Doob's inequality, Optional stopping theorem, Convergence of Martingales. Definition and basic properties of Brownian motion.

References

• P. Billingsley: Probability and Measure (second edition) J. Wiley (1986). Chapters 1-6 (except starred sections).
• K.L. Chung: A Course in Probability Theory, Academic Press (1974) (2nd Edition). All chapters.
• S. Karlin, H. M. Taylor: A First Course in Stochastic Processes, Academic Press, 1975 (2nd Edition). All chapters.
• L. Koralov, Y. Sinai: Theory of Probability and Random Processes, Springer, 2007.

MATHEMATICAL STATISTICS

STAT 700-701 (Revised Nov. 2023)

Sampling Distributions: standard distributions, functions of samples of normal variables, order statistics, conjugate families of priors.

Parameters and statistics: identifiability of parameters, sufficiency, completeness, minimality, Basu’s Theorem, Exponential family definitions and properties 

Point Estimation: unbiasedness and consistency, methods of estimation including method of moments, maximum likelihood, Estimating Equations, UMVU estimators, Rao-Blackwell and Lehmann-Scheffe Theorems, efficiency, Fisher Information, Cramer-Rao lower bound

Algorithms for Estimation, including Newton-Raphson and EM Algorithm

Testing and Interval Estimation: Neyman-Pearson lemma, monotone likelihood ratio, UMP tests, likelihood ratio test, including multivariate normal, chi square tests, duality between testing and interval estimation.

Asymptotics: modes of convergence, Slutsky's theorem, multivariate central limit theorem, delta method, consistency and asymptotic behavior of estimators, including maximum likelihood and estimating-equation estimators. Asymptotic properties of likelihood-ratio and Rao-score tests.

Linear Models and Least Squares: general model, multivariate normal distribution, Gauss-Markov theorem, multiple regression, projection and prediction

Count Data: multinomial goodness of fit and chi-square tests.

Decision Theory: basic concepts, loss, risk, priors, admissibility and complete classes, Minimax principle, Bayes estimators and tests.

Non-Parametrics: quantiles, ranks, empirical distribution function

References:

• P.J. Bickel and K.A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I, 2nd ed. Chapman & Hall/CRC, April 2015.
• Casella, G. and Berger, R., Statistical Inference, 2nd ed. Duxbury, 2002.
• Jun Shao, Mathematical Statistics, 2nd ed. Springer, 2003.

V. Rohatgi, and A.K. Saleh, An Introduction to Probability and Statistics, 2nd ed., Wiley 2001..

APPLIED STATISTICS

(PhD Level)

STAT 440 Sampling Theory

STAT 740-741 (Linear Models I,II).

1. Sampling Theory. Simple random sampling. Sampling for proportions. Estimation of sample size. Sampling with varying probabilities. Sampling: stratified, systematic, cluster, double, sequential, incomplete. Ratio and regression estimates. Neyman allocation.

2. General Linear Models. Matrix formulation multivariate normal distribution, geometric formulation, least squares, estimable functions. Confidence sets, tests of linear hypotheses under normality, connection with likelihood-based methods. Analysis of residuals, graphical diagnostics, assessment of model fit. Special regression models: polynomial regression and dummy variables. Generalized linear models (GLM).

3. Fixed Effect Analysis of Variance. Comparison of means and one way analysis of variance (ANOVA), full rank and reduced rank models, estimable functions and contrasts, multiple comparisons. Two way ANOVA, interaction, analysis of unbalanced layouts. Nested and crossed factors, incomplete designs.

4. Random Effects and mixed models. Definitions, ANOVA estimates in balanced models, distribution theory. Unbalanced random effect designs, maximum likelihood (ML) and restricted maximum likelihood (REML) estimates. Goodness of fit.

References:

• Cochran, W.G. Sampling Techniques, (1977, 3rd ed.) New York: J. Wiley.
• Cody, R.P. and Smith, J.K. Applied Statistics and the SAS Programming Language, (1997) Upper Saddle River, NJ: Prentice-Hall.
• Draper, N.R. and Smith, H. Applied Regression Analysis. (1998, 3rd ed.) New York: J. Wiley.
• Hocking, R. Methods and Applications of Linear Models. (1996) New York: J. Wiley.
• Lohr, S.L. Sampling: Design and Analysis. (1999) Pacific Grove, CA: Duxbury.
• McCullagh, P. and Nelder, J.A. Generalized Linear Models . (1989, 2nd ed.) New York: Chapman and Hall.
• Milliken, G. and Johnson, D. Analysis of Messy Data, Vol. I: Designed Experiments (1984) New York: Van Nostrand Reinhold.
• Rao, C.R. Linear Statistical Inference and Its Applications (1973, 2nd ed.) New York: J. Wiley.
• Rao, P.S.R.S. Variance Components Estimation (1997) New York: Chapman and Hall.
• Rencher, A.C. Linear Models in Statistics (1999) New York: J. Wiley.
• Sarndal, C.E., Swensson, B., and Wretman, J. Model Assisted Survey Sampling (1992) New York: Springer-Verlag.
• Scheffe, H. The Analysis of Variance (1958) New York: J. Wiley.
• Searle, S.R., Casella, G., and McCulloch, C.E. Variance Components (1992) New York: J. Wiley.
• Stapleton, J.H. Linear Statistical Models (1995) New York: J. Wiley.

APPLIED STATISTICS (MA Level)

STAT 440, 450, 740

1. Sampling Theory. Simple random sampling, stratification, ratio and regression estimates, systematic sampling, cluster sampling, Horvitz-Thompson estimator, two stage sampling, double sampling.
2. Linear Statistical Models. Method of least squares, estimability, Gauss-Markov theorem, hypothesis testing and confidence ellipsoids under normality.
3. Regression and Correlation. Simple and multiple regression models,distribution of correlation coefficient, inference on coefficients (t and F tests), multiple and partial correlation, weighted least squares, effects of model misspecification, analysis of residuals, multicollinearity, alternatives to least squares.
4. Analysis of Variance. One way classification, multiple comparison, balanced two-way classification, fixed vs. Random effects, ANOVA in regression context, incomplete designs, factorial designs, analysis of covariance, effect of non-normality, heteroscedasticity and dependence of errors.

References

• Cochran, W.G. Sampling Techniques, (1977, 3rd.) J. Wiley (Chapters 1-5, 6-9, 9A.1-9A.3, 9A.7, 10.1-10.4, 12.1-12.9).
• Draper, N. and Smith, H. Applied Regression Analysis. (1981, 2nd ed.)J. Wiley (Chapters 1-6, 9).
• Scheffe, H. The Analysis of Variance (1959) J. Wiley (Chapters 1,2.1-2.9, 3, 4.1-4.3, 5-8, 10).
• Rao, C.R. Linear Statistical Inference and Its Applications (1973, 2nd ed.) J. Wiley Chapter 4)

GEOMETRY/TOPOLOGY

Students prepare for the geometry/topology exam by taking the first year topology sequence MATH 730, MATH 740.

MATH 730

1. Review of basics of relevant general topology: topological spaces, compactness, connectedness, the Hausdorff axiom, metrizability and second countability, compactly generated spaces (1 week)
2. Quotient spaces, attaching cells (1 week) (Hatcher, Ch. 0)
3. Homotopy extension theorem, CW complexes (rest of Hatcher, Ch. 0)
4. Fundamental group (Hatcher, Section 1.1)
5. Van Kampen's Theorem (Hatcher, Section 1.2)
6. Path lifting, Covering spaces (Hatcher, Section 1.3)
7. Classification of (topological) surfaces, with calculation of their fundamental groups
8. Basics of homology theory (Hatcher, Ch. 2)

REFERENCES for MATH 730:

• Hatcher, "Algebraic Topology" (primary reference)
• Kinsey, "Topology of Surfaces"
• Singer and Thorpe, "Lecture notes on Elementary Topology and Geometry"
• Bredon, "Topology and Geometry"
• Spanier, "Algebraic Topology"

MATH 740

1. Differentiable manifolds: transversality, inverse and implicit function theorems, immersions and submersions, submanifolds.
2. Fiber bundles, basics of Lie groups, vector bundles, tangent and cotangent bundles.
3. Differential forms, Lie derivative, integration on manifolds and Stokes' theorem.
4. Riemannian metrics, connections, curvature, covariant differentiation.
5. Minimizing properties of geodesics, Hopf-Rinow theorem, Jacobi equations.

REFERENCES for MATH 740:

• M. DoCarmo, "Riemannian Geometry"
• F. Warner, "Foundations of Differentiable Manifolds and Lie Groups"
• J. Lee, "Introduction to Smooth Manifolds"
• B. O'Neill, "Semi-Riemannian Geometry"
• P. Petersen, "Riemannian Geometry"
• J. Milnor, "Topology from the Differentiable Viewpoint"

Last updated 07/05/17

Upcoming Exam Dates

August 2025 Qualifying Exams Schedule. All exams will be located in Kirwan Hall 3206. Students entering the program in Fall 2025 can register for the August 2025 exams here.

Monday, August 18
Algebra 9:00am -1:00pm 
Mathematical Statistics 9:00am -1:00pm

Wednesday, August 20
Analysis 9:00am -1:00pm 
Applied Statistics 9:00am -1:00pm

Friday, August 22
Probability 9:00am -1:00pm 
Geometry 9:00am -1:00pm

Please note the following: 

• Students in the pure math program who entered the program prior to Fall 2025 are required to pass 2 exams by January of their third year (fifth semester in the program). 
• Students in the pure math program who enter the program Fall 2025 or after are required to pass 2 exams by January of their second year (third semester in the program).

Please contact or if you have any questions.

Requirements for the Ph.D. in Mathematics (Exams and Courses)

The requirements below are for students in pure mathematics, not in statistics. For students in Statistics: Qualifying Exams must be passed in Statistics, Probability, and Applied Statistics. 

1. MATH students must pass at least 2 exams from the following list: 

*Algebra (Math 600, 601)
*Analysis (Math 630, 660)
Probability (Stat 600, 601)
Statistics (Stat 700, 701)
Geometry (Math 730, 740)

*One of the 2 exams should be Algebra OR Analysis

2. Each student must pass an equivalent of 8 courses via coursework or qualifying exams

Each qualifying exam counts for two courses, the exam and its corresponding courses can be seen above. However, no more than 4 courses (including those counted via passing qualifying exams) can come from the same list: 

More information (including 2 examples) can be found here.

----

Important note: The qualifying requirements for the Scientific Computation concentration of the AMSC program are  different. In addition, students in the Applied Mathematics concentration of the AMSC program usually must take one or more exams outside of the mathematics department; see here for further information.

• The written exams and course options for MATH can be found  here for the MA degree.
• Syllabi for the written qualifying exams
• Archived written qualifying exams
• Suggestions on preparing for the qualifying exams