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MSCS > graduate studies > current students > PhD prelims > topics

Prelim Exams

The written prelims are based on a sequence of graduate courses identified below. At most one written prelim may be selected from the Probability and Statistics, Special Topics Group (written prelims 11-13) and the Doctor of Arts Group (written prelims 14-15, for DA students only). The sum of the scores on the two written prelims must not exceed 4; combined with the minor sequence, the sum cannot exceed 6. Students should consult the Graduate Handbook pdf for additional details.

Note for students planning to take two Probability and Statistics prelims: each course can be used in at most one prelim; Stat 511 and Stat 571 appear in two prelims.

Written Prelims and their associated courses:

  1. Algebra

    • Math 516 (Second Course in Abstract Algebra I)
    • Math 517 (Second Course in Abstract Algebra II)

  2. Analysis

    • Math 533 (Real Analysis I)
    • Math 535 (Complex Analysis I)

  3. Geometry and Topology

    • Math 547 (Algebraic Topology I)
    • Math 549 (Differentiable Manifolds I)

  4. Logic

    • Math 502 (Metamathematics I) and at least one of the following:
    • Math 503 (Metamathematics II)
    • Math 504 (Set Theory I)
    • Math 506 (Model Theory I)

  5. Applications-Oriented Mathematics (select two of the following four courses)

    • Math 576 (Boundary Value Problems)
    • Math 577 (Applied Partial Differential Equations)
    • Math 578 (Asymptotic Methods)
    • Math 579 (Singular Perturbations)

  6. Mathematical Science (take two of the following four courses)

    • Math 574 (Applied Optimal Control)
    • Math 580 (Introduction to the Mathematics of Fluid Dynamics)
    • Math 582 (Wave Propagation and Scattering I)
    • Math 586 (Computational Finance)

  7. Combinatorics

    • MCS 521 (Combinatorial Optimization)
    • MCS 531 (Error-Correcting Codes)
    • MCS 591 (Advanced Topics in Combinatorial Theory)

  8. Algorithms and Complexity

    • MCS 501 (Computer Algorithms II)
    • MCS 503 (Mathematical Methods of Algorithm Analysis)
    • MCS 541 (Computational Complexity)

  9. Computational Science

    • MCS 563 (Analytic Symbolic Computation)
    • MCS 571 (Numerical Methods for Partial Differential Equations)
    • MCS 572 (Introduction to Supercomputing)
    • MCS 575 (Computer Performance Evaluation)

  10. Probability and Statistics, General Topics

    • Stat 501 (Probability Theory I) plus one of the following:
    • Stat 502 (Probability Theory II)
    • Stat 511* (Advanced Statistical Theory I)
    • Stat 571* (Non-cooperative Games)

    Probability and Statistics, Special Topics Group (11-13, select at most one exam)

  11. Linear Inference, Sampling, and Design

    • Stat 521 (Linear Statistical Inference) plus one of the following:
    • Stat 522 (Multivariate Statistical Analysis)
    • Stat 531 (Sampling Theory I)
    • Stat 535 (Optimal Design Theory I)

  12. Game Theory (select two of the following courses)

    • Stat 571* (Non-cooperative Games)
    • Stat 572 (Cooperative Game Theory)
    • Stat 591 (Advanced Topics in Statistics, Probability, and Operations Research)

  13. Statistical Theory

    • Stat 511* (Advanced Statistical Theory I)
    • Stat 512 (Advanced Statistical Theory II)

    Doctor of Arts Group (for DA students only, select at most one from 14-15)

  14. Mathematics Education

  15. History of Mathematics