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

Prelim Exam Clusters

The written preliminary exams are listed by major subject area within clusters. Prelims must be selected from two different clusters. 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 (clusters 10 and 11): each course can be used in at most one prelim; Stat 511 and Stat 571 appear in two prelims.

Clusters and their associated courses:

  1. Algebra Cluster

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

  2. Analysis Cluster

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

  3. Algebraic Topology Cluster (Exam Syllabus)

    Math 547 (Algebraic Topology I)
    Math 548 (Algebraic Topology II)

  4. Logic and Universal Algebra Cluster

    • Logic:

      Math 502 (Metamathematics I) and at least one from:

      • Math 500 (Recursion Theory I)
      • Math 504 (Set Theory I)
      • Math 506 (Model Theory I)

    • Universal Algebra:

      • Math 509 (Universal Algebra I)
      • Math 510 (Universal Algebra II)

  5. Applications-Oriented Mathematics Cluster (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 Cluster (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 Cluster

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

  8. Algorithms and Complexity Cluster

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

  9. Computational Science Cluster

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

  10. General Topics Cluster - Probability and Statistics

    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)

  11. Special Topics Cluster (select at most one exam)

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

  12. Doctor of Arts Cluster

    Mathematics Education
    History of Mathematics