Prelim Exams

The written prelims are based on a sequence of graduate courses identified below. 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: All statistics PhD students are required to pass Probability and Statistics and select one of the remaining Statistics prelims (Linear Inference, Sampling, and Design or Game Theory).

Written Prelims and their associated courses:

Algebra

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

Analysis

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

Geometry and Topology

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

Logic

  • Math 502 (Metamathematics I) and at least one of the following
  • Math 504 (Set Theory I)
  • Math 506 (Model Theory I)
  • Math 511 (Descriptive Set Theory)

(starting fall 2014) Differential Equations

  • Math 576 (Classical Methods of Partial Differential Equations)
  • Math 585 (Ordinary Differential Equations)

(starting fall 2014) Methods in Applied Analysis

  • Math 539 (Functional Analysis I)
  • MCS 571 (Numerical Analysis of Partial Differential Equations)

Applied Mathematics (select two)

  • Math 580 (Mathematics of Fluid Dynamics)
  • Math 582 (Linear and Nonlinear Waves)
  • Math 586 (Computational Finance)

Combinatorics

  • MCS 521 (Combinatorial Optimization)
  • MCS 591 (Advanced Topics in Combinatorial Theory)

Algorithms and Complexity

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

Computational Science

  • MCS 563 (Analytic Symbolic Computation)
  • MCS 571 (Numerical Analysis for Partial Differential Equations)
  • MCS 572 (Introduction to Supercomputing)

Probability and Statistics

  • This prelim is required FOR all Statistics PhD students)
  • Stat 501 (Probability Theory I)
  • Stat 511 (Advanced Statistical Theory I)

Linear Inference, Sampling, and Design

  • Statistics PhD students must select one prelim from Linear Inference, Sampling, and Design or Game Theory
  • 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

  • Statistics PhD students must select one prelim from Linear Inference, Sampling, and Design or Game Theory
  • Stat 571 (Non-cooperative Games) plus one of the following:
  • Stat 572 (Cooperative Game Theory)
  • Stat 591 (Advanced Topics in Statistics, Probability, and Operations Research)

Mathematics Education

  • Only Doctor of Arts students may take this prelim

History of Mathematics

  • Only Doctor of Arts students may take this prelim
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