# 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 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)

#### Number Theory

- Math 514 (Number Theory I)
- MATH 515 (Number Theory II)

#### 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
requiredFOR 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