Graduate Course Descriptions
*We offer the following graduate level courses. Some courses are taught annually, while others are taught less frequently. For some courses, the content may vary as determined by the instructor.*

21-600 Mathematical Logic I

21-602 Introduction to Set Theory

21-603 Introduction to Model Theory

21-604 Introduction to Recursion Theory

21-605 Teaching Mathematics

21-606 Mathematics Course Design

21-610 Algebra I

21-611 Topics in Algebra

21-620 Real Analysis

21-621 Introduction to Lebesgue Integration

21-622 Finite-Dimensional Analysis

21-623 Complex Analysis I

21-624 Topics in Analysis

21-630 Ordinary Differential Equations

21-632 Introduction to Differential Equations

21-633 Mathematical Techniques in Engineering

21-640 Functional Analysis

21-651 General Topology

21-660 Introduction to Numerical Analysis I

21-661 Numerical Solution of Partial Differential Equations I

21-662 Numerical Solution of Partial Differential Equations II

**21-679** Foundations of Probability

**21-680** Topics in Probability

21-690 Fundamentals of Optimization

21-700 Mathematical Logic II

21-701 Discrete Mathematics

21-702 Set Theory II

21-703 Model Theory II

21-715 Commutative Algebra

21-720 Measure and Integration

21-721 Probability

21-723 Advanced Real Analysis

21-724 Sobolev Spaces

21-725 Intermediate Topics in Analysis

21-732 Partial Differential Equations I

**21-737** Probabilistic Combinatorics

**21-738** Extremal Combinatorics

21-741 Nonlinear Functional Analysis

21-742 Calculus of Variations

21-743 Control Theory

21-759 Differential Geometry

21-760 Numerical Analysis I

21-761 Finite Difference Methods

21-762 Finite Element Methods

21-765 Intro Parallel Computing and Scientific Computation

21-770 Introduction to Continuum Mechanics

21-772 Fluid Dynamics

21-800 Advanced Topics in Logic

21-801 Advanced Topics in Discrete Mathematics

21-803 Model Theory III

21-804 Seminar in Mathematical Logic

21-805 Lambda Calculus

21-810 Advanced Topics in Algebra

21-820 Advanced Topics in Analysis

21-830 Advanced Topics in Partial Differential Equations

21-832 Partial Differential Equations II

21-860 Advanced Topics in Numerical Analysis

21-870 Advanced Topics in Continuum Mechanics

21-880 Advanced Stochastic Calculus I

21-881 Advanced Stochastic Calculus II

21-882 Advanced Topics in Financial Mathematics

21-890 Advanced Topics in Operations Research

21-900 Reading and Research

21-901 Master Degree Research

21-902 Doctoral Thesis Research

### Selected Courses in the Tepper School of Business

**47-720 **Seminar in Finance I

**47-721** Seminar in Finance II

**47-724** Seminar in Finance IV

**47-800** Microeconomics

**47-830** Integer Programming (6 units)

**47-831** Graphs and Network Flows in Operations Research (12 units)

**47-832 **Linear Programming (6 units)

**47-838** Advanced Linear Programming (6 units)

**Selected Courses in the Department of Statistics**

**36-703** Intermediate Probability

**36-705** Intermediate Statistics

**36-707** Regression Analysis

**36-755** Advanced Statistical Theory I

**36-756** Advanced Statistical Theory II

See the Department of Statistics course descriptions for more information.

### Selected Courses in the School of Computer Science

**15-754** Complexity Theory

**15-758** Pure and Applied Logic

**15-850** Advanced Topics in Theory