# Courses

## MATH-5030 (3) Intermediate Mathematical Physics 1

## MATH-5040 (3) Intermediate Mathematical Physics 2

Surveys classical mathematical physics, starting with complex variable theory and finite dimensional vector spaces. Discusses topics in ordinary and partial differential equations, the special functions, boundary value problems, potential theory, and Fourier analysis. Prereq., MATH 5030. Undergraduates must have approval of the instructor. Same as PHYS 5040.

## MATH-5120 (3) Introduction to Operations Research

Prereq., MATH 3130 or APPM 3310. Undergraduates must have approval of the instructor. Same as MATH 4120, APPM 5120.

## MATH-5150 (3) Linear Algebra

Highlights vector spaces, linear transformations, eigenvalues and eigenvectors, and canonical forms. Prereq., MATH 3130. Undergraduates must have approval of the instructor.

## MATH-5330 (3) Fourier Analysis

## MATH-5430 (3) Ordinary Differential Equations

## MATH-5440 (3) Mathematics of Coding and Cryptography

## MATH-5470 (3) Partial Differential Equations 1

## MATH-5520 (3) Introduction to Mathematical Statistics

## MATH-5540 (3) Introduction to Time Series

Prereqs., MATH 4510/APPM 3570 and MATH 4520/APPM 4520. Undergraduates must have approval of the instructor. Same as MATH 4540/APPM 5540.

## MATH-5600 (3) Numerical Analysis 1

## MATH-5610 (3) Numerical Analysis 2

Solution of linear systems, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Prereq., MATH 5600 or APPM 5600. Undergraduates must have approval of the instructor.

## MATH-5905 (1) Mathematics Teacher Training

## MATH-6000 (3) Model Theory

## MATH-6010 (3) Computability Theory

## MATH-6110 (3) Introduction to Number Theory

## MATH-6130 (3) Algebra 1

## MATH-6140 (3) Algebra 2

Studies modules, fields, and Galois theory. Prereq., MATH 6130. Undergraduates need instructor consent.

## MATH-6150 (3) Commutative Algebra

## MATH-6170 (3) Algebraic Geometry

Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms, and differentials and divisors. Additional topics might include Bezout's Theorem, the Riemann-Roch Theorem, elliptic curves, and sheaves and schemes. Prereq., MATH 6140. Undergraduates must have approval of the instructor.

## MATH-6180 (3) Algebraic Number Theory

Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition, and ramification groups. Prereqs., MATH 6110 and 6140. Undergraduates must have approval of the instructor.

## MATH-6190 (3) Analytic Number Theory

Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function, and the prime number theorem. Prereqs., MATH 6110 and 6350. Undergraduates must have approval of the instructor.

## MATH-6210 (3) Introduction to Topology 1

## MATH-6220 (3) Introduction to Topology 2

Introduces elements of general topology, algebraic topology, and differentiable manifolds. See also MATH 6210. Prereq., MATH 6210. Undergraduates must have approval of the instructor.