- Three courses to be chosen from the following list:
- MAT 310 ABSTRACT ALGEBRA I
- MAT 311 ABSTRACT ALGEBRA II
- MAT 335 REAL ANALYSIS I
- MAT 336 REAL ANALYSIS II
- Three additional mathematics courses from the following list:
- MAT 301 HISTORY OF MATHEMATICS
- MAT 302 COMBINATORICS
- MAT 303 THEORY OF NUMBERS
- MAT 304 DIFFERENTIAL EQUATIONS
- MAT 311 ABSTRACT ALGEBRA II
- MAT 312 ABSTRACT ALGEBRA III
- MAT 320 GEOMETRY I
- MAT 321 GEOMETRY II
- MAT 336 REAL ANALYSIS II
- MAT 337 COMPLEX ANALYSIS
- MAT 340 TOPOLOGY
- MAT 348 APPLIED STATISTICAL METHODS
- MAT 351 PROBABILITY AND STATISTICS I
- MAT 352 PROBABILITY AND STATISTICS II
- MAT 353 PROBABILITY AND STATISTICS III
- MAT 370 ADVANCED LINEAR ALGEBRA
- MAT 372 LOGIC AND SET THEORY
- MAT 384 MATHEMATICAL MODELING
- MAT 385 NUMERICAL ANALYSIS I
- MAT 386 NUMERICAL ANALYSIS II

Open elective credit also is required to meet the minimum graduation requirement of 192 hours.

- For students interested in graduate study in mathematics:
- MAT 310 ABSTRACT ALGEBRA I
- MAT 311 ABSTRACT ALGEBRA II
- MAT 312 ABSTRACT ALGEBRA III
- MAT 335 REAL ANALYSIS I
- MAT 336 REAL ANALYSIS II
- MAT 337 COMPLEX ANALYSIS
- For students interested in graduate study in economics, finance, or statistics:

The first quarter of a 3-quarter sequence. Topics in the sequence include the integers; abstract groups, rings, and fields; polynomial rings; isomorphism theorems; extension fields; and an introduction to Galois theory. MAT 303 is highly recommended.

A continuation of topics from MAT 310: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.

Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.

Properties of continuous functions, uniform continuity, sequences of functions, differentiation, integration. To follow 335 in the Winter Quarter.

History of mathematics with problem solving.

Methods of counting and enumeration of mathematical structures. Topics include generating functions, recurrence relations, inclusion relations, and graphical methods.

A study of properties of integers: divisibility; Euclid's Algorithm; congruences and modular arithmetic; Euler's Theorem; Diophantine equations; distribution of primes; RSA cryptography.

A continuation of topics from MAT 311: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.

Incidence and separation properties of planes; congruences; the parallel postulate; area theory; ruler and compass construction.

Introduction to solid geometry and noneuclidean geometry (hyperbolic and spherical models); other special topics.

Complex functions; complex differentiation and integration; series and sequences of complex functions.

Linear equations, systems with constant coefficients, series solutions, Laplace transforms, and applications. Formerly MAT 338. CO-REQUISITE(S): MAT 261.

An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.

Introduction to statistical software (which will be used throughout the course). Descriptive statistics; elementary probability theory; discrete and continuous probability models; principles of statistical inference; Simple linear regression and correlation analysis.

Probability spaces, combinatorial probability methods, discrete and continuous random variables and distributions, moment generating functions, development and applications of the classical discrete and continuous distributions.

Joint probability distributions and correlation; law of large numbers and the central limit theorem; sampling distributions and theory of estimation.

Principles of hypothesis testing; most powerful tests and likelihood ratio tests; linear regression; one-way analysis of variance; categorical data analysis, nonparametric statistics.

Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces; diagonalization of symmetric linear operators, principal-axis theorem, and applications. Cross-listed MAT 470.

Topics in axiomatic set theory, formal logic, and computability theory.

Use of a digital computer for numerical computation. Error analysis, Gaussian elimination and Gauss-Seidel method, solution of non-linear equations, function evaluation, cubic splines, approximation of integrals and derivatives, Monte Carlo methods. Cross-listed with MAT 485.

Theory and algorithms for efficient computation, including the Fast Fourier transform, numerical solution of non-linear systems of equations. Minimization of functions of several variables. Sparse systems of equations and corresponding eigenvalue problems. (CROSS-LISTED WITH MAT 486 & CSC 386/486)

Modeling of real world problems using mathematical methods. Includes a theory of modeling and a study of specific models, selected from deterministic, stochastic, continuous, and discrete models. Cross-listed with MAT 484.