Pure Mathematics Concentration

Concentration Requirements

Open Electives

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

Recommended Mathematics Courses:

MAT 310

ABSTRACT ALGEBRA I

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.
Prerequisites:
MAT 262 and (MAT 141 or MAT 215) are a prerequisite for this class.

MAT 311

ABSTRACT ALGEBRA II

Continuation of 310.
Prerequisites:
MAT 310 is a prerequisite for this class.

MAT 335

REAL ANALYSIS I

Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.
Prerequisites:
(MAT 149 or MAT 152 or MAT 162 or MAT 172) and (MAT 141 or MAT 215) are a prerequisite for this class.

MAT 336

REAL ANALYSIS II

Properties of continuous functions, uniform continuity, sequences of functions, differentiation, integration. To follow 335 in the Winter Quarter.
Prerequisites:
MAT 335 is a prerequisite for this class.

MAT 301

HISTORY OF MATHEMATICS

History of mathematics with problem solving.
Prerequisites:
MAT 141 or MAT 215 is a prerequisite for this class.

MAT 302

COMBINATORICS

Methods of counting and enumeration of mathematical structures. Topics include generating functions, recurrence relations, inclusion relations, and graphical methods.
Prerequisites:
MAT 141 or MAT 215 is a prerequisite for this class.

MAT 303

THEORY OF NUMBERS

A study of properties of integers: divisibility; Euclid's Algorithm; congruences and modular arithmetic; Euler's Theorem; Diophantine equations; distribution of primes; RSA cryptography.
Prerequisites:
MAT 141 or MAT 215 is a prerequisite for this class.

MAT 312

ABSTRACT ALGEBRA III

Continuation of 311.
Prerequisites:
MAT 311 is a prerequisite for this class.

MAT 320

GEOMETRY I

Incidence and separation properties of plane; congruence; parallel postulate; area theory; ruler and compass construction.
Prerequisites:
MAT 141 or MAT 215 is a prerequisite for this class.

MAT 321

GEOMETRY II

Introduction to solid geometry and noneuclidean geometry (hyperbolic and spherical models); other special topics.
Prerequisites:
MAT 320 is a prerequisite for this class.

MAT 337

COMPLEX ANALYSIS

Complex functions; complex differentiation and integration; series and sequences of complex functions.
Prerequisites:
MAT 261 and MAT 335 is a prerequisite for this class.

MAT 304

DIFFERENTIAL EQUATIONS

Linear equations, systems with constant coefficients, series solutions, Laplace transforms, and applications. Formerly MAT 338. CO-REQUISITE(S): MAT 261.
Prerequisites:
MAT 261 is a corequisite for this class.

MAT 340

TOPOLOGY

An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.
Prerequisites:
(MAT 141 or MAT 215) and (MAT 220 or MAT 262) is a prerequisite for this class.

MAT 348

APPLIED STATISTICAL METHODS

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.
Prerequisites:
MAT 148 or MAT 151 or MAT 161 or MAT 171 is a prerequisite for this class.

MAT 351

PROBABILITY AND STATISTICS I

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.
Prerequisites:
MAT 261 is a prerequisite for this class.

MAT 352

PROBABILITY AND STATISTICS II

Joint probability distributions and correlation; law of large numbers and the central limit theorem; sampling distributions and theory of estimation.
Prerequisites:
MAT 351 is a prerequisite for this class.

MAT 353

PROBABILITY AND STATISTICS III

Principles of hypothesis testing; most powerful tests and likelihood ratio tests; linear regression; one-way analysis of variance; categorical data analysis, nonparametric statistics.
Prerequisites:
MAT 352 is a prerequisite for this class.

MAT 370

ADVANCED LINEAR ALGEBRA

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.
Prerequisites:
MAT 262 and (MAT 141 or MAT 215) are a prerequisite for this class.

MAT 372

LOGIC AND SET THEORY

Topics in axiomatic set theory, formal logic, and computability theory.
Prerequisites:
MAT 141 or MAT 215 is a prerequisite for this class.

MAT 385

NUMERICAL ANALYSIS I

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.
Prerequisites:
(MAT 220 or MAT 262) and (MAT 149 or MAT 152 or MAT 162 or MAT 172) is a prerequisite for this class.

MAT 386

NUMERICAL ANALYSIS II (CROSS-LISTED WITH MAT 486 & CSC 386/486)

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.
Prerequisites:
MAT 385 is a prerequisite for this class.

MAT 384

MATHEMATICAL MODELING

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.
Prerequisites:
(MAT 220 or MAT 262) and (MAT 348 or MAT 351) are a prerequisite for this class.