The concentration in Applied and Computational Mathematics is intended for any student who enjoys mathematics, problem solving, and applications to solving practical problems in business, government, and science.  The concentration is especially intended for students seeking a career as quantitative analysts, computational scientists, and applied mathematicians, and for those thinking of continuing the study of applied or discrete mathematics at the graduate level.

Course Requirements

Students interested in graduate study in applied mathematics are encouraged to take MAT 335-336, 370, 385-386.

Open Electives

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

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 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 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.

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 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 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 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 381

FOURIER ANALYSIS AND SPECIAL FUNCTIONS

The course covers the basic principles of discrete and continuous Fourier analysis and some of its applications currently used in scientific modeling. Students will use the computer to implement the computational algorithms developed in the course. Some of the topics covered will include Fourier transforms and their application to signal and image processing, discrete Fourier series, the fast Fourier transform algorithm and applications to digital filtering, and the Radon transforms and its applications to tomography.
Prerequisites:
MAT 262 is a prerequisite for this class.

MAT 386

NUMERICAL ANALYSIS II

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)
Prerequisites:
MAT 385 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 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

A continuation of topics from MAT 310: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.
Prerequisites:
MAT 310 is a prerequisite for this class.

A&S 491

ADMINISTRATIVE THEORY AND BEHAVIOR

This course concerns theoretical concepts and empirical research relating to administrative behavior in organizations with special reference to educational organizations. Concepts are examined within the typical decisional framework of supervisors, chief school business officers, principles, and superintendents, and similar positions in the helping professions. Assignments are individualized.
Prerequisites:
Status as an Advanced Masters Education student is a prerequisite for this class.

MAT 331

METHODS OF COMPUTATION AND THEORETICAL PHYSICS II

Computational and theoretical methods in ordinary differential equations, complex numbers, systems of equations, phase plane analysis, bifurcations. Applications to damped, driven oscillators, electronics. Lab Fee. COREQUISITE(S): MAT 261.
Prerequisites:
MAT 261 is 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 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 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 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 355

STOCHASTIC PROCESSES

Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes. Cross-listed with MAT 455.
Prerequisites:
MAT 353 is a prerequisite for this class.

MAT 387

OPERATIONS RESEARCH I:LINEAR PROGRAMMING

The Linear Programming problem and its dual; the simplex method; transportation and warehouse problems; computer algorithms and applications to various fields. (CROSS-LISTED AS MAT 487)

MAT 388

OPERATIONS RESEARCH II: OPTIMIZATION THEORY

Integer programming; non-linear programming; dynamic programming; queuing theory; game theory. (CROSS-LISTED AS MAT 488)
Prerequisites:
MAT 387 is a prerequisite for this class.

MAT 330

METHODS OF COMPUTATION AND THEORETICAL PHYSICS I

Computational and theoretical methods in ordinary diffential equations, complex numbers, systems of equations, phase plane analysis, and bifurcations. Applications to damped, driven oscillators, and to electronics.

CSC 242

INTRODUCTION TO COMPUTER SCIENCE II

An intermediate course in problem solving, algorithms and programming. Programming skills are further strengthened through more complex and larger programming assignments. The assignments will also be used to introduce different Computer Science areas (e.g. a Client/Server application for the Distributed Systems area). Classes and object oriented programming are motivated and introduced. PREREQUISITE(S): CSC241