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.

- CSC 242 INTRODUCTION TO COMPUTER SCIENCE II or another approved computer science course.
- Three courses chosen from the following list:
- MAT 302 COMBINATORICS
- MAT 304 DIFFERENTIAL EQUATIONS
- MAT 384 MATHEMATICAL MODELING
- MAT 385 NUMERICAL ANALYSIS I
- Two additional courses chosen from among the above and the following list:
- MAT 335 REAL ANALYSIS I
- MAT 351 PROBABILITY AND STATISTICS I
- MAT 352 PROBABILITY AND STATISTICS II
- MAT 370 ADVANCED LINEAR ALGEBRA
- MAT 381 FOURIER ANALYSIS AND SPECIAL FUNCTIONS
- MAT 386 NUMERICAL ANALYSIS II
- One additional course chosen from among the above and the following list:
- MAT 303 THEORY OF NUMBERS
- MAT 310 ABSTRACT ALGEBRA I
- MAT 311 ABSTRACT ALGEBRA II
- MAT 330 METHODS OF COMPUTATION AND THEORETICAL PHYSICS I
- MAT 331 METHODS OF COMPUTATION AND THEORETICAL PHYSICS II
- MAT 336 REAL ANALYSIS II
- MAT 337 COMPLEX ANALYSIS
- MAT 340 TOPOLOGY
- MAT 353 PROBABILITY AND STATISTICS III
- MAT 355 STOCHASTIC PROCESSES
- MAT 387 OPERATIONS RESEARCH I:LINEAR PROGRAMMING
- MAT 388 OPERATIONS RESEARCH II: OPTIMIZATION THEORY

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

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

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

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

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.

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.

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

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.

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.

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.

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)

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

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.

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.

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.

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

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

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

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

Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes. Cross-listed with MAT 455.

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)

Integer programming; non-linear programming; dynamic programming; queuing theory; game theory. (CROSS-LISTED AS MAT 488)

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