Course Descriptions
Not every course is offered every quarter, and special topics courses change too often to be listed here.
Graduate credit cannot be earned in courses numbered below 3000. Courses numbered 4000 and above are open only to graduate students.
Some courses in abstract algebra have just been approved, and they might not show up in the catalog for a while, or might be listed under old numbers.
Note: enrollment in courses listed at the 4000-level and above is limited to graduate students.
MATH 3000 The Real World Seminar
Lectures by alumni and others on surviving culture shock when leaving the University and entering the job world. Open to all students regardless of major. Cross-listed as COMP 3000.
1 qtr. hr.
MATH 3050 Set Theory
Zermelo-Fraenkel axioms, axiom of choice, Zorn's Lemma, ordinals, cardinals, cardinal arithmetic. Prerequisites: MATH 2200 or MATH 2050.
4 qtr. hrs.
MATH 3070 Math Modeling and Comp Sim
Mathematical models in social, life, and management sciences; models include growth processes, epidemics, queues, land usage, etc.; Markov chains, optimization, game theory, graphy theory, etc. Prerequisites: completion of one 3000-level mathematics course and COMP 1672.
4 qtr. hrs.
MATH 3080 Introduction to Probability
Basic probablity models, combinatorial methods, random variables, independence, conditional probability, probability laws, applications to classical problems. Prerequisite: MATH 1952.
4 qtr. hrs.
MATH 3090 Mathematical Probability
Limit theorems for independent random variables, multivariate distributions, generating functions, random walks and statistical techniques. Prerequisites: MATH 1953 or MATH 1963 and MATH 3080.
4 qtr. hrs.
MATH 3120 Introduction to Topology
Point set topology including topological spaces, connectedness, compactness and separation axioms; preparation for advanced courses in analysis. Prerequisite: junior standing.
4 qtr. hrs.
MATH 3151 Linear Algebra I
Vector spaces, linear mappings, matrices, inner product spaces, eigenvalues and eigenvectors. Prerequisite: MATH 2060. 4 qtr. hrs.
MATH 3152 Linear Algebra II
Linear operators on finite dimensional vector spaces, eigenvalues, eigenvectors, Jordan forms; special properties of self-adjoint and normal operators; special topics. Prerequisite: MATH 3151.
4 qtr. hrs.
MATH 3161 Intro to Real Analysis I
A theoretical introduction to limits and continuity; sequences and series of numbers and functions; a theoretical introduction to the foundations of calculus. Prerequisite: MATH 2080.
4 qtr. hrs.
MATH 3162 Intro to Real Analysis II
A theoretical introduction to limits and continuity; sequences and serices of numbers and functions; a theoretical introduction to the foundations of calculus. Prerequisite: MATH 2080.
MATH 3170 Intro Abstract Algebra
Examples of groups, permutations, subgroups, cosets, Lagrange theorem, normal subgroups, factor groups, homomorphisms, isomorphisms, rings, integral domains, quaternions, rings of polynomials, Euclid algorithm, ideals, factor rings, maximal ideals, principal ideals, fields, construction of finite fields. Prerequisites: MATH 2200 or one year of university-level mathematics.
4 qtr. hrs.
MATH 3180 Mathematical Statistics
Mathematical foundations of statistical theory, random sampling, theoretical distributions, estimation, test of hypotheses, limit theorems, correlation and regression, nonparametric statistics, decision theory. Students may not receive credit for both MATH 3180 and 3190. Prerequisites: MATH 1953 or MATH 1963 and MATH 3080.
4 qtr. hrs.
MATH 3190 Stats for Soc & Behav Science
Basic statistical techniques commonly used in quantitative analysis in the fields of economics, political science and sociology; probability, sampling theory, hypothesis testing, analysis of variance and correlation, regression analysis. Students may not receive credit for both MATH 3190 and MATH 3180.
4 qtr. hrs.
MATH 3221 Automata & Formal Languages I
Introduction to computability, effective procedures, format languages, undecidability; finite automata and regular languages. Prerequisites: MATH 2200 or one year of university-level mathematics.
4 qtr. hrs.
MATH 3222 Automata & Formal Languages II
Pushdown automata and context-free languages; Turing machines; decidability, recursive and recursively enumerable sets. Prerequisite: MATH 3221. MATH 3221.
4 qtr. hrs.
MATH 3311 Intro to Operations Research I
Linear optimization models, simplex algorithm, sensitivity analysis and duality, network models, dynamic programming, applications to physical, social and management sciences. Prerequisite: MATH 2060.
4 qtr. hrs.
MATH 3312 Intro to Operations Research II
Nonlinear and stochastic models, elementary queuing theory, integer programming, introduction to simulation; applications to physical, social and management sciences. Prerequisites: MATH 1953 or MATH 1963 and MATH 3311.
4 qtr. hrs.
MATH 3400 Introduction to Geometry
Specific geometrical systems including finite, Euclidean, non-Euclidean and projective geometries. Prerequisites: junior standing and one year of university-level mathematics.
4 qtr. hrs.
MATH 3451 Chaos, Dynamics & Fractals I
Introduction to one-dimensional dynamical systems, fractals; fixed and periodic points; sources and sinks; period doubling and tangent node bifurcations; chaotic dynamical systems; Sarkovskii’s Theorem. Prerequisites: MATH 2080 and instructor’s permission.
4 qtr. hrs.
MATH 3452 Chaos, Dynamics & Fractals II
Dynamical systems in two (or more) real variables or one complex variable; stable manifold theorem; Henon attractor; Julia sets; Mandelbrodt set. Prerequisite: MATH 3451 or instructor’s permission. 4 qtr. hrs.
MATH 3550 Intro to Theory of Numbers
Concepts of nonanalytical number theory and its history; prime numbers, divisibility, continued fractions, modular arithmetic, Diophantine equations and unsolved conjectures. Prerequisites: MATH 2200 or MATH 2050.
4 qtr. hrs.
MATH 3571 Intro to Numerical Methods I
Algorithmic approach to numerical problems, solution of systems of linear equations, interpolation and approximation, numerical integration, and the numerical solution of ordinary and partial differential equations. Cross-listed as COMP 3571. Prerequisites: MATH 1952 or MATH 1962, and MATH 2060 and COMP 1672.
4 qtr. hrs.
MATH 3572 Intro to Numerical Methods II
Algorithmic approach to numerical problems, solution of systems of linear equations, interpolation and approximation, numerical integration, and the numerical solution of ordinary and partial differential equations. Cross-listed as COMP 3572. Prerequisites: MATH 3571 or COMP 3571.
4 qtr. hrs.
MATH 3651 Differential Equations and Applied Math I
Modeling of phenomena by ordinary differential equations; techniques of analysis and solution of such equations; oscillation theory and boundary value problems, power series methods, special functions, Laplace transforms and difference equations. Prerequisites: MATH 2060 and MATH 2070.
4 qtr. hrs.
MATH 3652 Differential Equations and Applied Math II
Modeling of phenomena by ordinary and partial differential equations; classification of second order partial differential equations; separation of variables, transform methods, special functions, method of characteristics. Prerequisite: MATH 3651.
4 qtr. hrs.
MATH 3701 Combinatorics
The principle of inclusion and exclusion, elementary counting techniques, systems of distinct representatives, partitions, recursions and generating functions, Latin squares, designs and projective planes. Prerequisites: MATH 2200.
4 qtr. hrs.
MATH 3705 Topics in Mathematics
4 qtr. hrs.
MATH 3706 Intro to Computer Algebra
Introduction to computer algebra, the algorithmic solution of mathematical problems; use of computer algebra software (MAPLE or MATHEMATICA); algorithms for analysis and manipulation of polynomial, algebraic and trigonometric expressions; algorithms for differentiation and integration; applications to calculus and differential equations. Cross-listed as COMP 3706. Prerequisites: MATH 2070 and either COMP 1672 or COMP 1680.
4 qtr. hrs.
MATH 3707 Math Methods Computer Algebra
Mathematical theory and algorithms used to design modern computer algebra systems. Includes selected topics from integer algorithms, greatest common divisor algorithms for polynomials, polynomial factorization algorithm, resultant computation and applications, polynomial decomposition, and the Risch integration algorithm. Cross-listed as COMP 3707. Prerequisite: MATH 3706, COMP 3706 or 1680.
4 qtr. hrs.
MATH 3730 Vector Analysis
Differential vector calculus, gradient, divergence, curl; introduction to differential geometry, integration, Stokes’ theorem in several variables. Prerequisite: MATH 2080.
4 qtr. hrs.
MATH 3851 Functions Complex Variable I
Complex numbers, analytic functions, complex integration, series expansions, residue theory, conformal maps, advanced topics and applications. Prerequisite: MATH 2080.
4 qtr. hrs.
MATH 3852 Functions Complex Variable II
Advanced topics in complex analysis with applications. Prerequisite: MATH 3851. MATH 3851.
4 qtr. hrs.
MATH 3950 Undergraduate Research Seminar
Opportunity to conduct mathematics research; bridges the gap between homework exercises and research problems with directed readings and challenging projects. Prerequisite: instructor's permission.
0 to 4 qtr. hrs.
MATH 3991 Independent Study
Cannot be arranged for any course that appears in regular course schedule for that particular year.
0 to 4 qtr. hrs.
MATH 4091 Mathematical Probability
Limit theorems for independent random variable, multivariate distributions, generating functions, random walks, statistical techniques. Prerequisite(s): MATH 1953 or equivalent, MATH 3080.
3 qtr. hrs.
MATH 4092 Stochastic Processes
Stochastic models in biology, physics, economics; Markov, Poisson, renewal branching, birth-death, queuing processes. Prerequisite: MATH 4091.
3 qtr. hrs.
MATH 4120 Algebraic Topology
Fundamental groups, simplicial homology, Euler characteristic, classification of surfaces, manifolds. Prerequisites: MATH 3170 and MATH 3120.
3 qtr. hrs.
MATH 4161 Group Theory
Groups and homomorphisms, isomorphism theorems, symmetric groups and G-sets, the Sylow theorems, normal series, fundamental theorem of finitely generated abelian groups. Prerequisite: MATH 3170.
3 qtr. hrs.
MATH 4162 Rings and Modules
Ideals, UFDs, PIDs, minimal polynomials, field extensions, ruler and compass constructions, modules, free modules, projective modules, tensor products, Noetherian and Artinian rings. Prerequisite: MATH 3170.
3 qtr. hrs.
MATH 4163 Universal Algebra and Categories
Universal algebras, congruences, lattices, distributive lattices, modular lattices, Boolean algebras, subdirectly irreducible algebras, Mal’cev theorems, varieties, Birkhoff theorem, objects, morphisms, categories, functors. Prerequisite: MATH 3170.
3 qtr. hrs.
MATH 4221 Automata and Formal Languages I
Computability, effective procedures, formal languages, undecidability; finite automata, regular languages. Prerequisite(s): MATH 2200.
3 qtr. hrs.
MATH 4222 Automata and Formal Languages II
Pushdown automata, context-free languages; Turing machines; computational complexity. Prerequisite(s): MATH 4221.
3 qtr. hrs.
MATH 4251,4252, 4253 Modern Analysis
Metric spaces, point set topology, Hilbert and Banach spaces, symmetric compact operators; Lebesgue integral, LP spaces, measure theory. Prerequisite(s): MATH 3152, MATH 3161.
3 qtr. hrs.
MATH 4501, 4502, 4503 Functional Analysis
Advanced topics in structure of linear spaces, generalized functions; spectral theory of operators in Hilbert spaces; applications to partial differential equations, semigroups, stochastic processes. Prerequisite(s): MATH 4253.
3 qtr. hrs.
MATH 4701 Combinatorial Algorithms
Basic enumeration techniques; representations of combinatorial objects; algorithms for searching, sorting, generating combinatorial objects; graph algorithms.
3 qtr. hrs.
MATH 4705 Special Topics in Mathematics
Varying selected advanced topics in mathematics, depending on student demand. Possible alternatives include calculus of variations, partial differential equations, algebraic topology, differential manifolds, special functions.
3 qtr. hrs.
MATH 4707 Mathematical Methods of Computer Algebra
Mathematical theory and algorithms used to design modern computer algebra systems; includes selected topics from: integer algorithms, greatest common divisor algorithms for polynomials, polynomial factorization algorithm, resultant computation and applications, polynomial decomposition, and the Risch integration algorithm. Cross-listed as MATH 3707 and COMP 4707. Prerequisite(s): MATH 3706 or COMP 3706.
3 qtr. hrs.
MATH 4851, 4852 Introduction to Functions of a Complex Variable
Concepts of complex numbers, functions of a complex variable, continuity and differentiability in complex plane; advanced topics, applications. Prerequisite(s): MATH 2080.
3 qtr. hrs.
MATH 4991 Independent Study (MA/MS)
Cannot be arranged for any course that appears in regular course schedule for that particular year. arr.
MATH 4995 Independent Research (MA/MS)
Research projects undertaken in conjunction with a faculty member. arr.
MATH 5000 Doctoral Seminar
Techniques, methods used in mathematical, computing research. Includes proofs, bibliographic searching, writing styles, what constitutes an acceptable dissertation. arr.
MATH 5991 Doctoral Independent Study
Cannot be arranged for any course that appears in the regular course schedule for that particular year. arr.
MATH 5995 Independent Research
Research leading to a dissertation. arr.