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.

MATH 3010 History of Mathematics
This course surveys major mathematical developments beginning with ancient Egyptians and Greeks and tracing the development through Hindu-Indian mathematics, Arabic mathematics, and European mathematics up to the 18th century. Prerequisite: MATH 1953. 4 qtr. hrs.

MATH 3040 Lattices and Order
Ordered sets, lattices as relational and as algebraic structures, ideals and filters, complete lattices, distributive and modular lattices, Boolean algebras, duality for finite distributive lattices. Prerequisite: MATH 2200 or MATH 2050. 4 qtr. hrs.

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 3060 Mathematical Logic
Classical propositional calculus (deductive systems and truth-table semantics), first-order logic (axiomatixation and completeness), elements of recursion theory, introduction to nonclassical logics. Prerequisite: MATH 2200 or MATH 2050. 4 qtr. hrs.

MATH 3080 Introduction to Probability
Basic probability models, combinatorial methods, random variables, independence, conditional probability, probability laws, applications to classical problems. Prerequisite: MATH 1953. 4 qtr. hrs.

MATH 3090 Mathematical Probability
Limit theorems for independent random variables, multivariate distributions, generating functions, random walks and statistical techniques. Prerequisites: MATH 2080 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 Advanced Linear Algebra
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.

MATH 3161 Intro to Real Analysis
A theoretical introduction to limits and continuity; sequences and series of numbers and functions; a theoretical introduction to the foundations of calculus. Prerequisite: MATH 2080and a theorem proving course. 4 qtr. hrs.

MATH 3166 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. 4 qtr. hrs.

MATH 3170 Intro to 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 3176 Rings and Fields
Rings, domains, fields; ideals, quotient rings, polynomials; PIDs, UFDs, Euclidean domains; maximal and prime ideals; chain conditions; extensions of fields, splitting fields, algebraic and transcendental extensions; Galois correspondence, fundamental theorem of Galois theory and applications. Prerequisites: MATH 3170. 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
Introduction to computability, effective procedures, format languages, undecidability; finite automata and regular languages. Cross-listed with COMP 3221. Prerequisite: MATH 2200 or COMP 2300.

MATH 3260 Metric Spaces
Metric spaces and continuous functions; completeness and compactness; examples including norm spaces; pointwise and uniform convergence; Baire Category Theorem. Prerequisite: MATH 3161 or equivalent. 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 Introduction 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.

MATH 3350 Mathematics of Finance
Mathematical aspect of options markets, interest rates and discounting; hedging and arbitrage; pricing options with binomial tree models; risk-neutral probabilities and martingales; Brownian motion, geometric Brownian motion and the Black-Scholes formula.  Prerequisite: MATH 3080.
MATH 3400 Introduction to Geometry
Specific geometrical systems including finite, Euclidean, non-Euclidean and projective geometries.  Prerequisite: MATH 2200.

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.

MATH 3550 Introduction to Theory of Numbers
Concepts of nonanalytic number theory and its history; prime numbers, divisibility, continued fractions, modular arithmetic, Diophantine equations and unsolved conjectures. Prerequisites: MATH 2200 or MATH 2050.

MATH 3701 Combinatorics
The principle of inclusion and exclusion, elementary counting techniques, systems of distinct representatives, partitions, recursion and generating functions, Latin squares, designs and projective planes. Prerequisite: MATH 2200.

MATH 3705 Topics in Mathematics
Varying selected advanced topics in mathematics, depending on student demand and instructor interest.

MATH 3710 Graph Theory
Paths, cycles, trees, Euler tours and Hamilton cycles, bipartite graphs, matchings, basic connectivity theorems, planar graphs, Kuratowski's theorem, chromatic number, n-color theorems, introduction to Ramsey theory.  Prerequisite: MATH 2200 or previous experience with abstract reasoning and basic combinations.

MATH 3720 Coding Theory
Goals of coding theory and information theory, instantaneous and Huffman codes, Shannon theorems, block and linear codes, generating and parity-check matrices, Hamming codes, perfect codes, binary Golay code, Reed-Muller codes, cyclic codes, BCH codes, Reed-Solomon codes, ideas of convolutional and turbo codes.  Prerequisite: MATH 3170.

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.

MATH 3852 Functions Complex Variable II
Advanced topics in complex analysis with applications. Prerequisite: MATH 3851.

MATH 3991 Independent Study
Cannot be arranged for any course that appears in regular course schedule for that particular year.

+B  MATH 3992 Directed Study (1 to 10 qtr. hrs.) -B

Note: enrollment in courses listed at the 4000-level and above is limited to graduate students.

MATH 4110 Introduction to Topology
Point set topology including topological spaces, connectedness, compactness and separate axioms; preparation for advanced courses in analysis. Prerequisite: MATH 3161 or equivalent. 4 qtr. hrs.

MATH 4120 Algebraic Topology
Fundamental groups, simplicial homology, Euler characteristic, classification of surfaces, manifolds. Prerequisites: MATH 3170 and MATH 3110 or MATH 4110. 4 qtr. hrs.

MATH 4162 Rings and Modules

MATH 4163 Universal Algebra
Universal algebras, congruences, lattices, distributive lattices, modular lattices, Boolean algebras, subdirectly irreducible algebras, Mal'cev theorems, varieties, Birkhoff theorem. Prerequisite: MATH 3170 and either MATH 3040 or MATH 3060. 4 qtr. hrs.

MATH 4166 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. 4 qtr. hrs.

MATH 4176 Rings and Fields
Rings, domains, fields; ideals, quotient rings, polynomials; PIDs, UFDs, Euclidean domains; maximal and prime ideals; chain conditions; extensions of fields, splitting fields, algebraic and transcendental extensions; Galois correspondence, fundamental theorem of Galois theory and applications. Prerequisite: MATH 3170. 4 qtr. hrs.

MATH 4260 Metric Spaces
Metric spaces and continuous functions; completeness and compactness; examples including norm spaces; pointwise and uniform convergence; Baire Category Theorem. Prerequisite: MATH 3161 or equivalent. 4 qtr. hrs.

MATH 4270 Hilbert Spaces
Schwarz and triangle inequalities, Reisz lemma, subspaces and othogonal projections, orthonormal bases, spectrum of bounded linear operators, compact, self-adjoint, normal and unitary operators, spectral theorem and, if time permits, unbounded operators. Also, if time permits, applications to partial differential equations, physics and engineering. Prerequisite: MATH 3260/4260 or MATH 3110/4110. 4 qtr. hrs.

MATH 4280 Measure Theory and Applications
Definition of measure spaces, Lebesgue measure, limit theorems, Radon-Nikodym Theorem, introduction to Lp spaces. Prerequisites: MATH 3260/4260. 4 qtr. hrs.

MATH 4290 Dynamical Systems
Topological and measure theoretic dynamical systems; properties and invariants of systems; symbolic dynamics; Ergodic Theorems; applications. Prerequisites: MATH 3110/4110, MATH 3260/4260. 4 qtr. hrs.

MATH 4300 Graduate Seminar
Students research a topic of their choosing with the aid of a faculty member, and then prepare and present a formal lecture on the subject. Prerequisite: graduate standing or consent of the instructor. 1–4 qtr. hrs.

MATH 4501 Functional Analysis
Advanced topics in structure of linear spaces; Banach spaces; Hahn-Banach Theorem and Duality; Uniform Boundedness Theorem; Open Mapping and Closed Graph Theorems; Stone-Weierstrass Theorem; Topics in Hilbert Spaces. Prerequisite: MATH 4280. 4 qtr. hrs.

MATH 4700 - Special Topics in Mathematics
1–4 qtr. hrs.

MATH 4701 Combinatorial Algorithms
Basic enumeration techniques; representations of combinatorial objects; algorithms for searching, sorting, generating combinatorial objects; graph algorithms. 4 qtr. hrs.

MATH 4705 Special Topics Applied Math
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. 1–5 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 4992 Directed Study

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.

For More Information
The Department of Mathematics website offers the most current information on courses, requirements, faculty and student news. Visit the Mathematics Department website for more information on the program.

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