1150 Foundations Seminar (4 credits)

The seminars offer challenging and interesting mathematical topics with a computer science component that requires only high school mathematics. Examples of seminars are Introduction to Crytography, Patterns and Symmetry, Mathematical Art and Patterns of Voting.

1200 Calculus - Business & Soc Sci (0 or 4 credits)

This is a one-quarter course for students in Business, Social Sciences, and Liberal Arts. It covers elementary differential calculus with emphasis on applications to business and the social sciences. Topics include functions, graphs, limits, continuity, differentiation, and mathematical models. Students are required to attend weekly labs during which time they will complete related lab assignments on their laptops using a computer algebra software package.

1700 College Algebra (2 credits)

This is a self-paced, online course designed to review the required algebra skills to be successful in MATH 1200. The students receive individualized help in the following topics: review for basic algebra, equations and inequalities, rectangular coordinate system and graphing, functions, and exponential and logarithmic functions.

1750 College Algebra & Trigonometry (4 credits)

Selected topics in algebra and analytic trigonometry intended to prepare students for calculus sequence (MATH 1951, 1952, 1953). Cannot be used to satisfy the mathematics/computing core requirements.

1951 Calculus I (4 credits)

Limits, continuity, differentiation of functions of one variable, applications of the derivative. Students with high school trigonometry should enter th Calculus sequence in fall quarter. Others should complete prerequisite MATH 1750 and enter the Calculus sequence in winter quarter. Prerequisite: MATH 1750 or equivalent.

1952 Calculus II (4 credits)

Differentiation and integration of functions of one variable. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1951.

1953 Calculus III (4 credits)

Integration of functions of one variable, infinite sequences and series. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1952.

1962 Honors Calculus II (4 credits)

Same topics as MATH 1952 enriched in the same ways as MATH 1961 enriches MATH 1951. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1961 or permission of instructor.

1963 Honors Calculus III (4 credits)

Same topics as MATH 1953 enriched in the same ways as MATH 1961 enriches MATH 1951. Use of a laptop computer and a computer algebra system is an integral component of the course. Prerequisite: MATH 1962 or permission of instructor.

1992 Directed Study (1 to 10 credits)

2050 Symbolic Logic (4 credits)

Modern propositional logic; symbolization and calculus of predicates, especially predicates of relation. Cross-listed with PHIL 2160.

2060 Elements of Linear Algebra (4 credits)

Matrices, systems of linear equations, vectors, eigenvalues and eigenvectors; idea of a vector space; applications in the physical, social, engineering and life sciences. Prerequisite: MATH 1750 or equivalent.

2070 Intro Differential Equations (4 credits)

Solution of linear differential equations; special techniques for nonlinear problems; mathematical modeling of problems from physical and biological sciences. Prerequisite: MATH 1953 or MATH 1963.

2080 Calculus of Several Variables (4 credits)

Multivariable processes encountered in all sciences; multiple integration, partial differentiation and applications; algebra of vectors in Euclidean three-space; differentiation of scalar and vector functions. Prerequisites: MATH 1953 or MATH 1963.

2200 Intro to Discrete Structures (4 credits)

Introduction to theory of sets; relations and functions; logic, truth tables and propositional calculus; proof techniques; introduction to combinatorial techniques. Prerequisite: high school algebra.

2992 Directed Study (1 to 10 credits)

3000 The Real World Seminar (1 credits)

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 with COMP 3000.

3010 History of Mathematics (4 credits)

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.

3040 Lattices and Order (4 credits)

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.

3050 Set Theory (4 credits)

Zermelo-Fraenkel axioms, axiom of choice, Zorn's Lemma, ordinals, cardinals, cardinal arithmetic. Prerequisite: MATH 2200 or MATH 2050

3060 Mathematical Logic (4 credits)

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.

3080 Introduction to Probability (4 credits)

Basic probability models, combinatorial methods, random variables, independence, conditional probability, probability laws, applications to classical problems. Prerequisite: MATH 1952.

3090 Mathematical Probability (4 credits)

Limit theorems for independent random variables, multivariate distributions, generating functions, random walks and statistical techniques. Prerequisites: MATH 1953 or MATH 1963 and MATH 3080.

3110 Introduction to Topology (4 credits)

Point set topology including topological spaces, connectedness, compactness and separate axioms; preparation for advanced courses in analysis. Prerequisite: MATH 3161 or equivalent.

3120 Introduction to Topology (4 credits)

Point set topology including topological spaces, connectedness, compactness and separation axioms; preparation for advanced courses in analysis. Prerequisite: junior standing.

3151 Advanced Linear Algebra (4 credits)

Vector spaces, linear mappings, matrices, inner product spaces, eigenvalues and eigenvectors. Prerequisite: MATH 2060.

3152 Linear Algebra II (4 credits)

Linear operators on finite dimensional vector spaces, eigenvalues, eigenvectors, Jordan forms; special properties of self-adjoint and normal operators; special topics. Prerequisite: MATH 3151.

3161 Intro to Real Analysis (4 credits)

A theoretical introduction to the foundations of calculus including sequences, limits, continuity, derivatives and Riemann integration. Prerequisite: MATH 2080 and a theorem proving course.

3166 Group Theory (4 credits)

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.

3170 Intro to Abstract Algebra (4 credits)

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. Prerequisite: MATH 2200 or one year of university-level mathematics.

3180 Mathematical Statistics (4 credits)

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.

3221 Automata & Formal Languages I (4 credits)

Introduction to computability, effective procedures, format languages, undecidability; finite automata and regular languages. Prerequisite: MATH 2200 or one year of university-level mathematics.

3222 Automata & Formal Languages II (4 credits)

Pushdown automata and context-free languages; Turing machines; decidability, recursive and recursively enumerable sets. Prerequisite: MATH 3221.

3260 Metric Spaces (4 credits)

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

3311 Intro to Operations Research I (4 credits)

Linear optimization models, simplex algorithm, sensitivity analysis and duality, network models, dynamic programming, applications to physical, social and management sciences. Prerequisite: MATH 2060.

3312 Intro-Operations Research II (4 credits)

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.

3350 Mathematics of Finance (4 credits)

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.

3400 Introduction to Geometry (4 credits)

Specific geometrical systems including finite, Euclidean, non-Euclidean and projective geometries. Prerequisites: junior standing and one year of university-level mathematics.

3451 Chaos, Dynamics & Fractals I (4 credits)

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.

3452 Chaos, Dynamics & Fractals II (4 credits)

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.

3550 Intro to Theory of Numbers (4 credits)

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.

3651 Diff Eqns and Applied Math I (4 credits)

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.

3652 Diff Eqns and Applied Math II (4 credits)

Continuation of 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.

3701 Combinatorics (4 credits)

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.

3705 Topics in Mathematics (4 credits)

Varying selected advanced topics in mathematics, depending on student demand and instructor interest. Possible alternatives include calculus of variations, partial differential equations, algebraic topology, differential manifolds, special functions.

3706 Intro to Computer Algebra (4 credits)

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 1951, MATH 1952, MATH 1953 and permission of instructor.

3707 Math Methods Computer Algebra (4 credits)

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 or COMP 3706.

3710 Graph Theory (4 credits)

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.

3720 Coding Theory (4 credits)

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.

3851 Functions Complex Variable I (4 credits)

Complex numbers, analytic functions, complex integration, series expansions, residue theory, conformal maps, advanced topics and applications. Prerequisite: MATH 2080.

3852 Functions Complex Variable II (4 credits)

Advanced topics in complex analysis with applications. Prerequisite: MATH 3851.

3950 Undergraduate Research Seminar (1 to 4 credits)

Opportunity to conduct mathematics research; bridges the gap between homework exercises and research problems with directed readings and challenging projects. Prerequisite: instructor's permission.

3991 Independent Study (1 to 10 credits)

Cannot be arranged for any course that appears in regular course schedule for that particular year.

3992 Directed Study (1 to 10 credits)

4110 Introduction to Topology (4 credits)

Point set topology including topological spaces, connectedness, compactness and separate axioms; preparation for advanced courses in analysis. Prerequisite: MATH 3161 or equivalent.

4120 Algebraic Topology (4 credits)

Fundamental groups, simplicial homology, Euler characteristic classification of surfaes, manifolds. Prerequisites: MATH 3170 and MATH 3110/4110.

4162 Rings and Modules (3 credits)

4163 Universal Algebra (4 credits)

Universal algebras, congruencies, lattices, distributive lattices, modular lattices, Boolean algebras, subdirectly irreducible algebras, Mal'cev theorems, varieties, Birkhoff theorem. Prerequisites: MATH 3170 and either MATH 3040 or MATH 3060.

4166 Group Theory (4 credits)

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.

4270 Hilbert Spaces (4 credits)

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.

4290 Dynamical Systems (4 credits)

Topological and measure theoretic dynamical systems; properties and invariants of systems; symbolic dynamics; Ergodic Theorems; applications. Prerequisites: MATH 3120, MATH 4110, MATH 3260, or MATH 4260.

4300 Graduate Seminar (1 to 4 credits)

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.

4501 Functional Analysis (4 credits)

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.

4700 Special Topics in Mathematics (1 to 4 credits)

4701 Combinatorial Algorithms (4 credits)

Basic enumeration techniques; representations of combinatorial objects; algorithms for searching, sorting, generating combinatorial objects, graph algorithms.

4705 Special Topics Applied Math (1 to 5 credits)

varying selected advanced topics in mathematics, depending on student demand. Possible alternatives include of variations, partail differential equations, algebraic topology, differential manifolds, special functions.

4991 Independent Study (1 to 10 credits)

Cannot be arranged for any course that appears in course schedule for that particular year.

4992 Directed Study (1 to 10 credits)

4995 Independent Research (1 to 10 credits)

Research projects undertaken in conjunction with a faculty member.

5000 Doctoral Seminar (3 credits)

Techniques, methods used in mathematical, computing research. Includes proofs, bibliographic searching, writing styles, what constitutes an acceptable dissertation.

5991 Independent Study (1 to 10 credits)

Cannot be arranged for any course that appears in the regular course schedule for that particular year.

5995 Independent Research (1 to 10 credits)

Research leading to a dissertation.