Not every course is offered every quarter, and special topics courses change too often to be listed here. See the course schedules page for other views of the department's courses.
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.
MATH 1750
College Algebra & Trigonometry
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.
4 qtr. hrs.
MATH 1951 Calculus I
Differentiation of functions of one variable. Use of a laptop
computer and a computer algebra system is an integral component
of the course. Students with high school trigonometry should enter
sequence in fall quarter. Others should complete prerequisite
MATH 1750 and enter sequence in winter
quarter. Prerequisite: MATH 1750 or equivalent.
4 qtr. hrs.
MATH 1952 Calculus II
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. 4 qtr. hrs.
MATH 1953 Calculus III
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. 4 qtr. hrs.
MATH 1961 Honors Calculus I
Same topics as MATH 1951, enriched in one or more of the following
ways: challenging group projects and presentations, use of Web-based
course materials, greater emphasis on theory of calculus and applications.
Use of a laptop computer and a computer algebra system is an integral
component of the course. Can be used for partial fulfillment of
academic requirements in Honors Program. Prerequisites: MATH
1750 or equivalent; a strong background, facility and interest
in mathematics; or instructor's permission. 4 qtr. hrs.
MATH 1962 Honors Calculus II
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 Prerequisites: MATH
1962. 4 qtr. hrs.
MATH 1963 Honors Calculus III
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. Prerequisites: MATH
1962 4 qtr. hrs.
MATH 2050 Symbolic Logic
Modern propositional logic; symbolization and calculus of predicates,
especially predicates of relation. Cross-listed as PHIL 2160.
4 qtr. hrs.
MATH 2060 Elements of Linear
Algebra
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. 4 qtr. hrs.
MATH 2070 Intro Differential
Equations
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. 4 qtr. hrs.
MATH 2080 Calculus of Several
Variables
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. Prerequisite: MATH
1953 or MATH 1963. 4 qtr. hrs.
MATH 2200 Intro to Discrete
Structures
Introduction to theory of sets; relations and functions; logic,
truth tables and propositional calculus; proof techniques; introduction
to combinatorial techniques. Prerequisite: high school algebra.
4 qtr. hrs.
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 3010 History of Mathematics
The course will survey 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.
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.
Prerequisites: MATH 2200 or MATH 2050.
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 non-classical logics.
Prerequisites: MATH 2200 or MATH 2050.
MATH 3080 Introduction to
Probability
Basic probablity models, combinatorial methods, random variables,
independence, conditional probablility, 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 series of numbers and functions; a theoretical introduction
to the foundations of calculus. Prerequisite: MATH
3161.
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.
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 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.
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 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. 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 nonanalytic 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 Diff Eqns 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 Diff Eqns 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, recursion 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 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. Prerequisites: MATH 2200 or previous experience with abstract reasoning and basic combinatorics.
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. Prerequisites: MATH 3170.
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. 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 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 & 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 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 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 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.