Mathematics (MATH)

MATH 0225 - Basic Mathematics

Credit(s): 3 Credits

Prep course designed to expose students to signed Numbers: common fraction, decimals and percentages; ratio and proportion; area and volume; powers and roots; algebraic expressions and operations; linear equations; basic trig metric functions; factoring polynomials.

Attributes: Prof. Studies Students Only

MATH 0235 - Intro Elementary Algebra

Credit(s): 3 Credits

Prerequisite: Math Assessment.

Attributes: Prof. Studies Students Only

MATH 0240 - Intro Elementary Algebra I

Credit(s): 3 Credits

Review of the real number system; linear equations, and inequalities in one and two variables; functions; systems of linear equations. Fall. MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters.

MATH 0250 - Intro to Elementary Algebra II

Credit(s): 3 Credits

Exponents, polynomials and polynomial functions; factoring; rational expressions and functions; roots, radicals and root functions; quadratic equations, inequalities and functions. Spring. MATH 0240 and MATH 0250 together cover the same material as MATH 0260, but in two semesters.

Prerequisite(s): MATH 0240 with a grade of C- or higher

MATH 0260 - Intermediate Algebra

Credit(s): 0-3 Credits

Review of the real number system; linear equations, and inequalities in one and two variables; functions; systems of linear equations; exponents, polynomials and polynomial functions; factoring; rational expressions and functions; roots, radicals and root functions; quadratic equations, inequalities and functions. Fall and spring.

MATH 0265 - Intermediate Algebra

Credit(s): 3 Credits

Review of the real number system; linear equations, and inequalities in one and two variables; functions; systems of linear equations; exponents, polynomials and polynomial functions; factoring; rational expressions and functions; roots, radicals and root functions; quadratic equations, inequalities and functions. Fall and spring. Credit not given for both MATH 0260 and any of the following: MATH 0240, MATH 0250. Prerequisite: MATH 0230 or Math Assessment.

Prerequisite(s): MATH 0230

Attributes: Prof. Studies Students Only

MATH 1200 - College Algebra

Credit(s): 0 or 3 Credits

Brief review of algebraic essentials, graphs, functions and their graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, systems of linear equations. Intended for students needing more preparation before taking MATH-1320 or MATH-1400. Fall, spring and summer.

Prerequisite(s): (MATH 0260 with a grade of C- or higher or Math Waiver per Advisor with a minimum score of 0260)

Attributes: Mathematics BA Req (A&S)

MATH 1205 - College Algebra

Credit(s): 3 Credits

Brief review of algebraic essentials, graphs, functions and their graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, systems of linear equations. Intended for students needing more preparation before taking MATH-1320 or MATH-1400. Fall, spring and summer. Prerequisite(s): MATH-0260 or Math Assessment.

Prerequisite(s): MATH 0260

Attributes: Prof. Studies Students Only

MATH 1220 - Finite Mathematics

Credit(s): 3 Credits

Brief review of algebraic essentials, graphs, functions and their graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, systems of linear equations. Intended for students needing more preparation before taking MATH-1320 or MATH-1400. Fall, spring and summer.

Prerequisite(s): (1 Course from MATH 0260-1200 or Math Waiver per Advisor with a minimum score of 0260)

Attributes: Mathematics BA Req (A&S)

MATH 1240 - Mathematics and the Art of M.C. Escher

Credit(s): 3 Credits

An inquiry course open to all undergraduates. The art of M.C. Escher is used to explore topics in geometry such as symmetry, tessellations, wallpaper patterns, the geometry of the sphere and hyperbolic geometry. Taught in a computer classroom.5 years of high school mathematics or a grade of C- or better in MATH-1200.

Attributes: Mathematics BA Req (A&S)

MATH 1250 - Math Thinking in Real World

Credit(s): 3 Credits

An inquiry course open to all undergraduates. In this course, aimed at students in the humanities and social sciences, we study some of the greatest ideas of mathematics that are often hidden from view in lower division courses. Topics selected from number theory, the infinite, geometry, topology, chaos and fractals, and probability. Taught in a computer classroom. (An understanding beyond MATH-0260 is needed.)

Attributes: Mathematics BA Req (A&S)

MATH 1260 - Statistics Including Sports and Politics

Credit(s): 3 Credits

An inquiry course open to all undergraduates. Producing data through the use of samples and experiments; organizing data through graphs and numbers that describe the distribution of the data of one variable or the relationship between two variables; probability; statistical inference including confidence intervals and tests of significance.5 years of high school mathematics or a grade of ’C-’ or better in MATH-1200.

Attributes: Mathematics BA Req (A&S)

MATH 1300 - Elementary Statistics with Computers

Credit(s): 3 Credits

Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, t-test; correlation and regression; crosstabulations and chi-square. Students learn to use a statistical package such as SPSS. Credit not given for MATH-1300 and any of the following: STAT-1300 or OPM 2070.

Prerequisite(s): (1 Course from MATH 120-4999 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Mathematics BA Req (A&S)

MATH 1305 - Elementary Statistics with Computers

Credit(s): 3 Credits

Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, t-test; correlation and regression; crosstabulations and chi-square. Students learn to use a statistical package such as SPSS.

Prerequisite(s): (1 Course from MATH 120-4999 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Prof. Studies Students Only

MATH 1320 - Survey of Calculus

Credit(s): 3 Credits

Linear equations and graphs; functions and graphs; limits; the derivative; rules of differentiation; curve sketching and optimization; antiderivatives; the definite integral; multivariable calculus and partial derivatives. 5 years of high school mathematics or a grade of C- or better in MATH-1200. (Offered every Fall, Spring and Summer)

Prerequisite(s): (1 Course from MATH 120-4999 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Mathematics BA Req (A&S)

MATH 1325 - Survey of Calculus

Credit(s): 3 Credits

Linear equations and graphs; functions and graphs; limits; the derivative; rules of differentiation; curve sketching and optimization; antiderivatives; the definite integral; multivariable calculus and partial derivatives. 5 years of high school mathematics or a grade of C- or better in MATH-1200. (Offered every Fall, Spring and Summer)

Prerequisite(s): (1 Course from MATH 120-4999 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Prof. Studies Students Only

MATH 1400 - Pre-Calculus

Credit(s): 3 Credits

Functions, graphs and models; modeling with linear and quadratic functions; polynomial and rational functions; modeling with exponential and logarithmic functions; trigonometric functions; trigonometric identities and conditional equations; additional topics in trigonometry; additional topics in analytic geometry; parametric equations. Fall, spring and summer. 5 years of high school mathematics or a grade of C- or better in MATH-1200.

Prerequisite(s): (MATH 1200 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Mathematics BA Req (A&S)

MATH 1510 - Calculus I

Credit(s): 0 or 4 Credits

Functions; continuity; limits; the derivative; differentiation from graphical, numerical and analytical viewpoints; optimization and modeling; rates and related rates; the definite integral; antiderivatives from graphical, numerical and analytical viewpoints. Fall, spring and summer. 1818 Advanced College Credit.

Prerequisite(s): (Math Waiver per Advisor with a minimum score of 1400 or MATH 1400 with a grade of C- or higher)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 1520 - Calculus II

Credit(s): 4 Credits

Symbolic and numerical techniques of integration, improper integrals, applications using the definite integral, sequences and series, power series, Taylor series, differential equations. Fall, spring and summer. 1818 Advanced College Credit.

Prerequisite(s): (Math Waiver per Advisor with a minimum score of 1510, MATH 1510 with a grade of C- or higher, or AP Calculus AB with a minimum score of 4)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 1650 - Cryptology

Credit(s): 3 Credits

An inquiry course open to all undergraduates. Aimed at students who require a course at the level of calculus or higher and who are interested in the mathematical basis for cryptology systems. Topics include permutation based codes, block cipher schemes and public key encryption. Prerequisites: 4 years of high school mathematics.

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 1660 - Discrete Mathematics

Credit(s): 3 Credits

Concepts of discrete mathematics used in computer science; sets, sequences, strings, symbolic logic, proofs, mathematical induction, sums and products, number systems, algorithms, complexity, graph theory, finite state machines.

Prerequisite(s): (1 Course from MATH 120-4999 or Math Waiver per Advisor with a minimum score of 1200)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 1930 - Special Topics

Credit(s): 1-3 Credits (Repeatable for credit)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 1980 - Independent Study

Credit(s): 1-3 Credits (Repeatable for credit)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 2530 - Calculus III

Credit(s): 4 Credits

Three-dimensional analytic geometry, vector-valued functions, partial differentiation, multiple integration, and line integrals. Fall and Spring semesters.

Prerequisite(s): (1 Course from MATH 1520-4999 or Math Waiver per Advisor with a minimum score of 1520)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 2660 - Principles of Mathematics

Credit(s): 3 Credits

Introduction to the basic techniques of writing proofs and to fundamental ideas used throughout mathematics. Topics covered include formal logic, proof by contradiction, set theory, mathematical induction and recursion, relations and congruence, functions. Fall and Spring semesters.

Prerequisite(s): (1 Course from MATH 142-4999 or Math Waiver per Advisor with a minimum score of 1510)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 2690 - Mathematical Problem Solving

Credit(s): 1 Credit

Intended primarily to train students for the William Lowell Putnam Mathematical Competition, this course covers a mélange of ingenious techniques for solving mathematics problems cutting across the entire undergraduate spectrum, including pre-calculus, calculus, combinatorics, probability, inequalities. Coverage tailored to students' interests. May be repeated for credit. Fall semester. Prerequisite: None.

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 2930 - Special Topics

Credit(s): 1-4 Credits (Repeatable for credit)

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 2980 - Independent Study

Credit(s): 0-3 Credits (Repeatable for credit)

Prior approval of sponsoring professor and chair required.

Attributes: Mathematics BA Req (A&S), Mathematics BS Req (A&S)

MATH 3110 - Linear Algebra for Engineers

Credit(s): 3 Credits

Systems of linear equations, matrices, linear programming, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, linear transformations, and numerical methods. Credit not given for both MATH-3110 and MATH-3120. Does not satisfy any requirements for the mathematics major. Spring semester.

Prerequisite(s): 1 Course from MATH 1520-4999

MATH 3120 - Introduction to Linear Algebra

Credit(s): 3 Credits

Matrices, row operations with matrices, determinants, systems of linear equations, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors. Credit not given for both MATH-3110 and MATH-3120. Fall and Spring semesters. Prerequisites - MATH-2530 and MATH-2660.

Prerequisite(s): MATH 2660; MATH 2530

MATH 3230 - Vector Analysis

Credit(s): 3 Credits

Vector algebra, differential and integral calculus of vector functions, linear vector functions and dyadics, applications to geometry, particle and fluid mechanics, theory of vector fields. (Offered periodically)

Prerequisite(s): (MATH 2530 or Math Waiver per Advisor with a minimum score of 2530)

MATH 3240 - Numerical Analysis

Credit(s): 3 Credits

Review of calculus; root finding, nonlinear systems, interpolation and approximation; numerical differentiation and integration.

Prerequisite(s): (MATH 1520 or Math Waiver per Advisor with a minimum score of 1520)

MATH 3270 - Advanced Mathematics for Engineers

Credit(s): 3 Credits

Vector algebra; matrix algebra; systems of linear equations; eigenvalues and eigenvectors; systems of differential equations; vector differential calculus; divergence, gradient and curl; vector integral calculus; integral theorems; Fourier series with applications to partial differential equations. Fall and Spring semesters.

Prerequisite(s): MATH 3550*

* Concurrent enrollment allowed.

MATH 3550 - Differential Equations

Credit(s): 3 Credits

Solution of ordinary differential equations, higher order linear equations, constant coefficient equations, systems of first order equations, linear systems, equilibrium of nonlinear systems, Laplace transformations.

Prerequisite(s): (MATH 2530 or Math Waiver per Advisor with a minimum score of 2530)

MATH 3600 - Combinatorics

Credit(s): 3 Credits

Advanced counting methods: permutations and combinations, generalized permutations and combinations, recurrence relations, generating functions; algorithms: graphs and digraphs, graph algorithms: minimum-cost spanning trees, shortest path, network flows; depth first and breadth-first searches; combinational algorithms: resource scheduling, bin-packing: algorithmic analysis and NP completeness.

Prerequisite(s): (1 Course from MATH 1150-4999 or Math Waiver per Advisor with a minimum score of 115)

MATH 3760 - Financial Mathematics

Credit(s): 3 Credits

This course covers the theory of interest material for the Financial Mathematics exam of the Society of Actuaries. Time permitting, supplemental material covering financial derivatives will be discussed.

Prerequisite(s): MATH 1520

MATH 3800 - Elementary Theory of Probability

Credit(s): 3 Credits

Counting theory; axiomatic probability, random variables, expectation, limit theorems. Applications of the theory of probability to a variety of practical problems. Credit not given toward the math major or minors for both MATH-3800 and either MATH-3810 or MATH-4800. (Offered fall)

Prerequisite(s): MATH 2530

MATH 3810 - Probability and Statistics for Engineers

Credit(s): 3 Credits

Analyzing and producing data; probability; random variables; probability distributions; expectation; sampling distributions; confidence intervals; hypothesis testing; experimental design; regression and correlation analysis. Credit not given toward the math major or minors for both MATH-3810 and either MATH-3800 or MATH-3850. (Offered fall and spring)

Prerequisite(s): MATH 2530

MATH 3850 - Foundation of Statistics

Credit(s): 3 Credits

Descriptive statistics, probability distributions, random variables, expectation, independence, hypothesis testing, confidence intervals, regression and ANOVA. Applications and theory. Taught using statistical software. Prerequisite: MATH 1520. Credit not given toward the math major or minors for both MATH/STAT 3810 and MATH/STAT 3850.

Prerequisite(s): MATH 1520

MATH 3910 - Internship

Credit(s): 1-6 Credits (Repeatable for credit)

MATH 3930 - Special Topics

Credit(s): 0-3 Credits (Repeatable for credit)

MATH 3980 - Independent Study

Credit(s): 1-3 Credits (Repeatable for credit)

MATH 4050 - History of Mathematics

Credit(s): 3 Credits

The development of several important branches of mathematics, including numeration and computation, algebra, non-Euclidean geometry, and calculus. (Offered periodically)

Prerequisite(s): 1 Course from MATH 1520-4999

MATH 4110 - Introduction to Abstract Algebra

Credit(s): 3 Credits

Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields. Fall semester.

Prerequisite(s): MATH 3120

MATH 4120 - Linear Algebra

Credit(s): 3 Credits

Advanced linear algebra, including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators and spectral theory. Spring semester.

Prerequisite(s): MATH 4110

MATH 4150 - Number Theory

Credit(s): 3 Credits

Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year. (Offered periodically)

Prerequisite(s): MATH 4110

MATH 4210 - Introduction to Analysis

Credit(s): 3 Credits

Real number system, functions, sequences, limits, continuity, differentiation, integration and series. Fall semester.

Prerequisite(s): MATH 2530; MATH 3120 with a grade of C- or higher

MATH 4220 - Metric Spaces

Credit(s): 3 Credits

Set theory, metric spaces, completeness, compactness, connected sets, category. Spring semester.

Prerequisite(s): MATH 4210

MATH 4230 - Multivariable Analysis

Credit(s): 3 Credits

Introduction to analysis in multidimensional Euclidean space. Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green's Theorem, Stokes' Theorem, Divergence Theorem). Spring semester.

Prerequisite(s): MATH 4210

MATH 4310 - Introduction to Complex Variables

Credit(s): 3 Credits

Complex number system and its operations, limits and sequences, continuous functions and their properties, derivatives, conformal representation, curvilinear and complex integration, Cauchy integral theorems, power series and singularities. Fall semester.

Prerequisite(s): (MATH 2530 or Math Waiver per Advisor with a minimum score of 2530)

MATH 4320 - Complex Variables II

Credit(s): 3 Credits

This course is a continuation of MATH-4310. Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces. Spring semester.

Prerequisite(s): MATH 4310

MATH 4360 - Geometric Topology

Credit(s): 3 Credits

An introduction to the geometry and topology of surfaces and three dimensional spaces. Topics covered Include Euclidean, spherical and hyperbolic geometry, topology of surfaces, knot theory, and the fundamental group.

MATH 4410 - Foundations of Geometry

Credit(s): 3 Credits

Historical background of the study of Euclidean geometry; development of two-dimensional Euclidean geometry from a selected set of postulates. (Offered periodically)

Prerequisite(s): (1 Course from MATH 142-4999 or Math Waiver per Advisor with a minimum score of 1510)

MATH 4430 - Non-Euclidean Geometry

Credit(s): 3 Credits

The rise and development of the non-Euclidean geometries with intensive study of plane hyperbolic geometry. (Offered periodically)

Prerequisite(s): (1 Course from MATH 142-4999 or Math Waiver per Advisor with a minimum score of 1510)

MATH 4480 - Differential Geometry

Credit(s): 3 Credits

Classical theory of smooth curves and surfaces in 3-space. Curvature and torsion of space curves, Gaussian curvature of surfaces, the Theorema Egregium of Gauss. Offered occasionally.

Prerequisite(s): MATH 2530

MATH 4550 - Nonlinear Dynamics and Chaos

Credit(s): 3 Credits

Bifurcation in one-dimensional flows. Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles. Poincare-Bendixson theory, bifurcations. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors.

Prerequisite(s): MATH 3550

MATH 4570 - Partial Differential Equations

Credit(s): 3 Credits

Fourier series, Fourier Integrals, the heat equation, Sturm-Liouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods.

Prerequisite(s): MATH 3550

MATH 4630 - Graph Theory

Credit(s): 3 Credits

Basic definitions and concepts, undirected graphs (trees and graphs with cycles), directed graphs, and operation on graphs, Euler's formula, and surfaces. (Offered periodically)

Prerequisite(s): (MATH 2530 or Math Waiver per Advisor with a minimum score of 2530)

MATH 4650 - Cryptography

Credit(s): 3 Credits

Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues. Related and supporting mathematical concepts and structures. Prerequisite(s): MATH-1520.

Prerequisite(s): MATH 1520

MATH 4800 - Probability Theory

Credit(s): 3 Credits

Axioms of probability, conditional probability. Discrete and continuous random variables, expectation, jointly defined random variables. Transformations of random variables and limit theorems. Theory and applications, taught using statistical software. Prerequisites: MATH/STAT 3850, MATH 2530 and MATH 1660 or MATH 2660. Credit not given toward the math major or minors for any two of MATH 3800, MATH 4800 and MATH 4810.

Prerequisite(s): (MATH 3850 or STAT 3850); MATH 2530; (MATH 1660 or MATH 2660)

MATH 4840 - Time Series

Credit(s): 3 Credits

Applied time series. Topics include exploratory data analysis, regression, ARIMA. Spectral analysis, statespace models. Theory and applications, taught using statistical software. Prerequisite: MATH/STAT 3850.

Prerequisite(s): (MATH 3850 or STAT 3850)

MATH 4850 - Mathematical Statistics

Credit(s): 3 Credits

Theory of estimators, sampling distributions, hypothesis testing, confidence intervals, regression, bootstrapping, and resampling. Theory and applications, taught using statistical software. Prerequisite: MATH 4800. Students may not take both MATH 4850 and MATH 4820.

Prerequisite(s): MATH 4800

MATH 4860 - Statistical Models

Credit(s): 3 Credits

Poisson processes, Markov chains, hidden Markov models, continuous time Markov chains, queuing theory. Theory and applications, taught with statistical software. Prerequisite: MATH 4800.

Prerequisite(s): MATH 4800

MATH 4870 - Applied Regression

Credit(s): 3 Credits

Linear regression, model selection, nonparametric regression, classification and graphical models. Theory and applications using statistical software. Prerequisites: MATH/STAT 3850 and MATH 3110 or MATH 3120.

Prerequisite(s): (MATH 3850 or STAT 3850); (MATH 3110 or MATH 3120)

MATH 4910 - Internship

Credit(s): 1-6 Credits (Repeatable for credit)

MATH 4930 - Special Topics

Credit(s): 3 Credits (Repeatable for credit)

MATH 4980 - Advanced Independent Study

Credit(s): 0-6 Credits (Repeatable for credit)

Prior permission of sponsoring professor and chair required.

MATH 5011 - Introduction to Abstract Algebra

Credit(s): 3 Credits

Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields.

MATH 5012 - Linear Algebra

Credit(s): 3 Credits

Advanced linear algebra including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators, and spectral theory. Offered every other spring semester.

MATH 5015 - Number Theory

Credit(s): 3 Credits

Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year. Offered every other year.

MATH 5021 - Introduction to Analysis

Credit(s): 3 Credits

Real number system, functions, sequences, limits, continuity, differentiation, integration and series.

MATH 5022 - Metric Spaces

Credit(s): 3 Credits

Set theory, real line, separation properties, compactness, metric spaces, metrization. Offered every other spring semester.

MATH 5023 - Multivariable Analysis

Credit(s): 3 Credits

Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multi-variable Calculus (Green’s Theorem, Stokes Theorem, Divergence Theorem).

MATH 5080 - Probability Theory

Credit(s): 3 Credits

Axioms of probability, conditional probability. Discrete and continuous random variables, expectation, jointly defined random variables. Transformations of random variables and limit theorems. Theory and applications, taught using statistical software. Prerequisites: MATH/STAT 3850, (MATH 2660 or MATH 1660), MATH 2530.

MATH 5110 - Algebra I

Credit(s): 3 Credits

Simple properties of groups, groups of transformations, subgroups, homomorphisms and isomorphisms, theorems of Schreier and Jordan-Hoelder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules. Offered every Fall semester. Prerequisites: Math 4120, 4150, 5102, or 5105.

MATH 5120 - Algebra II

Credit(s): 3 Credits

Rings, fields, bases and degrees of extension fields, transcendental elements, normal fields and their structures. Galois theory, finite fields; solutions of equations by radicals, general equations of degree n. Offered every Spring semester.

Prerequisite(s): MATH 5110

MATH 5210 - Real Analysis

Credit(s): 3 Credits

The topology of the reals, Lebesgue and Borel measurable functions, properties of the Lebesque integral, differential of the integral. Offered every Fall semester.

MATH 5220 - Complex Analysis

Credit(s): 3 Credits

Holomorphic and Harmonic functions and power series expansions. Complex integration. Cauchy's theorem and applications. Laurent series, singularities, Runge's theorem, and the calculus of residues. Additional topics may include Analytic continuation, Riemann surfaces, and conformal mapping. Recommended: MATH-4310. (Offered periodically)

Prerequisite(s): MATH 5210; MATH 5310

MATH 5230 - Functional Analysis

Credit(s): 3 Credits

Banach and Hilbert spaces. Linear functions and linear operators. Dual spaces, weak and weak topologies. Hahn-Banach, Closed Graph and Open Mapping Theorems. Topological Vector spaces. (Offered periodically)

Prerequisite(s): MATH 5210; MATH 5310

MATH 5240 - Harmonic Analysis

Credit(s): 3 Credits

Fourier Series on the circle, Convergence of Fourier series, Conjugate and maximal functions, Interpolation of Linear Operators, Lacunary Sequences, Fourier Transform on the line, Fourier transform on locally compact Abelian groups. Recommended: MATH-5310.

Prerequisite(s): MATH 5210

MATH 5310 - General Topology I

Credit(s): 3 Credits

Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces. Offered every Fall semester.

MATH 5320 - General Topology II

Credit(s): 3 Credits

Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampen theorem, covering spaces. Offered every Spring semester.

Prerequisite(s): MATH 5310

MATH 5930 - Special Topics in Mathematics

Credit(s): 1-3 Credits (Repeatable for credit)

MATH 5980 - Graduate Reading Course

Credit(s): 1-3 Credits (Repeatable for credit)

Prior permission of instructor and chairperson required.

MATH 5990 - Thesis Research

Credit(s): 0-6 Credits (Repeatable for credit)

MATH 6110 - Algebra III

Credit(s): 3 Credits

Categories and functors, properties of hom and tensor, projective and injective modules, chain conditions, decomposition and cancellation of modules, theorems of Masche, Wedderburn, and Artin-Wedderburn, tensor algebras. Offered every other year.

Prerequisite(s): MATH 5120

MATH 6180 - Topics in Algebra

Credit(s): 3 Credits

Various topics are discussed to bring graduate students to the forefront of a research area in algebra. Times of offering in accordance with research interests of faculty. Offered occasionally.

MATH 6210 - Lie Groups and Lie Algebras

Credit(s): 3 Credits

Lie groups and Lie algebras, matrix groups, the Lie algebra of a Lie group homogeneous spaces, solvable and nilpotent groups, semi-simple Lie groups. Offered every other year.

Prerequisite(s): MATH 5110; MATH 5220; MATH 5310

MATH 6220 - Rep Theory of Lie Groups

Credit(s): 3 Credits

Representation theory of Lie groups, irreducibility and complete reducibility, Cartan subalgebra and root space decomposition, root system and classification, coadjoint orbits, harmonic analysis on homogeneous spaces. Offered every other year.

Prerequisite(s): MATH 6210

MATH 6280 - Topics in Analysis

Credit(s): 3 Credits (Repeatable for credit)

Various topics are offered to bring graduate students to the forefront of a research area in analysis. Times of offering in accordance with research interests of faculty. Offered occasionally.

Prerequisite(s): MATH 5220

MATH 6310 - Algebraic Topology

Credit(s): 3 Credits

Homotopy theory, homology theory, exact sequences, Mayer-Vietoris sequences, degrees of maps, cohomology, Künneth formula, cup and cap products, applications to manifolds including Poincare-Lefshetz duality. Offered every other year.

Prerequisite(s): MATH 5320

MATH 6320 - Topology of Manifolds

Credit(s): 3 Credits

Examples of manifolds, the tangent bundle, maps between manifolds, embeddings, critical values, transversality, isotopies, vector bundles and bubular neighborhoods, cobordism, intersection numbers and Euler characteristics. May be taught in either the piecewiselinear or differentiable categories. Offered every other year.

Prerequisite(s): MATH 6310

MATH 6380 - Topics in Topology

Credit(s): 3 Credits (Repeatable for credit)

Various topics are offered to bring graduate students to the forefront of a research area in topology. Times of offering in accordance with research interests of faculty. Offered occasionally.

MATH 6410 - Differential Geometry I

Credit(s): 3 Credits

The theory of differentiable manifolds, topological manifolds, differential calculus of several variables, smooth manifolds and submanifolds, vector fields and ordinary differential equations, tensor fields, integration and De Rham cohomology. Offered every Fall semester.

MATH 6420 - Differential Geometry II

Credit(s): 3 Credits

Continuation of MATH-6410. (Offered every Spring)

Prerequisite(s): MATH 6410

MATH 6480 - Topics in Geometry

Credit(s): 3 Credits

Various topics are offered to bring graduate students to the forefront of a research area in geometry. Times of offering in accordance with research interests of faculty. Offered occasionally.

Prerequisite(s): MATH 5320

MATH 6930 - Special Topics

Credit(s): 3 Credits (Repeatable for credit)

MATH 6980 - Graduate Reading Course

Credit(s): 1-3 Credits (Repeatable for credit)

Prior permission of instructor and chairperson required.

MATH 6990 - Dissertation Research

Credit(s): 0-6 Credits (Repeatable for credit)