Department of Mathematics (MATH)

The department offers programs leading to the Master of Arts and the Doctor of Philosophy degrees. The department offers courses in the following areas: algebra, analysis, topology, differential equations, mathematical methods for engineering, mathematics for finance, mathematics education, mathematical statistics, numerical analysis, fluid dynamics, control theory, and optimization theory.

Visit Department Website

Faculty

Chair
  • Cruz-Uribe, David
Graduate Director
  • Halpern, David C.M.J.
Professors
  • Allen, Paul J.
  • Corson, Jon M.
  • Cruz-Uribe, David
  • Evans, Martin
  • Dixon, Martyn R.
  • Gleason, Jim
  • Hadji, Layachi
  • Halpern, David C.M.J.
  • Liem, Vo
  • Moore, Robert L.
  • Olin, Robert F.
  • Sidje, Roger
  • Sun, Min
  • Wang, James L.
  • Wang, Pu
  • Zhao, Shan
Associate Professors
  • Belbas, Stavros
  • Roberts, Lawrence
  • Moen, Kabe
  • Trace, Brace S.
  • Zhu, Wei
Assistant Professors
  • Ames, Brendan
  • Beznosova, Oleksandra
  • Chen, Yuhui
  • Ferguson, Timothy
  • Kwon, Hyun-Kyoung
  • Tosun, Bulent
  • Xu, Yangyang

Courses

MATH
502
Hours
3
History Of Mathematics

Designed to increase awareness of the historical roots of the subject and its universal applications in a variety of settings, showing how mathematics has played a critical role in the evolution of cultures over both time and space.

MATH
503
Hours
3
Adv Math Connections & Devlpmn

Explore the interconnections between the algebraic, analytic, and gemetric areas of mathematics with a focus on properties of various number systems, importance of functions, and the relationship of algebraic structures to solving analytic equations. This exploration will also include the development and sequential nature of each of these branches of mathematics and how it relates to the various levels within the algebra mathematics curriculum.

MATH
504
Hours
1-3
Topics Mod Math Teachers

Diverse mathematical topics designed to enhance skills and broaden knowledge in mathematics for secondary mathematics teachers.

MATH
505
Hours
3
Geometry For Teachers

A survey of the main features of Euclidean geometry, including the axiomatic structure of geometry and the historical development of the subject. Some elements of projective and non-Euclidean geometry are also discussed.

MATH
508
Hours
3
Topics In Algebra

Content changes from semester to semester to meet the needs of students. Designed for graduate students not majoring in mathematics.

MATH
509
Hours
3
Advanced Data Analysis

Concepts and techniques of posing questions and collecting, analyzing, and interpreting data. Topics include: univariate and bivariate statistics, probability, simulation, confidence intervals and hypothesis testing.

Prerequisite(s): MATH 125 and ST 260
MATH
510
Hours
3
Numerical Linear Algebra

Further study of matrix theory emphasizing computational aspects. Topics include direct solution of linear algebraic systems, analysis of errors in numerical methods for solutions of linear systems, linear least-squares problems, orthogonal and unitary transformations, eigenvalues and eigenvectors, and singular value decomposition.

Prerequisite(s): MATH 237 and (CS 100, AEM 249, ECE 285, or RRS 101)
MATH
511
Hours
3
Numerical Analysis I

Mathematical principles of numerical analysis and their application to the study of certain methods. Topics includes numerical methods for solving nonlinear equations; iterative methods for solving linear systems of equations; approximation and interpolation methods; numerical differentiation and integration techniques; and numerical methods for solving initial-value problems for ordinary differential equations.

Prerequisite(s): MATH 238, MATH 237 and (CS 100, AEM 249, ECE 285, or RRS 101)
MATH
512
Hours
3
Numerical Analysis II

This is the second course in the numerical analysis sequence for graduate students in mathematics, science or engineering with an emphasis on numerical methods for solving boundary value problems, ordinary differential equations and partial differential equations, multistep methods for initial value problems, and approximation theory (least-squares problems, fast Fourier Transforms).

Prerequisite(s): MATH 343 and MATH 511
MATH
520
Hours
3
Linear Optimization Theory

This course is an introduction to theory of linear programming. Topics include: basic theory (fundamental theorem of LP, equivalence of basic feasible solutions and extreme points, duality and sensitivity results), simplex algorithm and its variations, and special applications to transportation and network problems. Non-simplex methods are also briefly introduced.

Prerequisite(s): MATH 237 or MATH 371.
MATH
521
Hours
3
Optimization Theory II

This course is an introduction to nonlinear programming. Topics will include necessary and sufficient conditions for optimality, as well as basic theory and numerical algorithms for several traditional optimization methods, e.g., basic descent methods, conjugate direction methods, quasi-Newton methods, penalty and barrier methods, Lagrange multiplier methods. A brief introduction to selected modern topics may be added if time permits.

Prerequisite(s): MATH 237 or MATH 371
MATH
522
Hours
3
Mathematics For Finance I

An introduction to financial engineering and mathematical model in finance. This course covers basic no-arbitrage principle, binomial model, time value of money, money market, risky assets such as stocks, portfolio management, forward and future contracts and interest rates.

MATH
532
Hours
3
Graph Theory & Applictns

Survey of several of the main ideas of general graph theory with applications to network theory. Topics include oriented and nonoriented linear graphs, spanning trees, branchings and connectivity, accessibility, planar graphs, networks and flows, matchings, and applications.

MATH
537
Hours
3
Applied Math Topics I

This course is a survey of topics in applied mathematics.

Prerequisite(s): Permission of the department.
MATH
538
Hours
3
Spec Top Appld Math II

No description available.

MATH
541
Hours
3
Boundary Value Problems

Emphasis on boundary value problems for classical partial differential equations of physical sciences and engineering. Other topics include Fourier series, Fourier transforms, asymptotic analysis of integrals and boundary-value problems for ordinary differential equations.

Prerequisite(s): C- or higher in MATH 343
MATH
542
Hours
3
Integral Transf & Asympt

Introduction to complex variable methods, integral transforms, asymptotic expansions, WKB method, matched asymptotics, and boundary layers.

Prerequisite(s): C- or higher in MATH 541 OR permission of the instructor.
MATH
551
Hours
3
Math Stats W/Applictn I

Introduction to mathematical statistics. Topics include bivariate and multivariate probability distributions, functions of random variables, sampling distributions and the central limit theorem, concepts and properties of point estimators, various methods of point estimation, interval estimation, tests of hypotheses and Neyman-Pearson lemma with some applications. Usually offered in the Fall semester.

MATH
552
Hours
3
Math Stats W/Applictn II

Considers further applications of the Neyman-Pearson lemma, likelihood ratio tests, chi-square test for goodness of fit, estimation and test of hypothesis for linear statistical models, the analysis of variance, analysis of enumerative data, and some topics in nonparametric statistics. Credit for this course will not be counted toward an advanced degree in mathematics.

MATH
554
Hours
3
Math Statistics I

Distributions of random variables, moments of random variables, probability distributions, joint distributions, and change of variable techniques.

MATH
555
Hours
3
Math Statistics II

Order statistics, asymptotic distributions, point estimation, interval estimation, and hypothesis testing.

MATH
557
Hours
3
Stochastics Processes I

Introduction to the basic concepts and applications of stochastic processes. Markov chains, continuous-time Markov processes, Poisson and renewal processes, and Brownian motion. Applications of stochastic processes including queueing theory and probabilistic analysis of computational algorithms.

Prerequisite(s): MATH 355
MATH
559
Hours
3
Stochastic Processes II

Continuation of MATH 557. Advanced topics of stochastic processes including Martingales, Brownian motion and diffusion processes, advanced queueing theory, stochastic simulation, and probabilistic search algorithms such as simulated annealing.

Prerequisite(s): MATH 457 or MATH 557
MATH
560
Hours
3
Intro Differential Geom

Introduction to basic classical notions in differential geometry: curvature, torsion, geodesic curves, geodesic parallelism, differential manifold, tangent space, vector field, Lie derivative, Lie algebra, Lie group, exponential map, and representation of a Lie group.

Prerequisite(s): MATH 586 or equivalent
MATH
565
Hours
3
Intro General Topology

Basic notions in topology that can be used in other disciplines in mathematics. Topics include topological spaces, open sets, closed sets, basis for a topology, continuous functions, separation axioms, compactness, connectedness, product spaces, quotient spaces, and metric spaces.

Prerequisite(s): MATH 586 or equivalent
MATH
566
Hours
3
Intro Algebraic Topology

Homotopy, fundamental groups, covering spaces, covering maps, and basic homology theory, including the Eilenberg Steenrod axioms.

MATH
570
Hours
3
Prin Modern Algebra I

Designed for graduate students who did not major in mathematics. A first course in abstract algebra. Topics include groups, permutations groups, Cayley's theorem, finite Abelian groups, isomorphism theorems and Lagrange’s theorem. Usually offered in the spring semester. Credit for this course will not be counted toward an advanced degree in mathematics.

Prerequisite(s): MATH 237
MATH
571
Hours
3
Prin Modern Algebra II

An introduction to ring theory. Topics include rings, polynomial rings, matrix rings, modules, fields and semi-simple rings. Usually offered in the fall semester.

Prerequisite(s): MATH 570
MATH
573
Hours
3
Abstract Algebra I

Fundamental aspects of group theory are covered. Topics include Sylow theorems, semi-direct products, free groups, composition series, nilpotent and solvable groups, and infinite groups.

MATH
574
Hours
3
Cryptography I

Introduction to a rapidly growing area of cryptography, an application of algebra, especially number theory.

MATH
580
Hours
3
Real Analysis I

Topics covered include measure theory, Lebesgue integration, convergence theorems, Fubini's theorem, and LP spaces.

MATH
583
Hours
3
Complex Analysis I

The basic principles of complex variable theory are discussed. Topics include Cauchy-Riemann equations, Cauchy's integral formula, Goursat's theorem, the theory of residues, the maximum principle, and Schwarz's lemma.

MATH
585
Hours
3
Intro Complex Variables

Some basic notions in complex analysis. Topics include analytic functions, complex integration, infinite series, contour integration, and conformal mappings. Credit for this course will not be counted if it is taken after MATH 583.

Prerequisite(s): MATH 227
MATH
586
Hours
3
Introduction to Real Analysis I

Rigorous development of the calculus of real variables. Topics include the topology of the real line, sequences and series, limits, limit suprema and infima, continuity, and differentiation.

Prerequisite(s): MATH 301
MATH
587
Hours
3
Introduction to Real Analysis II

A continuation of MATH 586. Topics include Riemann integration, sequences and series of functions, uniform convergence, power series, Taylor series. Optional topics may include the Reimann-Stieltjes integration, Weierstrass Approximation Theorem and the Arzela-Ascoli Theorem, metric spaces, multi-variable calculus.

Prerequisite(s): MATH 586
MATH
588
Hours
3
Theory Diff Equations I

Topics covered include existence and uniqueness of solutions, Picard theorem, homogenous linear equations, Floquet theory, properties of autonomous systems, Poincare-Bendixson theory, stability, and bifurcations.

Prerequisite(s): MATH 238 and MATH 586
MATH
591
Hours
3
Teaching College Math

Provides a basic foundation for teaching college-level mathematics; to be taken by graduate students being considered to teach undergraduate-level mathematics courses.

MATH
593
Hours
3
Collegiate Math Education Rsrc

This course is designed to enable students to understand and synthesize current research in college mathematics education involving subjects usually taught during the first two years of college. This will include a survey of a range of educational research models and will discuss qualitative, quantitative, and mixed methods research design in mathematics education research.

MATH
598
Hours
1-3
Non-Thesis Research

Research not related to thesis.

MATH
599
Hours
1-6
Thesis Research

No description available.

MATH
610
Hours
3
Iteratve Meth Linear Sys

Describes some of the best iterative techniques for solving large sparse linear systems.

MATH
611
Hours
3
Numerical Methods for Partial Differential Equations

Finite difference methods for hyperbolic, parabolic, and elliptical partial differential equations; consistency, convergence, and order of accuracy of finite difference schemes; stability analysis and the Courant-Friedrichs-Lewy (CFL) condition; numerical dispersion and dissipation; finite difference schemes in higher dimensions; implicit methods and alternating direction implicit (ADI) schemes; a brief introduction to additional topics, such as spectral methods, pseudo-spectral methods, finite volume methods, and finite element methods, may be offered at the discretion of instructor.

Prerequisite(s): MATH 512 or equivalent, and ability to program in a high-level programming language (MATLAB, C++, or FORTRAN).
MATH
642
Hours
3
Partial Differential Equations

This is an introductory course in partial differential equations. It covers the theory, methods of solution as well as applications related to the three main equations of mathematical physics, namely the Laplace’s equation, the heat equation and the wave equation. This course serves as the first part of the sequence for the qualifying exam in partial differential equations.

Prerequisite(s): MATH 238 and MATH 486 or permission of instructor
MATH
644
Hours
3
Singular Perturbations

This is an introductory course in perturbation methods. It covers both the theory and the methods of solution for a variety of equations ranging from algebraic, ordinary differential equations, to partial differential equations containing either small or large parameters. This course serves as the second part of the sequence for the qualifying exam in partial differential equations.

Prerequisite(s): MATH 238, some familiarity with ODE’s and PDE’s or permission of the instructor
MATH
661
Hours
3
Algebraic Topology I

In-depth study of homotopy and homology. The theory of cohomology is also introduced as are characteristic classes.

MATH
669
Hours
3
Topics in Topology

Introduction to basic knowledge of Geometry of Manifolds, especially to three and four dimensional manifolds: symplectic and contact geometry; handle body and Kirby calculus.

Prerequisite(s): MATH 565 and MATH566, or departmental approval
MATH
674
Hours
3
Abstract Algebra II

Fundamental aspects of ring theory are covered. Topics include Artinian rings, Wedderburn's theorem, idempotents, polynomial rings, matrix rings, Noetherian rings, free and projective modules, and invariant basis number.

MATH
677
Hours
3
Topics Algebra I

Content decided by instructor. Recent topics covered include linear groups, representation theory, commutative algebra and algebraic geometry, algebraic K-theory, and theory of polycyclic groups.

MATH
681
Hours
3
Real Analysis II

A continuation of MATH 580. Topics covered include basic theory of LP spaces, convolutions, Hahn decomposition, the Radon-Nikodym theorem, Riesz representation theorem, and Banach space theory, including the Hahn-Banach theorem, the open mapping theorem, and the uniform boundedness principle.

Prerequisite(s): MATH 580
MATH
684
Hours
3
Complex Analysis II

Typical topics covered include analytic functions, the Riemann mapping theorem, harmonic and subharmonic functions, the Dirichlet problem, Bloch's theorem, Schottley's theorem, and Picard's theorems.

MATH
686
Hours
3
Functional Analysis I

Topics covered in recent courses include Hilbert spaces, Riesz theorem, orthonormal bases, Banach spaces, Hahn-Banach theorem, open-mapping theorem, bounded operators, and locally convex spaces.

MATH
687
Hours
3
Functional Analysis II

A continuation of MATH 686. Topics may include spectral theory, Banach algebras, operator theory, unbounded operators.

Prerequisite(s): MATH 686
MATH
688
Hours
3
Seminar: Topics in Analysis

Advanced course in real analysis. Topics may include harmonic analysis (the Fourier transform, Hardy-Littlewood maximal operator, interpolation, singular integral operators, BMO and Hardy spaces, weighted norm inequalities) or analysis and PDEs (Sobolev spaces, weak solutions to PDEs, Lax-Milgram theory, the Fredholm alternative, existence and regularity for elliptic and parabolic equations).

Prerequisite(s): MATH 681
MATH
698
Hours
3-9
Non-Dissertation Research

This course will examine a topic not included in the student's dissertation.

MATH
699
Hours
1-12
Dissertation Research

No description available.