Mathematics Courses

MATH
501
Hours
1
Pathway to Graduate Studies in Mathematics

This course is to help students transition into graduate studies in math, and improve their understanding of math topics in introductory real analysis and advanced linear algebra. Credits for this course will not count toward any degree program.

MATH
502
Hours
2
Teaching Workshop

This course is to prepare graduate students to teach lower-division mathematics courses. Students will explore topics related to preparing for class, methods for engaging students and cultivating a learning-centered classroom environment, and methods for understanding and assessing student thinking. This course does not count towards any degree program.

MATH
503
Hours
3
Algebraic Structures for Secondary Teachers

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.

Prerequisite(s): C- or higher in MATH 237 and C- or higher in MATH 301
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.

Special Topics Course
MATH
505
Hours
3
Geometry for Secondary Teachers

This course will give an overview of geometry from a modern point of view. Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of complex numbers, and trigonometry will be emphasized.

Prerequisite(s): C- in MATH 403 or C- in MATH 503
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.

Special Topics Course
MATH
509
Hours
3
Data Analysis for Secondary Teachers

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): C- or higher in MATH 125 and C- or higher in 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 371 or MATH 572
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 237 and MATH 238 and MATH 537) or permission of instructor
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 572 or permission of instructor
MATH
521
Hours
3
Non-Linear Optimization Theory

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 572 or permission of instructor
MATH
530
Hours
3
Mathematical Foundations of Data Science and Programming

An introduction to the mathematical foundations of data science, machine learning, and programming. The fundamental roles of linear algebra and probability theory in data science will be explored. Heuristics for a variety of learning tasks, such as methods for clustering, classification, regression, or deep learning will be discussed in tandem with mathematical justifications for their use and effectiveness, as well as exercises illustrating their practical use in data analysis. Theoretical models for the feasibility of machine learning and for different types of learning problems will be introduced. Python programming will also be introduced.

Prerequisite(s): (MATH 355 and MATH 572) or permission of instructor
MATH
538
Hours
3
Topics in Mathematics

This is a general topics course in mathematics. The contents will vary depending on department needs.

Special Topics Course
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): MATH 343 and MATH 486 or MATH 586.
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.

Prerequisite(s): MATH 355
MATH
552
Hours
3
Math Stats W/Applictn II

This course considers further applications of the Neyman-Pearson lemma, likelihood ratio tests, Chi-square test for goodness of fit, estimation and test of hypotheses for linear statistical models, analysis of variance, analysis of enumerative data, and some topics in nonparametric statistics.

Prerequisite(s): MATH 551
MATH
554
Hours
3
Advanced Math Statistics I

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

Prerequisite(s): MATH 237 and MATH 355 and (MATH 486 or MATH 586) or permission of instructor
MATH
555
Hours
3
Advanced Math Statistics II

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

Prerequisite(s): MATH 554 or equivalent
MATH
557
Hours
3
Stochastic 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.

Prerequisite(s): MATH 565 or equivalent
MATH
570
Hours
3
Prin Modern Algebra I

This is 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 a Ph. D. in Mathematics.

Prerequisite(s): (MATH 237 and MATH 301) or MATH 371 or MATH 572
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
572
Hours
3
Advanced Linear Algebra

A proof-oriented classes covering the theory of vector spaces; bases and coordinates; linear transformations and matrices; determinants; eigenvalues, eigenvectors and diagonalization; inner product spaces; adjoint operators; the spectral theorem; and Jordan Canonical Form.

Prerequisite(s): (MATH 237 and MATH 301) pr permission of instructor
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.

Prerequisite(s): MATH 570
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 or MATH 247
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, Taylor polynomials.

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, topology of metric spaces, the Weierstrass approximation theorem, the Arzela-Ascoli theorem, derivatives of multivariable functions, implicit function theorem, inverse function theorem.

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

Preparation for future mathematics faculty for the teaching component of a faculty position at community colleges, four-year colleges or universities, comprehensive universities, or research universities. Topics include active learning strategies and course development, including syllabi, textbook selection, and assessment strategies.

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
597
Hours
3
Directed Individual Studies

This is a course on directed individual studies in mathematics. The contents will vary depending on department needs.

Prerequisite(s): permission of instructor
Special Topics Course
MATH
598
Hours
1-3
Non-Thesis Research

Research not related to thesis. Students are required to write a project report that summarizes their research activities and findings.

Prerequisite(s): Instructor Permission
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
638
Hours
3
Advanced Topics in Mathematics

This is an advanced topics course in mathematics. The contents will vary depending on department needs.

Prerequisite(s): permission of instructor
Special Topics Course
MATH
642
Hours
3
Partial Differential Equations I

This is an introductory course in partial differential equations. It covers the theory, methods of solution, and applications related to the three second order equations of mathematical physics (the Laplace’s equation, the heat equation, and the wave equation), and the nonlinear first order equations.

Prerequisite(s): MATH 238 and MATH 586 or equivalent or Instructor Permission
MATH
643
Hours
3
Partial Differential Equations II

Topics include a variety of techniques that are useful for finding explicit solutions for various partial differential equations (similarity solutions, transform methods, asymptotics, power series) and the fundamental theory of second order partial differential equations (Sobolev spaces, weak solutions, energy estimates, regularity, and maximum principles).

Prerequisite(s): MATH 642 and MATH 587 or Instructor Permission
MATH
648
Hours
3
Topics in Partial Differential Equations

This course concerns the modern theory of partial differential equations (PDE). We will concentrate on modern techniques in the theoretical study of linear and nonlinear PDEs. Topics include Sobolev spaces, weak solutions for second order elliptic, parabolic, and hyperbolic equations, the calculus of variations, nonvariational techniques, systems of conservation laws, fluid dynamics, and other topics decided by instructor.

Prerequisite(s): (MATH 541 or MATH 642) and MATH 580, or permission of 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
674
Hours
3
Abstract Algebra II

Topics include the theory of fields, including Galois theory, Noetherian and Artinian rings and their modules, polynomial rings, and free and projective modules.

Prerequisite(s): MATH 573
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.

Special Topics Course
MATH
680
Hours
3
Real Analysis I

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

Prerequisite(s): MATH 587
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
683
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.

Prerequisite(s): MATH 586
MATH
684
Hours
3
Complex Analysis II

We will cover various topics in Complex Analysis. Some possible topics include: Riemann mapping theorem, conformal mapping, normal families, Zalcman's lemma, Picard's theorem, Bloch's theorem, the monodromy theorem, elliptic functions, ultrahyperbolic metrics, harmonic measure, Hardy spaces, special functions.

Prerequisite(s): MATH 583
MATH
686
Hours
3
Functional Analysis I

An introduction to functional analysis. Topics include Banach spaces, duality, weak and weak* topologies, Banach-Alaoglu Theorem, Hilbert spaces, Riesz theorem, orthonormal bases, operator theory on Banach and Hilbert spaces, spectral theory, compact operators.

Prerequisite(s): MATH 681 and (MATH 583 or MATH 585)
MATH
688
Hours
3
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
Special Topics Course
MATH
697
Hours
3
Directed Individual Studies of Advanced Topics

This is a course on directed individual studies of advanced topics in mathematics. The contents will vary depending on department needs.

Prerequisite(s): permission of instructor
Special Topics Course
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.