[3 hours] This course is a review of operations with whole numbers, fractions, decimals, ratios, and percents. Problem solving techniques and how to study math are emphasized. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements.

MATH - 0910 ELEMENTARY ALGEBRA I

[4 hours] This course covers a review of operations with whole numbers, fractions,
decimals, ratios and percents. Also covered are integer operations, variables, algebraic expressions, graphs, and solving linear equations.
Problem solving techniques are emphasized. Course is not applicable toward the undergraduate Mathematics major requirements.

MATH - 0930 ALGEBRA CONCEPTS II

[3 hours] This course introduces the student to functions, solving systems of linear
equations, graphing, polynomials, and mathematics modeling. Problem solving techniques are emphasized. 7.5 week module. Course is not
applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0910 or placement

MATH - 0950 ELEMENTARY ALGEBRA II

[4 hours] This course introduces the student to junctions, solving systems of linear
equations, graphing, polynomials, rational and quadratic functions, rational numbers and mathematics modeling. Problem solving techniques are
emphasized. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0910 or placement

MATH - 0970 GEOMETRY CONCEPTS

[3 hours] This course covers lines, angles, similarity and congruence of polygons, areas of
polygons, volumes of solids, and constructions. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: MATH 0950 or placement

MATH - 0980 INTERMEDIATE ALGEBRA

[4 hours] Review of algebra, linear and quadratic equations, graphs, exponents and
radicals, exponential and log functions, simultaneous equations. P/NC credit only. No credit toward graduation. Course is not
applicable toward the undergraduate Mathematics major requirements. Prerequisite: Satisfactory placement test score, or satisfactory ACT score,
or MATH 0950.

MATH - 1010 APPLIED BUSINESS MATHEMATICS

[3 hours] Mathematics used in solving business problems related to simple and
compound interest, annuities, payroll, taxes, promissory notes, consumer credit, insurance, markup and markdown, mortgage loans, discounting,
financial statement ratios and break-even analysis. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: MATH 0900 or placement

MATH - 1180 MATHEMATICS FOR LIBERAL ARTS

[3 hours] A general liberal arts course for non-science students designed to
acquaint students with the nature of mathematics and applications such as probability, statistics, functions, and graphs. Course is not
applicable toward the undergraduate Mathematics major requirements. Prerequisite: College entrance requirements (Algebra I, Algebra II, and
Geometry) or MATH 0980.

MATH - 1210 MATHEMATICS FOR EDUCATION MAJORS I

[3 hours] Principles of elementary number theory, base systems, development of the
rational numbers, and problem solving techniques. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: Satisfactory placement test score or MATH 0980

MATH - 1220 MATHEMATICS FOR EDUCATION MAJORS II

[3 hours] Development of the real numbers, probability, statistics, informal
geometry, geometric figures and measurements. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: MATH 1210

MATH - 1260 MODERN BUSINESS MATHEMATICS I

[3 hours] Equations and their graphs, linear systems, vectors and matrices,
introduction to linear optimization, exponentials and logs, elementary probability, limits, functions, introductions to differential calculus.
Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: Satisfactory placement test score or satisfactory
ACT score or MATH 0980.

MATH - 1270 MODERN BUSINESS MATHEMATICS II

[3 hours] Continuation of differential calculus and integral calculus with
business applications. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 1260

MATH - 1320 COLLEGE ALGEBRA

[3 hours] Number system; elementary theory of equations and inequalities; functions and
relations; exponentials and logarithms; systems of equations and topics in analytic geometry. Course is not applicable toward the
undergraduate Mathematics major requirements. No credit given for students who have credit for MATH 1340. Prerequisite: Satisfactory placement
test score or satisfactory ACT score or MATH 0980.

MATH - 1330 TRIGONOMETRY

[3 hours] Definitions and graphs of trigonometric functions and their inverses, solving
trigonometric equations, applications, and topics in analytic geometry. Course is not applicable toward the undergraduate Mathematics major
requirements. No credit given for students who have credit for MATH 1340. Prerequisite: Satisfactory placement test or satisfactory ACT score or
MATH 0980.

MATH - 1340 COLLEGE ALGEBRA AND TRIGONOMETRY

[4 hours] Functions and graphs, exponential and logarithmic functions,
trigonometric functions and applications, systems of equations, and topics in analytic geometry. No credit for students who have credit for
MATH 1320 or 1330. Prerequisite: Three years of high school math and a course in trigonometry and either satisfactory placement test score
or satisfactory ACT score or MATH 0980.

MATH - 1750 MATHEMATICS FOR THE LIFE SCIENCES I

[4 hours] Definitions of trigonometric functions, solving trigonometric
equations, functions, limits and derivatives, exponential and logarithmic functions, and applications. Course is not applicable toward the
undergraduate Mathematics major requirements. Prerequisite: Satisfactory placement test score or satisfactory ACT score or MATH 0980.

MATH - 1760 MATHEMATICS FOR THE LIFE SCIENCES II

[3 hours] Indefinite and definite integrals, probability, functions of
several variables, least squares, differential equations. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: MATH 1750.

MATH - 1780 INTRODUCTION TO MAPLE

[1 hour] Brief review of the computer algebra system Maple; graphing; simplifying
algebraic expressions; finding solutions of equations symbolically, graphically, and numerically; various typical problems from precalculus and
beginning calulus. Prerequisite: MATH 1340 or MATH 1320 and 1330 or 4 years of high school math and passing score on the placement
exams

MATH - 1850 SINGLE VARIABLE CALCULUS I

[4 hours] Limits, differentiation, Fundamental Theorem of Calculus, Mean Value
Theorem, curve sketching, maxima/minima, definite and indefinite integrals, applications. Course is not applicable toward the undergraduate
Mathematics major requirements. Prerequisite: MATH 1340, or 1320 & 1330 or a satisfcatory placement test score.

MATH - 1860 SINGLE VARIABLE CALCULUS II

[4 hours] Inverse functions, techniques and applications of integration, polar
coordinates, sequences and series. Prerequisite: MATH 1850.

MATH - 1880 SINGLE VARIABLE CALCULUS II USING MAPLE

[4 hours] Inverse functions, techniques and applications of integration,
polar coordinates, sequences and series. Maple is used to visualize concepts and to analyze, solve, and interpret problems graphically,
symbolically, and numerically. Prerequisite: MATH 1850. Corequisite: MATH 1780

MATH - 1890 ELEMENTARY LINEAR ALGEBRA

[3 hours] Matrix algebra, systems of linear equations, determinants, vector spaces,
linear transformations, eigenvalues and eigenvectors, and applications. Prerequisite: MATH 1860

MATH - 1920, 1930 HONORS CALCULUS I and II

[4 hours] Theory and applications of derivatives and integrals of a function of
one variable. Prerequisite: For MATH 1920: satisfactory ACT score and satisfactory trigonometry placement score; for MATH 1930: MATH
1920.

MATH - 1960 TRANSITIONAL MATHEMATICS COURSES

[1-4 hours] Mathematics courses for the following sections:

:022
Transitional Mathematics for Education Majors II. [2 hours] The rational numbers; decimals and real numbers; probability and
statistics. Prerequisite: MATH 121

:023 Transitional Mathematics for Education Majors III. [2 hours] Informal
geometry, geometric figures, and measurements. Prerequisite: MATH 122

MATH - 1980 TOPICS IN MATHEMATICS

[1-4 hours] Selected topics in mathematics. Prerequisite: Varies with topic.

MATH - 2280 INTRODUCTION TO COMPUTING

[3 hours] An overview of the role of microcomputers and information systems. Provides
training in word processing, presentation graphics, and spreadsheets or problem solving. Course is not applicable toward the undergraduate
Mathematics major requirements. Prerequisite: MATH 1180 or equivalent.

MATH - 2450 CALCULUS FOR ENGINEERING TECHNOLOGY I

[4 hours] Differential calculus of algebraic and trigonometric functions,
including limits, curve sketching, motion, maxima/minima, related rates, integral calculus of algebraic functions. Prerequisite: MATH 1320,
MATH 1330, passing the Prerequisite Skills Test.

MATH - 2460 CALCULUS FOR ENGINEERING TECHNOLOGY II

[4 hours] Methods of integration and use of integral tables, numerical
integration, applications of integration, transcendental functions, limits involving infinity, introduction to polar coordinates, and complex
numbers. Prerequisite: MATH 2450, passing the Prerequisite Skills Test.

MATH - 2600 INTRODUCTION TO STATISTICS

[3 hours] An introduction to descriptive and inferential statistical methods
including point and interval estimation, hypothesis testing, and regression. No credit allowed if taken after MATH 3610 or 4680; credit not
allowed for both MATH 2600 and 2630. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH
0980, 1180 or equivalent.

MATH - 2620 DISCRETE PROBABILITY

[3 hours] Sample spaces, events, counting techniques, probability distributions and their
applications. No credit if taken after 4680. Course is not applicable toward the undergraduate Mathematics major requirements.
Prerequisite: MATH 0980, 1180, or equivalent.

MATH - 2630 STATISTICS FOR BUSINESS AND ECONOMICS

[3 hours] An introduction to descriptive and inferential statistical
methods, including numerical and graphical data description, basic probability concepts and distributions, point and interval estimation and
hypothesis testing. Credit not allowed for both MATH 2600 & 2630. Course is not applicable toward the undergraduate Mathematics major
requirements. Prerequisite: MATH 1270

MATH - 2850 ELEMENTARY MULTIVARIABLE CALCULUS

[4 hours] Geomery of functions of several variables, partial differentiation,
multiple integrals, vector algebra and calculus (including Theorems of Green, Gauss, and Stokes), and applications. Prerequisite: MATH
1860.

MATH - 2880 ELEMENTARY MULTIVARIABLE CALCULUS USING MAPLE

[4 hours] Geometry of functions of several variables,
partial differentiation, multiple integrals, vector algebra, and calculus (including Theorems of Green, Gauss and Stokes) and applications. Maple
is used to solve problems graphically, symbolically and numerically. Prerequisite: MATH 1860 or MATH 1880 Corequisite: MATH 1780

MATH - 2890 NUMERICAL METHODS AND LINEAR ALGEBRA

[3 hours] Topics include: matrices, characteristic roots, solution of
linear and nonlinear equations, curve fitting, integration, differentiation, and numerical solution of ordinary differential equations. MATLAB is
introduced and used to analyze problems. Prerequisite: MATH 1850 Corequisite: MATH 1860

MATH - 2950 HONORS CALCULUS III

[4 hours] Theory and applications of the calculus of functions of two or more variables. The
fundamental theorems of vector calculus. Prerequisite: MATH 1930 or consent of instructor.

MATH - 3000 SYMBOLIC LOGIC

[3 hours] A study of propositional and predicate logic, the symbolic techniques used to evaluate
deductive arguments. Topics may include computability, set theory, Bayesianism and other formal systems with mathematical or philosophical
relevance. Prerequisite: MATH 1180 or PHIL 1100

MATH - 3190 INTRODUCTION TO MATHEMATICAL ANALYSIS

[3 hours] Designed to prepare students for higher mathematics. Techniques
and fundamentals of proving theorems including proofs by induction. The course will include elementary logic and set theory, a discussion
of the real number system and the proofs of the basic theorems of differential calculus. Prerequisite: MATH 1860

MATH - 3200 NUMBER THEORY

[3 hours] Divisibility, congruences, diophantine equations, numerical functions, quadratic
reciprocity. Prerequisite: MATH 3190

MATH - 3320 INTRODUCTION TO ABSTRACT ALGEBRA

[3 hours] Sets and mappings, integers, groups, rings, and applications.
Prerequisite: MATH 3190

MATH - 3440, 3450 FUNDAMENTALS OF MODERN GEOMETRY I

[3 hours] Primarily for students in secondary education. Euclidean
geometry from a modern viewpoint, constructions, and transformations. Prerequisite: for MATH 3440: MATH 1860. Prerequisite: for MATH
3450: MATH 3440

MATH - 3510 HISTORY OF MATHEMATICS

[3 hours] Contributions to the development of mathematics by various groups and
individuals from the earliest history to the present, with special emphasis on the elementary branches: arithmetic, algebra, geometry and
calculus. Prerequisite: MATH 1860

MATH - 3610 STATISTICAL METHODS I

[3 hours] Basic probability, sampling, descriptive statistics, statistical inference,
regression, correlation, analysis of variance, goodness of fit, model formulation and testing. Prerequisite: MATH 1860, 3190 or consent of
instructor

MATH - 3620 STATISTICAL METHODS II

[3 hours] Multiple regression, analysis of covariance, standard experimental designs,
contingency tables, nonparametric methods, and methods for sample surveys. Prerequisite: MATH 3610

MATH - 3820 HONORS ELEMENTARY DIFFERENTIAL EQUATIONS

[3 hours] Theory, applications, and systems of ordinary differential
equations. Prerequisite: MATH 2950 or consent of instructor

MATH - 3860 ELEMENTARY DIFFERENTIAL EQUATIONS

[3 hours] An introduction to the analysis and solution of ordinary
differential equations with emphasis on the fundamental techniques for solving linear differential equations. Prerequisite: MATH 2850

MATH - 3880* ELEMENTARY DIFFERENTIAL EQUATIONS USING MAPLE

[3 hours] An introduction to the analysis and solution of
ordinary differential equations with emphasis on the fundamental techniques for solving linear equations. MAple is used to solve problems
graphically, symbolically and numerically. Prerequisite: MATH 2850 or MATH 2880 Corequisite: MATH 1780

*course is pending final
approval

MATH - 3920 JUNIOR READINGS

[1 - 3 hours] Selected subjects in mathematics of special interest to students and the
professor. Prerequisite: Consent of department

MATH - 4290 INTRODUCTION TO SET THEORY

[3 hours] Sets, relations, functions, axiom of choice, Zorn�s lemma, well-ordering
theorem, cardinal and ordinal numbers, construction of the real numbers. Prerequisite: MATH 3190

MATH - 4300 LINEAR ALGEBRA I

[3 hours] Theory of vector spaces and linear transformations, including such topics as
matrices, determinants, inner products, eigenvalues and eigenvectors, and rational and Jordan canonical forms. Prerequisite: MATH 3190

MATH - 4310 LINEAR ALGEBRA II

[3 hours] Hermitian and normal operators, multilinear forms, spectral theorem and other
topics. Prerequisite: MATH 4300

MATH - 4330 ABSTRACT ALGEBRA I

[3 hours] Arithmetic of the integers, unique factorization and modular arithmetic; group
theory including normal subgroups, factor groups, cyclic groups, permutations, homomorphisms, the isomorphism theorems, abelian groups, and
p-groups. Prerequisite: MATH 3190

MATH - 4340 ABSTRACT ALGEBRA II

[3 hours] Ring theory including integral domains, field of quotients, homomorphisms, ideals,
Euclidean domains, polynomial rings, vector spaces, roots of polynomials, and field extensions. Prerequisite: MATH 4330

MATH - 4350 APPLIED LINEAR ALGEBRA

[3 hours] Matrices, systems of equations, vector spaces, linear transformations,
determinants, eigenvalues and eigenvectors, generalized inverses, rank, numerical methods and applications to various areas of science.
Prerequisite: MATH 1890

MATH - 4380 DISCRETE STRUCTURES AND ANALYSIS OF ALGORITHMS

[3 hours] Discrete mathematical structures for applications in
computer science such as graph theory, combinatorics, and groups theory, asymptotics, recurrence relations, and analysis of algorithms.
Prerequisite: Math 3320 or 4330

MATH - 4390 THEORY OF COMPUTATION

[3 hours] Theory of automata and formal languages, computability by Turing machines and
recursive functions, uncomputability, NP-Hard and NP-Complete problems. Prerequisite: MATH 4380

MATH - 4450 INTRODUCTION TO TOPOLOGY I

[3 hours] Metric spaces, topological spaces, continuous maps, bases and subbases,
closure and interior operators, products, subspaces, sums, quotients, separation axioms, compactness and local compactness. Prerequisite:
MATH 3190

MATH - 4460 INTRODUCTION TO TOPOLOGY II

[3 hours] Connectedness and local connectedness, convergence, metrization, function
spaces. The fundamental groups and its properties, covering spaces, classical applications, e.g. Jordan Curve Theorem, Fundamental Theorem
of Algebra, Brouwer�s Fixed Point Theorem.Prerequisite: Math 4450, 3320 or 4330

MATH - 4540 CLASSICAL DIFFERENTIAL GEOMETRY I

[3 hours] Smooth curves in Euclidean space including the Frenet formulae.
Immersed surfaces with the Gauss map, principal curvatures, and the fundamental forms. Special surfaces including ruled surfaces and
minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium. Prerequisite: MATH 3860

MATH - 4550 CLASSICAL DIFFERENTIAL GEOMETRY II

[3 hours] Tensors, vector fields, and the Cartan approach to surface theory,
Bonnet�s Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics parallel transport, and Jacobi Fields.
Theorems of a global nature such as Hilbert�s Theorem or the Theorem of Hopf-Rinow. Prerequisite: MATH 4540

MATH - 4600 APPLICATIONS OF STATISTICS I

[3 hours] Real data applications of statistical methods. Emphasis is placed
on exploratory data analysis and the use of computing facilities to analyze data and produce statistical reports. Statistical packages used
include: MINITAB, SAS, and/or S-PLUS; programming is performed in C or Fortran. Prerequisite: Permission of instructor

MATH - 4610 APPLICATIONS OF STATISTICS II

[3 hours] Continuation of Applications of Statistics I. Prerequisite: MATH
4600

MATH - 4630 THEORY AND METHODS OF SAMPLE SURVEYS

[3 hours] The mathematical basis to estimation in various sampling
contexts, including probability proportional to size sampling, stratified sampling, two-stage cluster sampling, and double sampling.
Prerequisite: MATH 4680 or consent of instructor. Corequisite: MATH 4690

MATH - 4640 STATISTICAL COMPUTING

[3 hours] Error analysis of statistical algorithms. Numerical linear algebra for
linear models. Approximation methods for distribution function probabilities and quantiles. Uniform and non-uniform random number
generation. Introduction to simulation methods. Prerequisite: Permission of instructor

MATH - 4660 APPLIED PROBABILITY

[3 hours] The basic probability models of applied mathematics and physics, including random
walks, Markov chains, branching processes, renewal processes, random graphs, and queuing. Prerequisite: MATH 4680 and 4300, or 4350

MATH - 4680 INTRODUCTION TO THEORY OF PROBABILITY

[3 hours] Probability spaces, random variables, probability distributions,
moments and moment generating functions, limit theorems, transformations, and sampling distributions. Prerequisite: MATH 3190 or consent of
instructor, and MATH 4350

MATH - 4690 INTRODUCTION TO MATHEMATICAL STATISTICS

[3 hours] Sampling distributions, point and interval estimation,
hypothesis testing, regression and analysis of variance. Prerequisite: MATH 4680

MATH - 4710 METHODS OF NUMERICAL ANALYSIS I

[3 hours] Floating point arithmetic; polynomial interpolation; numerical
solution of nonlinear equations; Newton�s method. Likely topics include: numerical differentiation and integration; solving systems of
linear equations; Gaussian elimination; LU decomposition; Gauss-Seidel method. Prerequisite: MATH 3860 and a computer programming course,
or consent of instructor

MATH - 4720 METHODS OF NUMERICAL ANALYSIS II

[3 hours] Likely topics include: Computation of eigenvalues and eigenvectors;
solving systems of nonlinear equations; least squares approximations; rational approximations; cubic splines; fast Fourier transforms; numerical
solutions to initial value problems; ordinary and partial differential equations. Prerequisite: MATH 4710

MATH - 4740 ADVANCED APPLIED MATHEMATICS I

[3 hours] Series and numerical solutions to ordinary differential equations,
special functions, orthogonal functions, Sturm-Liouville problems, self-adjointness, vector analysis. Prerequisite: MATH 3860

MATH - 4750 ADVANCED APPLIED MATHEMATICS II

[3 hours] Continuation of vector analysis, introduction to complex analysis,
partial differential equations, Fourier series and integrals. Prerequisite: MATH 4740

MATH - 4780 ADVANCED CALCULUS

[3 hours] Extrema for functions of one or more variables, Lagrange multipliers, indeterminate
forms, inverse and implicit function theorems, uniform convergences, power series, transformations, Jacobians, multiple integrals.
Prerequisite: MATH 2850

MATH - 4790 APPLIED OPTIMIZATION

[3 hours] Introduction to finite dimensional constrained optimization, linear and nonlinear
programming, Lagrange multiplier rules, equality and inequality constraints, normality, Karush-Kuhn-Tucker Theorem, convergence criteria for
penalty methods, steepest descent, simplex method for linear programming. Prerequisite: Math 3860, 1890

MATH - 4800 ORDINARY DIFFERENTIAL EQUATIONS

[3 hours] Modern theory of differential equations; transforms and matrix
methods; existence theorems and series solutions; and other selected topics. Prerequisite: MATH 3860

MATH - 4810 PARTIAL DIFFERENTIAL EQUATIONS

[3 hours] First and second order equations; numerical methods; separation of
variables; solutions of heat and wave equations using eigenfunction techniques; and other selected topics. Prerequisite: MATH 3860 and
consent of instructor

MATH - 4820 INTRODUCTION TO REAL ANALYSIS I

[3 hours] A rigorous treatment of the Calculus in one and several variables.
Topics to include: the real number system; sequences and series; elementary metric space theory including compactness, connectedness and
completeness; the Riemann Integral. Prerequisite: MATH 3190

MATH - 4830 INTRODUCTION TO REAL ANALYSIS II

[3 hours] Differentiable functions on Rn; the Implicit and Inverse Function
Theorems; sequences and series of continuous functions; Stone-Weierstrass Theorem; Arzela-Ascoli Theorem; introduction to measure theory;
Lebesgue integration; the Lebesque Dominated Convergence Theorem. Prerequisite: MATH 4820

MATH - 4850 OPERATIONAL MATHEMATICS

[3 hours] Theory of Laplace, Fourier and other transforms; use of complex variable
theory for inversions; applications. Prerequisite: MATH 4880 or equivalent

MATH - 4860 CALCULUS OF VARIATIONS AND OPTIMAL CONTROL I

[3 hours] Conditions for an extrema (Euler�s equations, Erdman
corner conditions, conditions of Legendre, Jacobi, and Weierstrass, fields of extremals, Hilbert�s invariant integral); Raleigh-Ritz method;
isoparametric problems; Lagrange, Mayer-Bolza problems. Recommended: MATH 4820. Prerequisite: MATH 1890

MATH - 4870 CALCULUS OF VARIATIONS AND OPTIMAL CONTROL II

[3 hours] Pontryagin�s maximum principle; necessary and sufficient
conditions for optimal control, controllability, time optimal control, existence of optimal controls, relationship to the calculus of variations.
Prerequisite: MATH 4860

MATH - 4880 COMPLEX VARIABLES

[3 hours] Analytic functions; Cauchy�s theorem; Taylor and Laurent series; residues; contour
integrals; conformal mappings, analytic continuation, and applications. Prerequisite: MATH 3860

MATH - 4900 SENIOR SEMINAR

[1 - 3 hours] Seminar on a topic not usually covered in a course. Library research and
paper to be expected. Prerequisite: consent of department

MATH - 4920 SENIOR READINGS

[1 - 3 hours] Selected subjects in mathematics of special interest to students and the
professor. (By arrangement with professor and student.) Prerequisite: Consent of instructor

MATH - 5300/7300 LINEAR ALGEBRA I

[3 hours] Theory of vector spaces and linear transformations, including such topics as
matrices, determinants, inner products, eigenvalues and eigenvectors, and rational and Jordan canonical forms. Prerequisite: MATH
3190

MATH - 5310/7310 LINEAR ALGEBRA II

[3 hours] Hermitian and normal operators, multilinear forms, spectral theorem and other
topics. Prerequisite: MATH 5300

MATH - 5330/7330 ABSTRACT ALGEBRA I

[3 hours] Arithmetic of the integers, unique factorization and modular arithmetic; group
theory including normal subgroups, factor groups, cyclic groups, permutations, homomorphisms, the isomorphism theorems, abelian groups and
p-groups. Prerequisite: MATH 3190

MATH - 5340/7340 ABSTRACT ALGEBRA II

[3 hours] Ring theory including integral domains, field of quotients, homomorphisms,
ideals, Euclidean domains, polynomial rings, vector spaces, roots of polynomials, and field extensions. Prerequisite: MATH 5330

MATH - 5350/7350 APPLIED LINEAR ALGEBRA

[3 hours] Matrices, systems of equations, vector spaces, linear
transformations, determinants, eigenvalues and eigenvectors, generalized inverses, rank, numerical methods and applications to various areas of
science. Prerequisite: MATH 1890

MATH - 5380/7380 DISCRETE STRUCTURES AND ANALYSIS ALGORITHMS

[3 hours] Discrete mathematical structures for applications in
computer science such as graph theory, combinatorics, and groups theory, asymptotics, recurrence relations, and analysis of algorithms.
Prerequisite: MATH 3320 or 5330

MATH - 5390/7390 THEORY OF COMPUTATION

[3 hours] Theory of automata and formal languages, computability by Turing machines
and recursive functions, uncomputability, NP-Hard and NP-Complete problems. Prerequisite: MATH 5380

MATH - 5450/7450 INTRODUCTION TO TOPOLOGY I

[3 hours] Metric spaces, topological spaces, continuous maps, bases and
sub-bases, closure and interior operators, products, subspaces, sums, quotients, separation axioms, compactness and local compactness.
Prerequisite: MATH 3190

MATH - 5460/7460 INTRODUCTION TO TOPOLOGY II

[3 hours] Connectedness and local connectedness, convergence, metrization,
function spaces. The fundamental groups and its properties, covering spaces, classical applications, e.g. Jordan Curve Theorem, Fundamental
Theorem of Algebra, Brouwer�s Fixed Point Theorem. Prerequisite: MATH 5450 and corequisite MATH 3320 or 5330

MATH - 5540/7540 CLASSICAL DIFFERENTIAL GEOMETRY I

[3 hours] Smooth curves in Euclidean space including the Frenet formulae.
Immersed surfaces with the Gauss map, principal curvatures, and the fundamental forms. Special surfaces including ruled surfaces and
minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium. Prerequisite: MATH 3860

MATH - 5550/7550 CLASSICAL DIFFERENTIAL GEOMETRY II

[3 hours] Tensors, vector fields, and the Cartan approach to surface
theory, Bonnet�s Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics, parallel transport, and Jacobi
Fields. Theorems of a global nature such as Hilbert�s Theorem or the Theorem of Hopf-Rinow. Prerequisite: MATH 5540

MATH - 5600/7600 APPLICATIONS OF STATISTICS I

[2 hours] Real data applications of statistical methods. Emphasis is placed on
exploratory data analysis and the use of computing facilities to analyze data and produce statistical reports. Statistical packages used include
MINITAB, SAS, and S-Plus. Prerequisite: Consent of instructor.

MATH - 5610/7610 APPLICATIONS OF STATISTICS II

[2 hours] Continuation of Applications of Statistics II. Prerequisite:
MATH 5600

MATH - 5620 /7620 LINEAR STATISTICAL MODELS

[3 hours] Multiple regression, analysis of variance and covariance, general linear
models and model building for linear models. Experimental designs include one-way, randomized block, latin square, factorial and nested designs.
Prerequisite: MATH 6650 or consent of instructor.

MATH - 5630/7630 THEORY AND METHODS OF SAMPLE SURVEYS

[3 hours] The mathematical basis to estimation in various sampling
contexts, including probability proportional to size sampling, stratified sampling, two-stage cluster sampling, and double sampling, is
developed. Prerequisite: MATH 5680 or consent of instructor. Corequisite: MATH 5690, or 6650.

MATH - 5640/7640 STATISTICAL COMPUTING

[3 hours] Error analysis of statistical algorithms. Numerical linear algebra
for linear models. Approximation methods for distribution function probabilities and quantiles. Uniform and non-uniform random number
generation. Introduction to simulation methods. Prerequisite: Consent of instructor

MATH - 5660/7660 APPLIED PROBABILITY

[3 hours] The basic probability models of applied mathematics and physics, including
random walks, Markov chains, branching processes, renewal processes, random graphs, and queuing. Prerequisite: MATH 5680 and 5300 or 5350

MATH - 5670/7670 DESIGN OF EXPERIMENTS

[3 hours] Confounding, fractional replication, complex designs, response surface
designs. Prerequisite: MATH 5620

MATH - 5680/7680 INTRODUCTION TO THEORY OF PROBABILITY

[3 hours] Probability spaces, random variables, probability
distributions, moments and moment generating functions, limit theorems, transformations, and sampling distributions. Prerequisite: MATH
3190 or consent of instructor and MATH 5350

MATH - 5690/7690 INTRODUCTION TO MATHEMATICAL STATISTICS

[3 hours] Sampling distributions, point estimation, interval
estimation, hypothesis testing, regression, and analysis of variance. Prerequisite: MATH 5680

MATH - 5710/7710 METHODS OF NUMERICAL ANALYSIS I

[3 hours] Floating point arithmetic; polynomial interpolation; numerical
solution of nonlinear equations; Newton�s method. Likely topics include: numerical differentiation and integration; solving systems of
linear equations; Gaussian elimination; LU decomposition; Gauss-Seidel method. Prerequisite: MATH 3860 and a computer programming course or
consent of instructor.

MATH - 5720/7720 METHODS OF NUMERICAL ANALYSIS II

[3 hours] Likely topics include: Computation of eigenvalues and
eigenvectors; solving systems of nonlinear equations; least squares approximations; rational approximations; cubic splines; fast Fourier
transforms; numerical solutions to initial value problems; ordinary and partial differential equations. Prerequisite: MATH 5710

MATH - 5740/7740 ADVANCED APPLIED MATHEMATICS I

[3 hours] Series and numerical solutions to ordinary differential equations,
special functions, orthogonal functions, Sturm-Liouville Problems, self-adjointness, vector analysis. Prerequisite: MATH 3860

MATH - 5750/7750 ADVANCED APPLIED MATHEMATICS II

[3 hours] Continuation of vector analysis, introduction to complex
analysis, partial differential equations, Fourier series and integrals. Prerequisite: MATH 5740

MATH - 5780/7780 ADVANCED CALCULUS

[3 hours] Extrema for functions of one or more variables, Lagrange multipliers,
indeterminate forms, inverse and implicit function theorems, uniform convergences, power series, transformations, Jacobians, multiple integrals.
Prerequisite: MATH 2850

MATH - 5790/7790 APPLIED OPTIMIZATION

[3 hours] Introduction to finite dimensional constrained optimization, linear and
nonlinear programming, Lagrange multiplier rules, quality and inequality constraints, normality, Karush-Kuhn-Tucker Theorem, convergence criteria
for penalty methods, steepest descent, simplex method for linear programming. Prerequisite: MATH 3860, 1890

MATH - 5800/7800 ORDINARY DIFFERENTIAL EQUATIONS

[3 hours] Modern theory of differential equations; transforms and matrix
methods; existence theorems and series solutions; and other selected topics. Prerequisite: MATH 3860

MATH - 5810/7810 PARTIAL DIFFERENTIAL EQUATIONS

[3 hours] First and second order equations; numerical methods; separation of
variables; solutions of heat and wave equations using eigenfunction techniques; and other selected topics. Prerequisite: MATH 3860 and
consent of instructor

MATH - 5820/7820 INTRODUCTION TO REAL ANALYSIS I

[3 hours] A rigorous treatment of the Calculus in one and several
variables. Topics to include: the real number system; sequences and series; elementary metric space theory including compactness,
connectedness and completeness; the Riemann Integral. Prerequisite: MATH 3190

MATH - 5830/7830 INTRODUCTION TO REAL ANALYSIS II

[3 hours] Differentiable functions on Rn; the Implicit and Inverse
Function Theorems; sequences and series of continuous functions; Stone-Weierstrass Theorem; Arsela-Ascoli Theorem; introduction to measure
theory; Lebesgue integration; the Lebesgue Dominated Convergence Theorem. Prerequisite: MATH 5820

MATH - 5850/7850 OPERATIONAL MATHEMATICS

[3 hours] Theory of Laplace, Fourier and other transforms; use of complex variable
theory for inversions; applications. Prerequisite: MATH 5880

MATH - 5860/7860 CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY I

[3 hours] Conditions for an extreme (Euler�s equations,
Erdman corner conditions, conditions of Legendre, Jacobi, and Weierstrass, fields of extremals, Hilbert�s invariant integral); Raleigh-Ritz
method; isoperimetric problems; Lagrange, Mayer-Bolza problems. Prerequisite: MATH 1890; Recommended MATH 5820

MATH - 5870/7870 CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY II

[3 hours] Pontryagin�s maximum principle; necessary
and sufficient conditions for optimal control, controllability, time optimal control, existence of optimal controls, relationship to the calculus
of variations. Prerequisite: MATH 5860

MATH - 5880/7880 COMPLEX VARIABLES

[3 hours] Analytic functions; Cauchy�s theorem; Taylor and Laurent series; residues;
contour integrals; conformal mappings, analytic continuation, and applications. Prerequisite: MATH 3860

MATH - 5980/7980 TOPICS IN MATHEMATICS

[3 hours] Special topics in mathematics.

MATH - 6150/8150 APPLIED FUNCTIONAL ANALYSIS

[3 hours] Normed linear spaces, Banach and Hilbert spaces, linear operators and
their spectrum, spectral analysis, illustrative examples from science and engineering. Prerequisite: MATH 5300

MATH - 6180/8180 LINEAR AND NONLINEAR PROGRAMMING

[3 hours] Simplex algorithm, ellipsoidal algorithm, Karmarkar�s method,
interior point methods, elementary convex analysis, optimality conditions and duality for smooth problems, convex programming, algorithms and
their convergence. Prerequisite: MATH 5820

MATH - 6190/8190 INFINITE DIMENSIONAL OPTIMIZATION

[3 hours] Introduction to nonlinear analysis, abstract optimization
problems on abstract spaces, applications to calculus of variations, optimal control theory, and game theory. Prerequisite: MATH 6150 or
MATH 6810 or equivalent

MATH - 6300/8300 and 6310/8310 ALGEBRA I and II

[3 hours each] Groups, Sylow�s theorems, permutation groups, nilpotent and
solvable groups, Abelian groups, rings, unique factorization domains, fields and field extensions, Galois theory, separable extensions of fields,
modules, Noetherian and Artinian rings, tensor products, primitive and semisimple rings. Wedderburn-Artin theorem. Prerequisite: MATH 5340
or equivalent

MATH - 6320/8320 and 6330/8330 RING THEORY I and II

[3 hours each] Topics in ring theory chosen from among radical theory,
rings of quotients, Goldie�s Theorem, chain conditions, dimensions of rings, module theory, topics in commutative rings, group rings, enveloping
algebras, almost split sequences, PI-rings, division rings, self injective rings, and ordered rings. Prerequisite: MATH 6310

MATH - 6340/8340 and 6350/8350 GROUP THEORY I and II

[3 hours each] Topics in group theory of wide applicability and of
fundamental importance. Topics chosen from among presentations, free products amalgams, permutation groups, trees and graphs, solvability,
nilpotence, linear representations, homological algebra, cohomology, character theory, classical groups, Lie rings, Sylow systems,
Schur-Zassenhaus theorem, linear methods, local analysis, finiteness conditions. Prerequisite: MATH 6310

MATH - 6400/8400 and 6410/8410 TOPOLOGY I and II

[3 hours each] Topological spaces, continuous functions, compactness,
product spaces, Tychonov theorem, quotient spaces, local compactness, homotopy, fundamental group, covering spaces, homology theory, excision,
homological algebra, Brouwer fixed point theorem, cohomology, smooth manifolds, orientation, tangent bundles, Sard�s theorem, degree theory.
Prerequisite: MATH 5450 or equivalent

MATH - 6420/8420 and 6430/8430 GENERAL TOPOLOGY I and II

[3 hours each] Categorical properties of and constructions in
topological spaces, compactness, connectedness, dimension theory, metrization, compactification and proximity spaces, uniform spaces,
completeness and completions, rings of continuous functions. Prerequisite: MATH 6400

MATH - 6440/8440 and 6450/8450 DIFFERENTIAL GEOMETRY I and II

[3 hours each] Differentiable structures on manifolds, vector
fields and flows, tensor bundles, distributions and Frobenius theorem, metric geometry, differential forms, Stokes theorem, Lie groups,
connections on manifolds, geodesics, geometry of tangent bundle, curvature, torsion, exponential map, Riemannian geometry, geometry of
submanifolds and submersion, relative Gauss-Bonnet theorem, homogeneous and symmetric spaces, topics in differential geometry.
Prerequisite: MATH 6410

MATH - 6460/8460 and 6470/8470 ALGEBRAIC TOPOLOGY I and II

[3 hours each] Simplicial and cellular complexes, simplicial and
cellular homology, universal coefficient theorem, Kunneth theorem, cohomology theories, cohomology operations, duality on manifolds, general
homotopy theory, fibration and cofibration, higher homotopy groups, weak homotopy equivalence,Hurewicz theorem, Eilenberg-Maclane spaces,
classifying spaces, spectral sequences. Prerequisite: MATH 6410

MATH - 6500/8500 ORDINARY DIFFERENTIAL EQUATIONS

[3 hours] Existence, uniqueness and dependence on initial conditions and
parameter, nonlinear planar systems, linear systems, Floquet theory, second order equations, Sturm-Liouville theory. Prerequisite: MATH
5830 or equivalent

MATH - 6510/8510 PARTIAL DIFFERENTIAL EQUATIONS

[3 hours] First order quasi-linear systems of partial differential
equations, boundary value problems for the heat and wave equation, Dirichlet problem for Laplace equation, fundamental solutions for Laplace,
heat and wave equations. Prerequisite: MATH 5830 or equivalent

MATH - 6520/8520 and 6530/8530 DYNAMICAL SYSTEMS I and II

[3 hours each] Flow-box theorem, Poincare maps, attractors, w
limit sets, Lyapunov stability, invariant manifolds, Hamiltonian systems and symplectic manifolds, local bifurcations of vector fields,
homoclinic orbits, symmetries and integrals, integrable systems, symbolic dynamics, chaos. Prerequisite: MATH 6500

MATH - 6540/8540 and 6550/8550 PARTIAL DIFFERENTIAL EQUATIONS I and II

[3 hours each] Sobolev spaces, Sobolev embedding
theorem, distribution theory, weak solution to partial differential equations, existence, uniqueness and regularity of solutions, potential
theory and harmonic functions, Hopf maximum principle, fundamental solutions and the parametrix, representation theorems, Cauchy-Kovalevskaya
Theorem, topics in partial differential equations. Prerequisite: MATH 6510

MATH - 6600/8600 and 6610/8610 STATISTICAL CONSULTING I and II

[2 hours each] Real data applications of various
statistical methods, project design and analysis including statistical consulting experience. Prerequisite: Consent of instructor

MATH - 6620/8620 CATEGORICAL DATA ANALYSIS

[3 hours] Important methods and modeling techniques using generalized linear
models and emphasizing loglinear and logit modeling. Prerequisite: MATH 5680 Corequisite: MATH 6650

MATH - 6630/8630 DISTRIBUTION FREE AND ROBUST STATISTICAL METHODS

[3 hours] Statistical methods based on counts and ranks;
methods designed to be effective in the presence of contaminated data or error distribution misspecification. Prerequisite: MATH 5680
Corequisite: MATH 5690 or MATH 6650

MATH - 6640/8640 TOPICS IN STATISTICS

[3 hours] Topics selected from an array of modern statistical methods such as survival
analysis, nonlinear regression, Monte Carlo methods, etc.

MATH - 6650/8650 STATISTICAL INFERENCE

[3 hours] Estimation, hypothesis testing, prediction, sufficient statistics, theory
of estimation and hypothesis testing, simultaneous inference, decision theoretic models. Prerequisite: MATH 5680

MATH - 6670/8670 MEASURE THEORETIC PROBABILITY

[3 hours] Real analysis, probability spaces and measures, random variables
and distribution functions, independence, expectation, law of large numbers, central limit theorem, zero-one laws, characteristic functions,
conditional expectations given a s-algebra, martingales. Prerequisite: MATH 5680 Corequisite: MATH 6800 recommended

MATH - 6680/8680 THEORY OF STATISTICS

[3 hours] Exponential families, sufficiency, completeness, optimality, equivariance,
efficiency. Bayesian and minimax estimation. Unbiased and invariant tests, uniformly most powerful tests. Asymptotic properties
for estimation and testing. Most accurate confidence intervals. Prerequisite: MATH 5960 or 6650 and 6670

MATH - 6690/8690 MULTIVARIATE STATISTICS

[3 hours] Multivariate normal sampling distributions, T tests and MANOVA, tests on
covariance matrices, simultaneous inference, discriminant analysis, principal components, cluster analysis and factor analysis.
Prerequisite: MATH 5690 or 6650

MATH - 6720/8720 and 6730/8730 METHODS OF MATHEMATICAL PHYSICS I and II

[3 hours each] Analytic functions, residues, method
of steepest descent, complex differential equations, regular singularities, integral representation, special functions, real and complex vector
spaces, matrix groups, Hilbert spaces, orthogonal polynomials, self-adjoint operators and eigenvalue problems, partial differential equations,
coordinate transformations and separation of variables, boundary value problems, Green�s functions, integral equations, tensor analysis, metrics
and curvature, calculus of variations, finite groups and group representations.

MATH - 6800/8800 and 6810/8810 REAL ANALYSIS I and II

[3 hours each] Completeness, connectedness and compactness in metric
spaces, continuity and convergence, Stone-Weierstrass Theorem, Lebesgue measure and integration on the real line, convergence theorems, Egorov
and Lusin theorem, derivatives, functions of bounded variation, Vitali covering theorem, absolutely continuous functions, Lebesgue-Stieltjes
integration, Banach spaces, Lp -spaces, abstract measures, Radon-Nikodym Theorem, measures on locally compact Hausdorff spaces. Prerequisite:
MATH 5840 or equivalent

MATH - 6820/8820 and 6830/8830 FUNCTIONAL ANALYSIS I and II

[3 hours each] Topological vector spaces, seminorms, Banach
spaces, open mapping and closed graph theorem, convexity, weak topologies, Hahn-Banach theorem, Banach-Alaoglu theorems, duality, Lp spaces,
Mackey-Ahrens Theorem, Banach algebras, spectra in Banach algebras, commutative Banach algebras, unbounded operators, spectral theorem for
bounded and unbounded operators, topics in functional analysis.Prerequisite: MATH 6810

MATH - 6840/8840 and 6850/8850 COMPLEX ANALYSIS I and II

[3 hours each] Elementary analytic functions, complex integration,
residue theorem and argument principle, sequences of analytic functions, Laurent expansions, entire functions, meromorphic functions, conformal
mapping, Riemann mapping theorem, monodromy, algebraic functions, Riemann surfaces, elliptic and modular functions. Prerequisite: MATH 6800

MATH - 6890/8890 PROBLEMS IN ALGEBRA, TOPOLOGY, AND ANALYSIS

[1 hour] Practicum in solving problems in graduate algebra,
topology, and analysis. Supplements 6300-10, 6400-10, and 6800-10 and prepares students for doctoral qualifying examination.

MATH - 6930/8930 COLLOQUIUM

[1 hour] Lectures by visiting mathematicians and staff members on areas of current interest in
mathematics.

MATH - 6940/8940 PROSEMINAR

[1 - 5 hours] Problems and techniques of teaching elementary college mathematics, supervised
teaching, seminar in preparation methods.

MATH - 6960 MASTER THESIS

[3 - 6 hours]

MATH - 6980/8980 TOPICS IN MATHEMATICAL SCIENCES

[3 hours] Special topics in Mathematics or Statistics.

MATH - 6990/8990 READINGS IN MATHEMATICS

[1 - 5 hours] Readings in areas of Mathematics of mutual interest to the student
and the professor.

MATH - 8960 DISSERTATION

[3 - 6 hours]

**Error processing SSI file**