MATH - MATHEMATICS

Department of Mathematics (ARS)


MATH - 0900 BASIC MATHEMATICS
[2 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 ALGEBRA CONCEPTS I
[2 hours] This course covers integer operations variables, algebraic expressions, graphs, and solving linear equations. Problem solving techniques are emphasized. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0900 or placement


MATH - 0920 ALGEBRA CONCEPTS I LABORATORY
[.5 hours] This is an optional laboratory to accompany, MATH 0910. Students will work in small groups on real life applications. They will do hands-on activities to help them understand the concepts in MATH 0910. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0900 or placement Corequisite: MATH 0910


MATH - 0930 ALGEBRA CONCEPTS II
[2 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 - 0940 ALGEBRA CONCEPTS II LABORATORY
[.5 hours] This is an optional laboratory to accompany MATH 0930. Students will work in small groups on real life applications. They will do hands-on activities to help them understand the concepts in MATH 0930. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0910 or placement Corequisite: MATH 0930


MATH - 0950 ALGEBRA CONCEPTS III
[2 hours] This course introduces the student to rational and quadratic functions and irrational numbers. Problem solving techniques are emphasized. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0930 or placement


MATH - 0960 ALGEBRA CONCEPTS III LABORATORY

[.5 hours] This is an optional laboratory to accompany MATH 0950. Students will work in small groups on real life applications. They will do hands-on activities to help them understand the concepts in MATH 0950. 7.5 week module. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: MATH 0930 or placement Corequisite: MATH 0950


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.

* course is pending final approval


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).


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 1150


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: Satisfactory placement test score or 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, calculus for business. Course is not applicable toward the undergraduate Mathematics major requirements. Prerequisite: Satisfactory placement test score or satisfactory ACT score or MATH 1150.


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 1150.


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 1150.


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 1150.


MATH - 1750 MATHEMATICS FOR THE LIFE SCIENCES I
[4 hours] Definitions of trigonometric functions, solving trigonometric equations, functions, calculus for the life sciences, 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 1150.


MATH - 1760 MATHEMATICS FOR THE LIFE SCIENCES II
[3 hours] Continuation of MATH 1750, topics in calculus, 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 *course is pending final approval


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

* course is pending final approval


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 - 1970 TRANSITIONAL MATHEMATICS COURSES
[1-4 hours] Mathematics courses for the following sections:

:027 Transitional Mathematics for Business Mathematics II. [4 hours] Limits, functions, differential calculus, integral calculus and business applications. Prerequisite: MATH 126

:086 Transitional Calculus II. [2 hours] Integration; Fundamental Theorem of Calculus; area between curves; volume; work; and average value of a function. Prerequisite: MATH 185

:087 Transitional Calculus III. [3 hours] Integration techniques; infinite sequences; infinite series; vectors and applications. Prerequisite: MATH 186


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. * course is pending final approval


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 1150, 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 1150, 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

*course is pending final approval


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

[3hours] 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 Cartlo 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]

Last Updated: 1/3/12