# MTH

See a list of all MTH courses. You can also:

## Undergraduate

### Mathematics

## MTH 1280 College Algebra

Level:UndergraduateCredit Hours:4Schedule Type:LectureGraphs of linear, polynomial and rational functions, exponential and logarithmic functions and equations, and systems of equations.

## MTH 1340 Precalculus

Level:UndergraduateCredit Hours:5Schedule Type:LectureFunctions and graphs, polynomial and rational functions, trigonometric and inverse trigonometric functions, conics, systems of equations, exponential and logarithmic functions, geometric series, binomial theorem.

## MTH 1350 Analytic Geometry and Trigonometry

Level:UndergraduateCredit Hours:3Schedule Type:LecturePolynomial equations, conic sections, trigonometric and inverse trigonometric functions, trigonometric identities, solution of triangles.

## MTH 1440 Mathematics and the Modern World with Algebra Review

Level:UndergraduateCredit Hours:4Schedule Type:LectureAn application of mathematics to modeling real world problems from the behavioral, computational, managerial, and social sciences.

## MTH 1450 Mathematics and the Modern World

Level:UndergraduateCredit Hours:3Schedule Type:LectureAn application of mathematics to modeling real world problems from the behavioral, computational, managerial, and social sciences. Includes such topics as probability, descriptive and inferential statistics, financial management, voting systems, codes and data storage.

## MTH 2240 Applied Calculus

Level:UndergraduateCredit Hours:4Schedule Type:LectureFunctions (including exponential and logarithmic functions), limits, derivatives and rates of change, applications of derivatives including graphing and optimization, and indefinite and definite integrals with applications.

## MTH 2280 Business Calculus

Level:UndergraduateCredit Hours:4Schedule Type:LectureFunctions, rates of change, limits, derivatives of algebraic functions, applications including maxima and minima, exponential and logarithmic functions, and indefinite and definite integrals with applications.

## MTH 2300 Calculus I

Level:UndergraduateCredit Hours:4Schedule Type:CombinationLabLectureExamines limits, the derivative, differentiation, applications of the derivative, antiderivatives, Riemann sums, the definite integral, and the fundamental theorem of calculus.

## MTH 2310 Calculus II

Level:UndergraduateCredit Hours:4Schedule Type:CombinationLabLectureIntegration techniques, applications of the definite integral, first-order differential equations, vectors and vector operations, parametric equations and polar coordinates, infinite series.

## MTH 2320 Calculus III

Level:UndergraduateCredit Hours:4Schedule Type:LectureVector functions and their derivatives, motion in two and three dimensions, lines, planes, and parametric surfaces, spherical and cylindrical coordinates. Partial derivatives and multiple integrals in two and three dimensions. Vector fields, line and surface integrals.

## MTH 2330 Differential Equations

Level:UndergraduateCredit Hours:3Schedule Type:LectureElementary first order equations, linear equations, existence and uniqueness, phase line and plane, linear systems, Laplace transform, and applications.

## MTH 2350 Differential Equations with Matrix Algebra

Level:UndergraduateCredit Hours:4Schedule Type:LectureIntroduction to differential equations with matrix theory.

## MTH 2410 Mathematics Concepts for Teachers I

Level:UndergraduateCredit Hours:3Schedule Type:LectureLabOverview of mathematical topics from a perspective appropriate for early and middle childhood educators. Number systems such as whole numbers, fractions, rationals and decimals. Place value and bases.

## MTH 2430 Mathematics Concepts for Teachers II

Level:UndergraduateCredit Hours:3Schedule Type:LectureLabOverview of mathematical topics from a perspective appropriate for early and middle childhood educators. Prime numbers and factorization, the operation of division on whole and rational numbers, ratio and proportion, probability, and data analysis.

## MTH 2450 Mathematics Concepts for Teachers III

Level:UndergraduateCredit Hours:3Schedule Type:LectureLabOverview of mathematical topics from a perspective appropriate for early and middle childhood educators. Introductory geometry in two and three dimensions, transformational geometry, and concepts of measurement.

## MTH 2530 Elementary Linear Algebra

Level:UndergraduateCredit Hours:3Schedule Type:LectureMatrices and their operations, linear systems of equations, Gaussian elimination, determinants, geometry of Euclidean space, vector spaces and subspaces, linear independence, basis, dimension and rank, orthogonality and the Gram-Schmidt process, linear transformations, eigenvalues and eigenvector

## MTH 2570 Discrete Mathematics for Computing

Level:UndergraduateCredit Hours:4Schedule Type:LectureDiscrete mathematics useful in computing. Emphasis on mathematical induction, recurrence relations, asymptotic behavior of functions, and algorithm analysis.

## MTH 2800 Writing Mathematical Proofs

Level:UndergraduateCredit Hours:3Schedule Type:LectureIntroduction to logic and techniques used in mathematical proofs. Students gain experience in constructing proofs as they study sets, relations, functions, algebraic structures, and the properties of real numbers. Integrated Writing course.

## MTH 3060 Mathematical Modeling

Level:UndergraduateCredit Hours:3Schedule Type:LectureIntroduction to mathematics as used in the real world. Graphical methods, curve-fitting, dimensional analysis, scaling, stability, growth, vibrations, circuits, probability, optimality, approximation, Monte Carlo simulation.

## MTH 3100 Mathematical Modeling in the Behavioral Sciences

Level:UndergraduateCredit Hours:3Schedule Type:LectureDifferential equations, axiomatics, probability theory, matrix algebra, simulation, and game theory, and their use in a variety of models in the social sciences, life sciences, and humanities. Includes deterministic models, probabilistic models, simulations.

## MTH 3120 Mathematical Theory of Interest

Level:UndergraduateCredit Hours:4Schedule Type:LectureTheory of financial transactions involving interests, annuities, derivatives, options and futures.

## MTH 3140 Mathematical Software

Level:UndergraduateCredit Hours:3Schedule Type:LectureSolving scientific problems using computational software packages MATLAB and Mathematica, including procedural and functional programming.

## MTH 3260 Numerical Methods for Computational Science

Level:UndergraduateCredit Hours:3Schedule Type:LectureNumerical methods for the sciences using modern programming languages. Solution of linear and nonlinear equations, symmetric matrix eigenvalue problems, interpolation and least squares.

## MTH 3320 Complex Variables

Level:UndergraduateCredit Hours:3Schedule Type:LectureOperations with complex numbers, derivatives, holomorphic functions and the Cauchy-Riemann equations. Integrals, Cauchy's Theorem, the Cauchy Integral Formula, and consequences. Definitions and properties of elementary functions. Power series, conformal maps, the calculus of residues.

## MTH 3330 Partial Differential Equations

Level:UndergraduateCredit Hours:3Schedule Type:LectureLinear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles. Green's functions and fundamental solutions.

## MTH 3430 Algebra and Functions for Middle School Teachers

Level:UndergraduateCredit Hours:4Schedule Type:LectureAlgebraic principles and linear, polynomial, rational, exponential, logarithmic, and trigonometric functions from a perspective appropriate for middle school teachers. Uses technology to explore how properties of functions appear in various representations.

## MTH 3450 Geometry for Middle School Teachers

Level:UndergraduateCredit Hours:3Schedule Type:LectureLabTwo- and three-dimensional Euclidean geometry from a perspective appropriate for grade 4-10 teachers. Compass constructions, triangle congruence, postulates, Pythagorean Theorem, and proofs. Surface area and volume. Coordinate geometry applied to proofs and transformations.

## MTH 3480 Concepts in Calculus for Middle School Teachers

Level:UndergraduateCredit Hours:3Schedule Type:LectureLabExplores the big ideas in calculus -- limit, derivative, and integral -- with the goal of a solid conceptual understanding. Emphasizes applications, connections to algebra, and how these concepts appear in middle school math classrooms.

## MTH 3990 Selected Topics in Mathematics

Level:UndergraduateCredit Hours:1 to 5Schedule Type:Independent StudySelected topics in mathematics.

## MTH 4070 Optimization Techniques

Level:UndergraduateCredit Hours:3Schedule Type:LectureAlgorithms for optimizing real functions of several variables subject to equality and inequality constraints.

## MTH 4150 Scientific Computation

Level:UndergraduateCredit Hours:3Schedule Type:LectureModern computational techniques for simulating scientific phenomena.

## MTH 4160 Matrix Computations

Level:UndergraduateCredit Hours:3Schedule Type:LectureNumerical linear algebra survey using high-level computing tools. Topics include linear equations, matrix factorizations, eigenvalue problems, least squares, applications of singular value decompositions, and iterative methods for large sparse matrices.

## MTH 4240 Coding Theory

Level:UndergraduateCredit Hours:3Schedule Type:LectureEssentials of error-correcting codes, including methods for efficient and accurate transfer of information. Perfect and related codes, linear and cyclic codes, BCH codes, Reed-Muller codes, Reed-Solomon cods, Self-dual codes, weight enumerators and bounds.

## MTH 4260 Matrix Computations

Level:UndergraduateCredit Hours:3Schedule Type:LectureNumerical linear algebra survey using high-level computing tools. Topics include linear equations, matrix factorizations, eigenvalue problems, least squares, applications of singular value decompositions, and iterative methods for large sparse matrices.

## MTH 4290 Cryptography and Data Security

Level:UndergraduateCredit Hours:3Schedule Type:LectureMathematical principles of cryptography and data security. Introduces relevant algebra and number theory.

## MTH 4310 Real Variables I

Level:UndergraduateCredit Hours:3Schedule Type:LectureThe real number system, inequalities, completeness, limits, sequences and the Cauchy criterion, functions, continuity, differentiablity, the mean value theorem, L'Hospital's rule, Taylor's theorem, the Riemann integral, fundamental theorem of calculus, approximate integration, improper integrals.

## MTH 4320 Real Variables II

Level:UndergraduateCredit Hours:3Schedule Type:LectureInfinite series, sequences and series of functions, power series, Taylor series, uniform convergence, topology of R^n, real-valued and vector-valued functions of several variables, derivatives and integrals of functions of several variables.

## MTH 4400 History of Mathematics

Level:UndergraduateCredit Hours:3Schedule Type:LectureMathematics as an on-going human activity. Historical development and contributions from diverse cultures of number systems, measurement, algebra, Euclidean and non-Euclidean geometries, calculus, discrete mathematics, probability and statistics. Integrated Writing course.

## MTH 4460 Problem Solving and Mathematical Modeling for Middle School Teachers

Level:UndergraduateCredit Hours:4Schedule Type:LectureLabLearning to think quantitatively through solving pure and applied mathematics problems and modeling real world problems. Focuses on working with the steps involved in modeling real-life situations and understanding how modeling and problem solving differ.

## MTH 4510 Modern Algebra I

Level:UndergraduateCredit Hours:3Schedule Type:LectureElementary number theory: divisibility, prime numbers, congruences, quadratic reciprocity, and number-theoretic functions. Introduction to rings, integral domains, and fields.

## MTH 4520 Modern Algebra II

Level:UndergraduateCredit Hours:3Schedule Type:LectureExamples and elementary properties of abstract algebraic structures, including groups, rings, integral domains, and fields.

## MTH 4550 Advanced Linear Algebra

Level:UndergraduateCredit Hours:3Schedule Type:LectureBasic principles of linear independence, spanning sets, bases, and dimension. Linear transformations, matrix representations of linear transformations, and determinants. Spectral theory of square matrices, Jordan canonical form. Perron-Frobenius results on positive matrices.

## MTH 4570 Combinatorics and Graph Theory

Level:UndergraduateCredit Hours:4Schedule Type:LecturePermutations, combinatorics, generating functions, recurrence relations, and Polya's theory of counting; methods, results, and algorithms of graph theory, with emphasis on graphs as mathematical models applicable to organizational and industrial situations.

## MTH 4710 Geometry

Level:UndergraduateCredit Hours:3Schedule Type:LectureIntroduction to hyperbolic and other geometries.

## MTH 4810 Applied Mathematics I

Level:UndergraduateCredit Hours:3Schedule Type:LectureSolution methods for ordinary differential equations commonly arising in physics and engineering. Systems of equations, stability theory, Liapunov's methods, autonomous systems, existence and uniqueness of solutions, and Poincare phase plane.

## MTH 4820 Applied Mathematics II

Level:UndergraduateCredit Hours:3Schedule Type:LectureUse of integral transforms in the solution of differential and integral equations, Fourier series, Fourier and Laplace transforms, distributions, integral equations, Green's functions, Sturm-Liouville theory, perturbation methods and asymptotics, orthogonal functions, and special functions.

## MTH 4880 Independent Reading in Mathematics

Level:UndergraduateCredit Hours:1 to 3Schedule Type:Independent StudySelected readings in mathematics.

## MTH 4910 High School Mathematics from an Advanced Perspective

Level:UndergraduateCredit Hours:3Schedule Type:LectureMathematics for high school teachers from an advanced perspective: real and complex numbers, functions, equations, integers and polynomials, number system structures. Integrated Writing course.

## MTH 4920 Undergraduate Mathematics Seminar

Level:UndergraduateCredit Hours:3Schedule Type:SeminarDetailed study of a single mathematics topic chosen by the student with the approval of the instructor. Integrated Writing course.

## MTH 4990 Selected Topics in Mathematics

Level:UndergraduateCredit Hours:1 to 3Schedule Type:Independent StudySelected topics in mathematics.

## Graduate

### Mathematics

## MTH 5260 Numerical Methods for Computational Science

Level:GraduateCredit Hours:3Schedule Type:LectureNumerical methods for the sciences using modern programming languages. Solution of linear and nonlinear equations, symmetric matrix eigenvalue problems, interpolation and least squares.

## MTH 5320 Complex Variables

Level:GraduateCredit Hours:3Schedule Type:LectureOperations with complex numbers; derivatives; holomorphic functions and the Cauchy-Riemann equations; integrals; Cauchy's Theorem, the Cauchy Integral Formula, and consequences; definitions and properties of elementary functions; power series; conformal maps; the calculus of residues.

**Departme**## MTH 5330 Partial Differential Equations

Level:GraduateCredit Hours:3Schedule Type:LectureLinear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles.

## MTH 5990 Selected Topics

Level:GraduateCredit Hours:1 to 5Schedule Type:Independent StudySelected topics in mathematics. May be taken for letter grade or pass/unsatisfactory.

## MTH 6050 Advanced Engineering Mathematics

Level:GraduateCredit Hours:3Schedule Type:LectureTopics include eigenvalues and eigenvectors, matrix factorizations, Fourier series, analytical and numerical solutions to the three classical partial differential equations, and complex functions, integration, and series and residues.

**Department Managed Prerequisite(s): Undergraduate level MTH**## MTH 6060 Mathematical Modeling

Level:GraduateCredit Hours:3Schedule Type:LectureAn introduction to mathematics as it is used in the real world. Graphical methods, curve-fitting, dimensional analysis, scaling, stability, growth, vibrations, circuits, probability, optimality, approximation, Monte Carlo simulation.

## MTH 6070 Optimization Techniques

Level:GraduateCredit Hours:3Schedule Type:LectureAlgorithms for optimizing real functions of several variables subject to equality and inequality constraints.

## MTH 6140 Mathematical Software

Level:GraduateCredit Hours:3Schedule Type:LectureSolving scientific problems using computational software packages MATLAB and Mathematica, including procedural and functional programming.

**Department Managed Prerequisite(s): (Undergraduate level MTH 2330 Minimum Grade of D and Undergraduate level MTH 2530 Minimum Grade of D) or Undergraduate**## MTH 6150 Scientific Computation

Level:GraduateCredit Hours:3Schedule Type:LectureModern computational techniques for simulating scientific phenomena.

**Department Managed Prerequisite(s): (Undergraduate level MTH 3140 Minimum Grade of D or Undergraduate level MTH 4160 Minimum Grade of D) and Undergraduate level MTH 3060 Minimum Grade of D**## MTH 6160 Matrix Computations

Level:GraduateCredit Hours:3Schedule Type:LectureNumerical linear algebra survey using high-level computing tools. Topics include linear equations, matrix factorizations, eigenvalue problems, least squares, applications of singular value decompositions, and iterative methods for large sparse matrices.

## MTH 6240 Coding Theory

Level:GraduateCredit Hours:3Schedule Type:LectureAn introduction to the essentials of error-correcting codes, including methods for efficient and accurate transfer of information.

## MTH 6260 Matrix Computations

Level:GraduateCredit Hours:3Schedule Type:Lecture## MTH 6290 Cryptography and Data Security

Level:GraduateCredit Hours:3Schedule Type:LectureMathematical principles of cryptography and data security. Preliminary algebra and number theory will be briefly introduced.

## MTH 6310 Real Variables I

Level:GraduateCredit Hours:3Schedule Type:LectureThe real number system, inequalities, completeness, limits, sequences and the Cauchy criterion, functions, continuity, differentiablity, the mean value theorem, L Hospital's rule, Taylor's theorem, the Riemann integral, fundamental theorem of calculus, approximate integration, improper integrals.

## MTH 6320 Real Variables II

Level:GraduateCredit Hours:3Schedule Type:Lecturenfinite series, sequences and series of functions, power series, taylor series, uniform convergence, topology of R^n, real-valued and vector-valued functions of several variables, derivatives and integrals of functions of several variables.

**Department Managed Prerequisite(s): Undergraduate lev**## MTH 6510 Modern Algebra I

Level:GraduateCredit Hours:3Schedule Type:LectureElementary number theory: divisibility, prime numbers, congruences, quadratic reciprocity, and number-theoretic functions. This provides an introduction to rings, integral domains, and fields.

**Department Managed Prerequisite(s): Undergraduate level MTH 2800 Minimum Grade of D**## MTH 6520 Modern Algebra II

Level:GraduateCredit Hours:3Schedule Type:LectureExamples and elementary properties of abstract algebraic structures: these include groups, rings, integral domains, and fields.

**Department Managed Prerequisite(s): Undergraduate level MTH 4510 Minimum Grade of D or Graduate level MTH 6510 Minimum Grade of D**## MTH 6550 Advanced Linear Algebra

Level:GraduateCredit Hours:3Schedule Type:LectureBasic principles of linear independence, spanning sets, bases, and dimension. Linear transformations, matrix representations of linear transformations, and determinants. Spectral theory of square matrices, Jordan canonical form.

## MTH 6570 Combinatorics and Graph Theory

Level:GraduateCredit Hours:4Schedule Type:LectureTopics include: permutations, combinatorics, generating functions, recurrence relations, and Polyas theory of counting; methods, results, and algorithms of graph theory, with emphasis on graphs as mathematical models applicable to organizational and industrial situations.

**Department Managed Pr**## MTH 6710 Geometry

Level:GraduateCredit Hours:3Schedule Type:LectureIntroduction to hyperbolic and other geometries.

**Department Managed Prerequisite(s): Undergraduate level MTH 2800 Minimum Grade of D**## MTH 6810 Applied Mathematics I

Level:GraduateCredit Hours:3Schedule Type:LectureSolution methods for ordinary differential equations commonly arising in physics and engineering.

## MTH 6820 Applied Mathematics II

Level:GraduateCredit Hours:3Schedule Type:LectureUse of integral transforms in the solution of differential and integral equations, Fourier series, Fourier and Laplace transforms, distributions, integral equations, Green's functions, Sturm-Liouville theory, perturbation methods and asymptotics, orthogonal functions, and special functions.

**De**## MTH 6880 Independent Reading

Level:GraduateCredit Hours:1Schedule Type:Independent StudySelected readings in mathematics.

## MTH 6990 Selected Topics

Level:GraduateCredit Hours:1 to 5Schedule Type:Independent StudySelected topics in mathematics.

## MTH 7000 Professional Experiences for Graduate Students

Level:GraduateCredit Hours:1 to 3Schedule Type:SeminarParticipation in seminars related to teaching and research.

## MTH 7160 Numerical Analysis I

Level:GraduateCredit Hours:4Schedule Type:LectureSolutions of systems of linear and nonlinear equations, numerical solution of matrix eigenvalue problems, interpolation and numerical integration, numerical solution of initial and boundary value problems for differential equations.

**Department Managed Prerequisite(s): Graduate level MTH 6550 M**## MTH 7170 Numerical Analysis II

Level:GraduateCredit Hours:4Schedule Type:LectureFinite difference and finite element methods for partial differential equations, including elliptic, parabolic and hyperbolic.

**Department Managed Prerequisite(s): Graduate level MTH 5330 Minimum Grade of D and Graduate level MTH 6550 Minimum Grade of D**## MTH 7310 Real Analysis I

Level:GraduateCredit Hours:4Schedule Type:LectureCardinality of sets. Metric spaces, convergence, completeness, compactness. Fixed point Theorems. Spaces of continuous functions, Arzela-Ascoli Theorem, Stone-Weierstrass Theorem. Lebesque measure and integration on R^n. Convergence theorems, Fubini's Theorem.

## MTH 7320 Real Analysis II

Level:GraduateCredit Hours:4Schedule Type:LectureHilbert spaces, Riesz representation theorem, orthonormal bases. Banach spaces, dual spaces, weak convergence. Bounded linear operators, adjoint operators, compact operators. Applications.

**Department Managed Prerequisite(s): Graduate level MTH 7310 Minimum Grade of D**## MTH 7370 Complex Analysis

Level:GraduateCredit Hours:4Schedule Type:LectureAnalytic functions, Cauchy-Riemann equations, Cauchy integral formula, Calculus of residues, Harmonic functions, Taylor series, Laurent series, Riemann Mapping Theorem

**Department Managed Prerequisite(s): Undergraduate level MTH 4320 Minimum Grade of D or Graduate level MTH 6320 Minimum Grade o**## MTH 7510 Algebra I

Level:GraduateCredit Hours:4Schedule Type:LectureGroups: isomorphism theorems, Jordan-Holder theorem, permutation groups, Sylow theorems, finitely generated Abelian groups, and free groups.

## MTH 7520 Algebra II

Level:GraduateCredit Hours:4Schedule Type:LectureRings and modules: Noetherian rings and modules, Artinian rings and modules, and Wedderburn-Artin structure theory.

## MTH 7710 Topology

Level:GraduateCredit Hours:4Schedule Type:LectureTopological spaces, continuous maps, open and closed maps, Connectedness, Separation Axioms, Convergence, Compactness, Homotopy, Basic concepts of algebraic topology.

**Department Managed Prerequisite(s): Undergraduate level MTH 4320 Minimum Grade of D or Graduate level MTH 6320 Minimum Grade of**## MTH 7770 Applied Analysis

Level:GraduateCredit Hours:4Schedule Type:LectureFixed point theorems and applications, Banach and Hilbert spaces and applications, compact operators, eigenvalues, eigenfunction expansions, Sturm-Liouville problems, inverse operators, variational methods, and basic approximate methods in analysis.

**Department Managed Prerequisite(s): Undergra**## MTH 7920 Special Problems

Level:GraduateCredit Hours:1 to 5Schedule Type:Independent StudyExamines a specific problem in advanced mathematics.

## MTH 7990 Selected Topics

Level:GraduateCredit Hours:1 to 5Schedule Type:Independent StudySelected topics in mathematics.

## MTH 8000 Graduate Seminar

Level:GraduateCredit Hours:1 to 4Schedule Type:SeminarSeminar on selected advanced topics in mathematics.

## MTH 8300 Topics in Analysis

Level:GraduateCredit Hours:1 to 4Schedule Type:Independent StudySelected advanced topic or topics in analysis.

## MTH 8500 Topics in Algebra

Level:GraduateCredit Hours:1 to 4Schedule Type:Independent StudySelected advanced topic or topics in algebra.

## MTH 8700 Topics in Geometry

Level:GraduateCredit Hours:1 to 4Schedule Type:Independent StudySelected advanced topic or topics in Geometry.

## MTH 8990 Graduate Research

Level:GraduateCredit Hours:1 to 4Schedule Type:Independent StudyResearch on a selected topic in mathematics.