MATH 0998 Support for Mathematical Modeling
Credit Hours 2
Corequisites Students who are enrolled in MATH 0998 must be concurrently enrolled in MATH 1101
Description

This course is intended to provide corequisite support for students requiring remediation in mathematics while they are enrolled in MATH 1101 Introduction to Mathematical Modeling.

MATH 0999 Support for College Algebra
Credit Hours 2
Prerequisites Appropriate placement and concurrent registration in MATH 1111
Description

This course is intended to provide corequisite support for students requiring remediation in mathematics while they are enrolled in MATH 1111 College Algebra.

MATH 1070 Elementary Statistics
Credit Hours 3.0
Description

Descriptive statistics, basic probability, and distribution of random variables, estimation and hypothesis tests for means and proportions, regression and correlation, analysis of count data.

MATH 1101 Introduction to Mathematical Modeling
Credit Hours 3.0
Description

Three lecture hours a week. Mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, on the use of appropriate supporting technology, and on the effective communication of quantitative concepts and results.

MATH 1111 College Algebra
Credit Hours 3.0
Prerequisites Exit or exemption from learning support mathematics, appropriate placement, or concurrent registration in MATH 0999
Description

This course provides an in-depth study of the properties of algebraic, exponential and logarithmic functions as needed for calculus. Emphasis is on using algebraic and graphical techniques for solving problems involving linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions.

MATH 1112 College Trigonometry
Credit Hours 3.0
Prerequisites MATH 1111 with a grade of C or higher, or appropriate placement
Description

This course is an in-depth study of the properties of trigonometric functions and their inverses. Topics include circular functions, special angles, solutions of triangles, trigonometric identities and equations, graphs of trigonometric functions, inverse trigonometric functions and their graphs, Law of Sines, Law of Cosines, and vectors.

MATH 1113 Precalculus
Credit Hours 3.0
Prerequisites MATH 1111 with a grade of C or higher, or appropriate placement
Description

This course is an intensive study of the basic functions needed for the study of calculus. Topics include algebraic, functional, and graphical techniques for solving problems with algebraic, exponential, logarithmic, and trigonometric functions and their inverses.

MATH 1220 Survey of Calculus
Credit Hours 3.0
Prerequisites MATH 1111 with grade of C or higher
Description

Differential and integral calculus of selected real-valued functions of one and several real variables with applications.

MATH 2008 Foundations of Numbers and Operations
Credit Hours 3.0
Prerequisites MATH 1001, MATH 1101, MATH 1111, MATH 1112, MATH 1113, MATH 2201, or MATH 2211 with grade of C or higher
Description

This course is an Area F introductory mathematics course for early childhood education majors. This course will emphasize the understanding and use of the major concepts of number and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics.

MATH 2201 Calculus for the Life Sciences I
Credit Hours 4.0
Prerequisites MATH 1112 or MATH 1113 with a grade of C or higher, or appropriate placement
Description

Limits, derivatives and applications. Exponential and logarithmic functions. Integrals, antiderivatives and the Fundamental Theorem of Calculus. Examples and Applications are drawn from the life sciences. This course is not appropriate for mathematics, computer science, geology, and physics majors or minors.

MATH 2202 Calculus for the Life Sciences II
Credit Hours 4.0
Prerequisites MATH 2201 with a grade of C or higher
Description

Matrices, functions of several variables, differential equations and solutions with applications. Examples and applications are drawn from the life sciences. This course is not appropriate for mathematics, computer science, geology, and physics majors or minors.

MATH 2211 Calculus of One Variable I
Credit Hours 4.0
Prerequisites MATH 1112 or MATH 1113 with grade of C or higher, or appropriate placement
Description

Limits and Continuity, Differentiation, Mean Value Theorem for Derivatives; applications of differentiation; definition of the integral; Fundamental Theorem of Calculus; applications of integration to area.

MATH 2212 Calculus of One Variable II
Credit Hours 4.0
Prerequisites MATH 2211 with grade of C or higher
Description

Applications and techniques of integration; transcendental and inverse trigonometric functions; polar coordinates; infinite sequences and series; indeterminate forms; improper integrals.

MATH 2215 Multivariate Calculus
Credit Hours 4.0
Prerequisites MATH 2212 with grade of C or higher
Description

Real-valued functions of several variables, limits, continuity, differentials, directional derivatives, partial derivatives, chain rule, multiple integrals, applications.

MATH 2420 Discrete Mathematics
Credit Hours 3.0
Prerequisites MATH 1112 or MATH 1113 or MATH 1220 with a grade of C or higher
Description

This course introduces the ideas of finite mathematical structures. Topics include set theory, logic, proof techniques, functions and relations, graphs, and trees.

MATH 2641 Linear Algebra I
Credit Hours 3.0
Prerequisites MATH 2212 with a grade of C or higher
Description

Theory and applications of matrix algebra, vector spaces, and linear transformations. Topics include linear equations and matrices, invertible matrices, determinants, vector spaces, subspaces, bases, eigenvalues and eigenvectors.

MATH 2652 Differential Equations
Credit Hours 3.0
Prerequisites MATH 2215 with grade of C or higher
Corequisites MATH 2641
Description

This course is an introduction to the basic ideas of ordinary differential equations. Topics include first-order equations, linear differential equations, series solutions, simple non-linear equations, systems of differential equations, and applications.

MATH 3000 Bridge to Higher Mathematics-CTW
Credit Hours 3.0
Prerequisites MATH 2641 and MATH 2420 with grades of C or higher
Description

Topics from set theory, real numbers, analysis, and algebra, which illustrate a formal approach to the presentation and development of mathematical concepts and proofs. Serves as the Critical Thinking Through Writing (CTW) course required of all mathematics majors.

MATH 3030 Mathematical Models for Computer Science
Credit Hours 3.0
Prerequisites MATH 2212 and MATH 2420 or CSC 2510 with grades of C or higher
Description

Elements of mathematical modeling including: multivariate functions, probability, distributions of random variables, sampling, statistical inference, operators, vector analysis; elements of linear algebra.

MATH 3050 Geometry and Spatial Sense
Credit Hours 3.0
Prerequisites MATH 2030 or MATH 2008 with grade of C or higher
Description

Building on Euclidean geometry this course is designed to develop a more visual understanding of geometry and enhance geometric intuition in two- and three-dimensions. Topics include measurement, two-dimensional geometry, three-dimensional geometry, spherical geometry, symmetry, tesselations, efficient shapes, transformations.

MATH 3070 Introduction to Probability and Statistics
Credit Hours 3.0
Prerequisites MATH 2030 or MATH 2008 with grade of C or higher, or consent of instructor
Description

Three lecture hours a week. This course will not be accepted as a part of the requirements for a major in mathematics. This course is intended to provide an overview of the basics of probability and descriptive statistics. Various forms of technology will be used.

MATH 3090 Algebraic Concepts
Credit Hours 3.0
Prerequisites MATH 2030 or MATH 2008 with grade of C or higher
Description

This course will not be accepted as a part of the requirements for a major in mathematics. This course is designed to broaden understanding of fundamental concepts of algebra with particular attention given to specific methods and materials of instruction. The principle algebra topics to be taught in this course are: the Language of Algebra; Patterns, Relations, and Functions; and Balance, Equations, and Inequalities.

MATH 3300 Problem Solving with Computers
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Three lectures a week. This course explores various mathematical contexts and develops mathematical knowledge necessary to solve, or attempt to solve, mathematical problems in the computer enhanced environment. The problems come from many sources and contexts. Computer programs such as Maple, Matlab, spreadsheets, Geometer’s Sketch Pad, Study Works, etc. will be used. No previous experience with computers is required.

MATH 3350 Scientific Computing
Credit Hours 3.0
Prerequisites C or higher in MATH 2215 and MATH 2641
Description

Introduction to programing in the Matlab, focusing on the knowledge and skills that are useful to scientific computing. The topics may include: basic Matlab concepts, matrix manipulations, linear algebra functions, plotting and visualizing functions, ordinary differential equations, basic statistical analyses and simple symbolic derivations. At the end of the class students should be able to use Matlab to address a variety of mathematical and statistical problems.

MATH 3420 Applied Combinatorics
Credit Hours 3.0
Prerequisites MATH 2212 or MATH 2420 with grade of C or higher
Description

Counting principles; topics include combinations, permutations, generating functions, recurrence relations, principle of inclusion and exclusion, and Polya’s theory of counting.

MATH 3610 Special Problems and Solving Strategies
Credit Hours 3.0
Prerequisites MATH 2212 with grade of B or higher, or consent of instructor
Description

The course will concentrate on developing solving strategies of difficult mathematical problems which require creativity and profound understanding of mathematics. Among topics to be covered: induction and pigeonhole principle, arithmetic, algebra, summation of series, intermediate real analysis, inequalities.

MATH 3690 Honors Readings
Credit Hours 1.0 - 3.0
Prerequisites Good standing with the Honors College and consent of instructor
Description

Discussion and readings on selected topics.

MATH 3820 Historical and Cultural Development of Mathematics I
Credit Hours 3.0
Prerequisites MATH 1101 or MATH 1111 with grade of C or higher
Description

Three lecture hours a week. Exploration of the historical and cultural development of mathematics between ~3000 B. C. and ~A. D. 1600. Mathematics topics to include the development of arithmetic, geometry (practical, deductive, and axiomatic), number theory, trigonometry, syncopated and symbolic algebra, probability, and statistics.

MATH 3821 Historical and Cultural Development of Mathematics II
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Three lecture hours a week. Exploration of the historical and cultural development of mathematics from ~A. D. 1600 to present. Mathematics topics to include the development of algebraic geometry, logarithms, calculus, non-Euclidean geometry, abstract algebra, probability, and analysis.

MATH 4010 Mathematical Biology
Credit Hours 3.0
Prerequisites MATH 2212 or MATH 1220 with grade of C or higher
Description

(Same as BIOL 4010.) This course provides an introduction to the use of continuous and discrete differential equations in the biological sciences. Biological topics will include single species and interacting population dynamics, modeling infectious and dynamic diseases, regulation of cell function, molecular interactions and receptor-ligand binding, biological oscillators, and an introduction to biological pattern formation. There will also be discussions of current topics of interest such as Tumor Growth and Angiogenesis, HIV and AIDS, and Control of the Mitotic Clock. Mathematical tools such as phase portraits, bifurcation diagrams, perturbation theory, and parameter estimation techniques that are necessary to analyze and interpret biological models will also be covered.

MATH 4030 Mathematical Music Theory
Credit Hours 3.0
Prerequisites Grade of C or higher in MATH 3000
Description

Specific aspects of group theory, algebraic combinatorics on words, similarity and distance measures, topology and geometry, and topos theory that are used in the analysis of general objects of music (scales, chords, rhythmic patterns) as well as in specific applications (development of software, music cognition, analysis of pieces from different time periods and genres). Acquire a repertoire of mathematical tools and techniques.

MATH 4211 Optimization
Credit Hours 3.0
Prerequisites Either MATH 3030 or both MATH 2641 and MATH 2215 with grades of C or higher
Description

Lagrange multipliers, gradient methods (steepest descent), search techniques, variational methods and control problems; other varying topics such as dynamic programming, nonlinear programming.

MATH 4250 Complex Analysis
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Complex numbers, analytic functions, complex series, Cauchy theory, residue calculus, conformal mapping.

MATH 4258 Vector Calculus
Credit Hours 3.0
Prerequisites MATH 2215 with grade of C or higher
Description

(Same as PHYS 4510.) Vector algebra, curvilinear motion, vector fields, gradient, divergence, Laplacian, line and surface integrals, integral theorems.

MATH 4265 Partial Differential Equations
Credit Hours 3.0
Prerequisites MATH 2652 with a grade of C or higher
Description

(Same as PHYS 4520.) First-order equations, classification of linear second-order equations, separation of variables, Fourier series, orthogonal functions, Green’s functions.

MATH 4275 Applied Dynamical Systems
Credit Hours 3.0
Prerequisites MATH 2652 and either MATH 2641 or MATH 3030 with grades of C or higher
Description

Three lecture hours per week. An introduction to discrete and continuous dynamical systems. Topics include: phase space; linear and nonlinear systems; structural stability; classification of equilibrium states, invariant manifolds; poincare maps, fixed points and period orbits; stability boundaries; local bifurcations; homoclinic orbits; routes to chaos in dissipative systems; applications from physics, biology, population dynamics, economics.

MATH 4301 College Geometry
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Axioms of planar Euclidean Geometry. The 5th postulate. Congruence and Similarity. Theorem of Thales. Similar Triangles: SAS, AA, and SSS. Theorem of Ceva. The Pythagorean Theorem. Polygons. Circles, secants and tangents, measurement of an angle with respect to a circle. Perimeters, areas, circumference. Inscribed and circumscribed polygons. Coordinate Geometry in the plane.

MATH 4371 Modern Geometry
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Euclidean and non-Euclidean geometry, including incidence, order, and the parallel postulate.

MATH 4381 General Topology
Credit Hours 3.0
Prerequisites Grade of C or higher in MATH 3000
Description

This course will provide an introduction to general topology, which is the study of spaces and how to classify spaces according to their characteristic properties. The class will begin with a brief review of basic set theory and metric spaces. Topics covered include topological spaces, continuous functions, topological properties (connectedness, compactness, countability, and separation axioms), the fundamental group, and covering spaces.

MATH 4382 Algebraic Topology
Credit Hours 3.0
Prerequisites Grade of C or higher in General Topology (MATH 4381/6381) and Modern Algebra I (MATH 4441)
Description

This course will provide an introduction to methods in algebraic topology. Topics covered include fundamental groups, covering space theory, simplicial complexes, simplicial homology, singular homology, singular cohomology, and higher homotopy groups.

MATH 4391 Introduction to Differential Geometry and Its Applications
Credit Hours 3.0
Prerequisites MATH 2215 with grade of C or higher
Description

(Same as PHYS 4391.) Three lecture hours a week. The theory of curves and surfaces in parametric and implicit form. Curvature and torsion of a curve; the shape operator and the total and mean curvature of a surface. The Gauss-Weingarten equations; the Egregium Theorem; surfaces of constant curvature and non-Euclidean geometry. Minimal surfaces; the Gauss Bonnet Theorem; submanifolds in Euclidian spaces, vector fields, differential forms, and the theorems of Frobenius and Stokes. Applications to physics.

MATH 4420 Graph Theory
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Introduction to graph theory; topics include structure of graphs, trees, connectivity, Eulerian and Hamiltonian graphs, planar graphs, graph colorings, matchings, independence, and domination. Additional topics may include symmetry of graphs, directed graphs, extremal graph theory and Ramsey theory, graph embeddings, and probabilistic methods in graph theory.

MATH 4435 Linear Algebra II
Credit Hours 3.0
Prerequisites MATH 2215, MATH 2641, and MATH 3000 with grades of C or higher
Description

Theory and applications of matrix algebra, vector spaces, and linear transformations. Topics include matrix representations of linear transformations, eigenvalues and eigenvectors, similarity, the spectral theorem, and orthogonality.

MATH 4441 Modern Algebra I
Credit Hours 3.0
Prerequisites MATH 2215, MATH 2641, and MATH 3000 with grades of C or higher
Description

Axiomatic approach to algebraic structures, groups, permutations, homomorphisms, and factor groups.

MATH 4442 Modern Algebra II
Credit Hours 3.0
Prerequisites MATH 4441 with grade of C or higher
Description

Rings, integral domains, and fields; polynomials over a field, matrices over a field, algebraic numbers and ideals.

MATH 4444 Polynomials
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Three lecture hours a week. The topic of polynomials is one of the oldest in mathematics and has applicability to almost every area of mathematics. The course will use algebra and analysis to study polynomials. Among topics to be covered: roots of polynomials (inequalities, relationship between the root of a polynomial and its derivative), resultants, discriminant, irreducible polynomials, special classes of polynomials (symmetric, cyclotomic, Chebysev).

MATH 4450 Theory of Numbers
Credit Hours 3.0
Prerequisites MATH 3000 with grade of C or higher
Description

Properties of integers, divisibility, congruence of problems.

MATH 4455 Error Correcting Codes
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 2641 with grades of C or higher
Description

This course provides an elementary, yet rigorous introduction to the theory of error correcting codes. Topics include survey of groups, finite fields and polynomials, linear algebra, Huffman codes, data compression and entropy, linear codes, Reed-Muller codes, cyclic codes, BCH codes, and fast decoding BCH codes.

MATH 4460 Cryptography
Credit Hours 3.0
Prerequisites MATH 3030 or MATH 2641 with grades of C or higher
Description

This course covers the mathematical background of computational and algorithmic methods for cryptography. This includes information theory, computational complexity and number theory. Methods covered include public key cryptosystems and secure methods for authentication and digital signatures.

MATH 4547 Introduction to Statistical Methods
Credit Hours 3.0
Prerequisites grade of C or higher in a course in calculus
Description

Degree credit will not be given for both MATH 4544 and MATH 4547. Data analysis, sampling, and probability; standard methods of statistical inference, including t-tests, chi-square tests, and nonparametric methods. Applications include use of a statistical computer package.

MATH 4548 Methods of Regression and Analysis of Variance
Credit Hours 3.0
Prerequisites grade of C or higher in a course in calculus, and a course covering methods of statistical inference
Description

Simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, design and analysis of experiments. Applications include use of a statistical computer package.

MATH 4610 Numerical Analysis I
Credit Hours 3.0
Prerequisites MATH 2215 with grade of C or higher and the ability to program in a high-level language
Description

(Same as CSC 4610.) Nature of error; iteration; techniques for nonlinear systems; zeros of functions; interpolation; numerical differentiation; Newton-Cotes formulae for definite integrals; computer implementation of algorithms.

MATH 4620 Numerical Analysis II
Credit Hours 3.0
Prerequisites Either MATH 3030 or both MATH 2641 and MATH 2215 with grades of C or higher, and the ability to program in a high level language
Description

(Same as CSC 4620.) Gaussian Elimination for linear systems; least squares; Taylor, predictor-corrector and Runge- Kutta methods for solving ordinary differential equations; boundary value problems; partial differential equations.

MATH 4650 Inverse and Ill-Posed Problems
Credit Hours 3.0
Prerequisites Either MATH 3030 or both MATH 2641 and MATH 2215, and Math/CSC 4610 or Math/CSC 4620 with grades of C or higher
Description

Ill-posed problems that arise in astrophysics, geophysics, spectroscopy, computerized tomography, and other areas of science and engineering are considered in this course. Topics to be covered: a general regularization theory; variational regularization and the discrepancey principle; iterative regularization; convergence analysis and stopping rules; numerical aspects.

MATH 4661 Analysis I
Credit Hours 3.0
Prerequisites MATH 2215, MATH 2641, and MATH 3000 with grades of C or higher
Corequisites MATH 4435
Description

The real number system, basic topology of metric spaces, sequences and series, limits and continuity.

MATH 4662 Analysis II
Credit Hours 3.0
Prerequisites MATH 4661 with grade of C or higher
Description

Differentiation of real functions, Reimann integrals, sequences and series of functions, differentation and integration of functions of several variables.

MATH 4671 Transforms in Applied Mathematics
Credit Hours 3.0
Prerequisites Either MATH 3030 or both MATH 2215 and MATH 2641 with grades of C or higher
Description

The Laplace transform, discrete and continuous Fourier Transforms, z-transforms, discrete filters, and wavelets.

MATH 4751 Mathematical Statistics I
Credit Hours 3.0
Prerequisites MATH 2215 with grade of C or higher
Description

Probability, random variables and their distributions, mathematical expectation, moment generating functions, sampling distributions.

MATH 4752 Mathematical Statistics II
Credit Hours 3.0
Prerequisites MATH 4751 with grade of C or higher
Description

Theory of estimation and hypothesis testing, applications of statistical inference, introduction to regression and correlation.

MATH 4767 Statistical Computing
Credit Hours 3.0
Prerequisites MATH 2215, MATH 2641, and either MATH 4752 or MATH 4548, with grades of C or higher and the ability to program in a high-level language
Description

Computational implementation of statistical methods such as descriptive statistics and graphs, testing for normality, one and two sample tests, Wilcoxon rank sum tests, Wilcoxon signed rank tests, basic regression and analysis of variance (ANOVA). Standard statistical packages (SAS) will be used as well as user-written programs.

MATH 4870 Honors Thesis: Research
Credit Hours 3.0
Prerequisites Good standing with the Honors College and consent of instructor
Description

Readings or research preparatory to Honors thesis or project. This course may include a Signature Experience component.

MATH 4880 Honors Thesis: Writing
Credit Hours 3.0
Prerequisites MATH 4870 with grade of C or higher, good standing with the Honors College and consent of instructor
Description

Writing or production of Honors thesis or project. This course may include a Signature Experience component.

MATH 4982 Undergraduate Research in Mathematics
Credit Hours 3.0
Prerequisites at least 12 upper-division hours in mathematics with grades of C or higher
Description

Authorization required. Independent investigation of topics of common interest to student and instructor. This course may include a Signature Experience component.

MATH 4991 Senior Seminar-CTW
Credit Hours 3.0
Prerequisites MATH 4435 with grade of C or higher
Description

This course introduces students to independent research in mathematics and related areas. Serves as one of the two Critical Thinking Through Writing (CTW) courses required of all mathematics majors.

MATH 4995 Directed Readings B.I.S.-CTW
Credit Hours 3.0 - 4.0
Description

Directed Readings designed for Bachelor of Interdisciplinary Studies students. This course may satisfy the junior and/or senior-level Critical Thinking Through Writing requirements.

MATH 4998 Selected Topics
Credit Hours 1.0 - 3.0
Prerequisites consent of instructor
Description

No more than six credit hours may be applied toward the major. May be repeated if topics are different.