Focused, just-in-time review of the background algebra skills needed to be successful in MTH 1309.

Focused, just-in-time review of the background algebra and trigonometry skills needed to be successful in MTH 1321.

Algebra review for students who need to take MTH 1320 (pre-calculus) but are not ready for MTH 1320. Topics include solving equations and inequalities, polynomials, rational functions, exponential functions, and logarithms. Begins 5 weeks into the semester. Does not apply on major. Does not satisfy the mathematics requirement for any degree.

Significant ideas of mathematics. Topics will be chosen from: voting theory, apportionment, financial analysis, linear and exponential growth, statistics and opinion polls. Designed primarily for liberal arts students. Does not apply toward the major.

A study of the types of function that arise in business calculus, including linear, quadratic, and other polynomial functions, rational functions, and exponential and logarithmic functions. Does not apply on the Arts and Sciences mathematics requirement nor on a mathematics major. Credit may not be received after receiving credit in MTH 1320.

Prerequisite (s): A grade of C or better in MTH 1320 or MTH 1308 or a satisfactory performance on the SAT or RSAT or the ACT or the ALEKS. Differentiation of rational, exponential, and logarithmic functions of one and several variables, integration of functions of one variable, and applications to business problems. Does not apply on the major. Credit may not be received after receiving credit in MTH 1321.

Advanced perspectives on topics taught in grades EC-8 including number concepts, patterns, and functions. Does not satisfy the liberal arts mathematics requirement and does not apply toward the mathematics major.

A continuation of MTH 1315. Topics in MTH 1316 will be geometric figures, motions of geometry, and measurement. Does not apply toward the mathematics major.

Basic concepts of college algebra, trigonometry, and elementary functions and an introduction to limits. Satisfactory performance on a department examination. Designed as preparation for MTH 1321; does not apply on the major.

Differential calculus of a single variable. Introduction to the definite integral and the Fundamental Theorem of Calculus.

Integral calculus of a single variable, differential equations, slope fields, and power series.

Vectors, matrix operations, linear transformations, fundamental properties of vector spaces, systems of linear equations, eigenvalues, and eigenvectors.

Designed for the prospective teacher seeking mathematics certification for grades 4-8. A study of the algebraic and transcendental functions which play a primary role in calculus. An emphasis will be placed on mathematical models which arise from lab-based activities, on connections to areas within and outside of mathematics, and on developing the ability to communicate mathematical ideas to individuals at various levels. Does not apply toward the mathematics major.

Designed for the prospective teacher seeking mathematics certification for grades 4-8. A continuation of MTH 2316. An investigation of the derivative and integral from an algebraic, geometric, and numerical perspective. Credit may not be received after completion of MTH 1321. Does not apply toward the mathematics major.

Differential and integral calculus of several variables, Green's Theorem.

Beginning independent study or research in topics not available in other courses. May be repeated for a maximum of 3 hours.

Core concepts of advanced mathematics: proofs, induction, sets, functions, equivalence relations, divisibility, modular arithmetic, real numbers, sequences and limits.

Elementary counting principles, fundamental properties of the integers, the ring of integers modulo n, rings of polynomials, and an introduction to groups, rings and fields.

Designed for the prospective teacher seeking an EC-4 mathematics certification. Core ideas from probability and statistics, including collection of data, patterns in data, and inference from data, in an active lab-like environment. Credit may not be received after completion of MTH 2381 or MTH 3381. Does not apply toward the mathematics major.

A rigorous treatment of the real number system, sequences of real numbers, limits, continuous functions, and elements of differentiation and integration.

See CSI 3324 for course information.

Differential equations of first order, linear equations of order two and higher, introduction to power series methods, elements of the Laplace Transform, some facts from linear algebra and systems of differential equations.

Partial differential equations of physics, the method of separation of variables, orthogonal sets of functions, Fourier Series, boundary value problems, Fourier integrals and applications.

Topics include linear and nonlinear transport equations, Hamilton-Jacobi equations, and diffusions, with some applications to game theory.

(This prerequisite cannot be satisfied using any hours transferred in under the generic titles MTH 1000 or MTH 2000.) Designed for the prospective mathematics teacher seeking certification for grades 4-8 or 8-12. Use of technology to explore, communicate, and reinforce mathematical concepts and problem solving from several areas of mathematics. Attention given to graphing calculators, interactive geometry computer packages, computer-based algebra packages, and spreadsheets or statistical packages. Written and oral presentations. Does not apply toward the mathematics major.

See PHI 4345 for course information.

A study of the foundations of Euclidean geometry by synthetic methods with a brief introduction to non-Euclidean geometry.

Concepts taken from probability and statistics, algebra and number concepts, and Euclidean and non-Euclidean geometry, with a focus on the role and history of proof and reasoning as the cornerstone in arriving at mathematical conclusions. Does not apply toward the mathematics major or as a secondary mathematics elective.

A survey of models and methods used in operations research. Topics include linear programming, dynamic programming, and game theory, with emphasis on the construction of mathematical models for problems arising in a variety of applied areas and an introduction to basic solution techniques.

An introduction to the process of mathematical modeling, including problem identification, model construction, model selection, simulation, and model verification. Individual and team projects.

Advanced independent study or research in topics not available in other courses. May be repeated for a maximum of 3 hours.

Undergraduate research undertaken with the supervision of a faculty member. May be taken for a maximum of 6 hours.

Introduction to cryptology, the study of select codes and ciphers. Included is a historical context, a survey of modern crypto systems, and an exposition of the role of mathematical topics such as number theory and elliptic curves in the subject. Mathematical software will be available.

Algebraic number theory including linear Diophantine equations, distribution of primes, congruence, number theoretic functions, Euler's and Wilson's theorems, Pythagorean triples, Mersenne and Fermat primes, Fibonacci numbers, and sums of squares. Continued fractions, quadratic reciprocity, Mobius inversion, Bertrand's postulate, prime number theorem, and zeta function may also be included.

Fundamentals of group, ring, and field theory. Topics include permutation groups, group and ring homomorphisms, direct products of groups and rings, quotient objects, integral domains, field of quotients, polynomial rings, unique factorization domains, extension fields, and finite fields.

Matrix calculus, eigenvalues and eigenvectors, canonical forms, orthogonal and unitary transformation, and quadratic forms. Applications of these concepts.

Numerical evaluation of derivatives and integrals, solution of algebraic and differential equations, and approximation theory.

A continuation of MTH 3325 with emphasis on systems of ordinary differential equations. Topics include matrix and first order linear systems of differential equations, eigenvalues and eigenvectors, two-dimensional autonomous systems, critical point analysis, phase plane analysis, Liapunov, stability theory, limit cycles and Poincare-Bendixson theorem, periodic solutions, perturbation methods, and some fixed point theory.

The real and complex number systems, basic topology, numerical sequences and series, continuity, differentiation, integration, sequences and series of functions.

Line and surface integrals, Green, Gauss, Stokes theorems with applications, Fourier series and integrals, functions defined by integrals, introduction to complex functions.

Numerical methods for solution of linear equations, eigenvalue problems, and least squares problems, including sparse matrix techniques with applications to partial equations.

Number systems: the complex plane; fractions, powers, and roots; analytic functions; elementary functions; complex integration; power series; mapping by elementary functions; calculus of residues.

Prospective middle and secondary school mathematics teachers engage in an in-depth analysis of mathematical topics encountered in the middle and secondary curriculum. Does not apply toward the mathematics major.

An introduction to the theory and applications of linear programming, including the simplex algorithm, duality, sensitivity analysis, parametric linear programming, and integer programming, with applications to transportation, allocation problems, and game theory.

Topics in contemporary mathematics not covered in other courses. May be repeated once for credit if content is different.

Undergraduate research undertaken with the supervision of a faculty member. May be taken for a maximum of 6 hours.