Schedule of Classes

Encouraging audience appreciation of mathematics by investigating some of the great ideas of mathematical history, seeing contemporary applications, and getting a feel for the way mathematicians think.

For students who need to strengthen their algebra skills: factoring polynomials; solving quadratic and other equations; exponents, logarithms, and graphing.

Data collection processes (observational studies, experimental design, sampling techniques, bias), descriptive methods using quantitative and qualitative data, bivariate data, correlation, and least- squares regression, basic probability theory, probability distributions (normal distributions and normal curve, binomial distribution), confidence intervals and hypothesis tests using p-values and selected applications. Additionally, statistical software will be used with an emphasis on interpretation and evaluation of statistical results.

For students needing further background in mathematics before enrolling in calculus (especially MTH 121). Thorough study of algebraic, transcendental, and trigonometric functions; emphasis on graphing and use of algebra.

A survey of the most common mathematical techniques used in business. Topics include: linear functions, non-linear functions (polynomials, exponentials, logarithms), systems of linear equations, linear programming, sets and probability, introduction to basic statistics.

Differential and integral calculus with emphasis on understanding through graphs. Topics in analytic geometry, limits, derivatives, antiderivatives, definite integrals, exponential and logarithmic functions, and partial derivatives.

Introduction to graph theory, Boolean algebra, mathematical induction, and elementary combinatorics.

Topics for this first course in calculus include functions, limits, continuity, the derivative, differentiation of algebraic, trigonometric, logarithmic and exponential functions with applications including curve sketching, anti-differentiation and applications of integrals, the Riemann sum, and the Fundamental Theorem of Calculus.

Topics for this second course in calculus include techniques of integration, applications of the definite integral, infinite series, Taylor series, polar coordinates, and parametrized curves in the plane.

Matrix algebra, determinants, theory of simultaneous equations, vector spaces, bases, Gram-Schmidt orthogonalization, eigenvalues, eigenvectors, transformations, and applications.

Topics for this third course in calculus including vector analysis of three-dimensional Euclidean space, functions of several variables, partial differentiation, multiple integrals, line integrals and surface integrals, the integral theorems of vector calculus.

Solutions of limited classes of first order equations; second order linear equations; Laplace transform methods; numerical methods; autonomous systems, including linear systems of two variables.

Topics of special interest which may vary each time course is offered, rotating among geometry, algebra/number theory, and problem-solving. Historical motivations will be provided within each topic. For middle school teacher certification; does not count toward a math major or math minor. May be repeated under different topics for a maximum of 9 hours credit.

An upper-level treatment of fundamental concepts in probability theory and statistics: discrete and continuous random variables; particular probability distributions of each type; multivariate probability distributions; conditional and marginal probabilities; moment-generating functions; Central Limit Theorem.

Topics may vary each time course is offered, rotating among compound interest, mathematics of life contingencies, and actuarial mathematics. Some topics will coincide with those on actuarial exams. May be repeated under different topics for a maximum of 9 hours credit.

Basic theory of groups, rings, and fields with an emphasis on groups and rings, including the Fundamental Theorem of Homomorphisms.

Theory of, and solution techniques for, partial differential equations of first and second order, including the heat equation, wave equation and Laplace equation in rectangular, cylindrical, and spherical coordinates. Topics include classification of PDE in terms of order, linearity, and homogeneity; solution techniques include separation of variables, Fourier series, and integral operators; and a subset of more advanced topics such as transform methods and numerical methods. Credit will be given for only one of MTH 414, MTH 514.

Real number system and functions of real variables: sequences, limits, continuity, differentiation, series, uniform convergence, and the Riemann-Stieltjes integral.

Conditional probability and expectation, probability models, Markov chains, Poisson process, renewal theory, Brownian motion processes.

Topics in mathematics selected, studied, and discussed by students under faculty guidance. Each student explores an area of mathematics and selects a topic in which he or she has a particular interest.

A selected topic in mathematics is studied by a student under faculty guidance. Each student writes a paper and gives a presentation on his or her topic.

Theory of, and solution techniques for, partial differential equations of first and second order, including the heat equation, wave equation and Laplace equation in rectangular, cylindrical, and spherical coordinates. Topics include classification of PDE in terms of order, linearity, and homogeneity; solution techniques include separation of variables, Fourier series, and integral operators; and a subset of more advanced topics such as transform methods and numerical methods.