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.

Continuation of MTH 115. Includes trig functions, integration techniques, series, differential equations, and multivariable calculus.

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.

Introduction to properties of formal axiom systems. Study of Euclidean and non-Euclidean geometries, including historical motivations. Topics will be explored using appropriate dynamic software.

Vector spaces, linear transformations, inner product spaces, Jordan canonical forms, spectral theorems, and selected topics.

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.

A continuation of MTH 325 which focuses on statistical inference by way of confidence intervals, hypothesis tests, least-squares regression models, and analysis of variance. Key concepts also include: measures of goodness for point estimators, minimum-variance unbiased estimators, uniformly most powerful tests, maximum likelihood estimators.

Introduction to complex calculus: analytic functions, integration, Cauchy's formula, Laurent series, the residue theorem and its applications; and a subset of more advanced topics such as conformal mapping, the Riemann mapping theorem, harmonic functions, and analytic continuation.

Introduction to numerical and computational aspects of various mathematical topics: finite precision, solutions of non-linear equations, interpolation, approximation, linear systems of equations, and integration.

Individual work in special areas of mathematics for advanced, qualified undergraduate students. May register for more than 6 hrs. credit only if enrolled in an approved special off campus program.

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.

Introduction to numerical and computational aspects of various mathematical topics: finite precision, solutions of non-linear equations, interpolation, approximation, linear systems of equations, and integration. Cross listed as CS 510.