Mathematics Course Descriptions

Math 107 Mathematics for Elementary Teachers (4)
Course is designed to strengthen understanding of the mathematics that prospective teachers will teach. Natural numbers, whole numbers, integers, rational numbers, real numbers, and their properties. Exploration of a variety of representations of different operations. Study of algebraic reasoning and representation. Investigations of measurements of area, perimeter, surface area, and volume. Geometry concepts including transformations, constructions, and similarities. Offered: Fall, Spring and possibly Jan Term and/or Summer.

Math 110 Contemporary Mathematics (4)
Development of problem-solving skills obtained by studying a wide range of contemporary applications of mathematics. Connections between contemporary mathematics and modern society are stressed. Prerequisite: Suitable score on placement exam. Offered: Fall, Jan Term, Spring, and Summer 1 only.

Math 150 Precalculus (4)
Introduction to a combination of the standard topics from college algebra and trigonometry. Introduces some modern mathematical modeling, ideas and applications with skills and knowledge needed for subsequent mathematics courses and/or real world applications. Covers linear, quadratic, exponential, power, logarithmic, polynomial, inverse, and trigonometric functions. A graphing calculator is required; consult department for recommended model. Prerequisite: Suitable score on placement exam. Offered: Fall, Jan Term, Spring, and Summer 1 only.

Math 210 Elementary Statistics (4)
Introduction of algebra-based statistics. Covers descriptive and inferential statistics with probability decision-making skills necessary for today's complex civilization. Covers frequency, probability, binomial, normal, chi-square and sampling distributions, estimation, hypothesis testing for one and two populations, linear correlation and regression, and analysis of variance. Uses the graphing calculator and statistical computing packages. Prerequisite: Suitable score on placement exam. Offered: Fall, Spring, Summer 1, possibly Summer 2 and/or Jan Term.

Math 240 Calculus I (4)
Study of calculus. Review of precalculus functions with an emphasis on graphical, numerical, and modeling applications. Calculus topics to be covered: limits, continuity, derivatives and their interpretations, tangent line approximations, the definite integral as a limit of Riemann sums, applications of the definite integral to area and average value, the Fundamental Theorem of Calculus, rules of derivatives, formulas for derivatives of precalculus functions, implicit functions, economics applications, optimization and modeling, and Newton's method. This course requires that each student have a graphing calculator; see the department chair for the recommended model. Also, students in the course will be required to complete assignments and/or projects using the computer algebra system, Mathematica. Prerequisite: Math 150 or suitable score on placement exam. Offered: Fall, Jan Term, Spring, possibly Summer 1 and/or Summer 2.

Math 260 Calculus II (4)
Sequel to Math 240 Calculus I. Topics include: Antiderivatives, integration by substitution, integration by parts, approximation of definite integrals, improper integrals, setting up of Riemann sums in applications, applications of definite integrals to geometry, physics, and economics, probability distributions, simple first order differential equations, slope fields, Euler's method, separation of variables, growth and decay, systems of differential equations, applications of second order equations to oscillations, Taylor approximations, and Taylor series. This course requires that each student have a graphing calculator; see the department chair for the recommended model. Also, students in the course will be required to complete assignments and/or projects using the computer algebra system, Mathematica. Prerequisite: Completion of Math 240 with a grade of C or better. Offered: Fall and Spring only.

Math 270 Calculus III (4)
Sequel to Calculus II. Topics include: Functions of two and three variables, graphs of surfaces, contour plots, vectors, dot products, cross products, partial derivatives, local linearity, differentials, directional derivatives, gradients, chain rule, partial differential equations, constrained and unconstrained optimization, multivariable integration, iterated integrals, numerical integration by the Monte Carlo method, change of variables in multivariable integrals, parameterized curves and surfaces. The course requires that each student have a graphing calculator; see the department chair for the recommended model. Also, students in the course will be required to complete assignments and/or projects using the computer algebra system, Mathematica. Prerequisite: Completion of Math 260 with a grade of C or better. Offered: Fall and Spring only.

Math 280 Introduction to Advanced Mathematics (4)
Transition from the calculus sequence to upper-level math courses. A major objective is learning how to read, understand, and write proofs. Hence logic and proof techniques and strategies are discussed heavily. The second major objective is the learning of certain basic math concepts needed for upper-level math courses, including set theory, functions, and relations. Other topics may include infinite sets, the set of integers, the set of real numbers, discrete math, and basic number theory. Prerequisite: Math 270 Calculus III as a prerequisite or corequisite. Offered: Fall and Spring only.

Math 320 Numerical Analysis (4)
Fine differences, interpolations, differentiation and integration, Lagrangian formulas, solutions of equations and systems of equations initial-value problems for ordinary differential equations, curve fitting, and approximation theory. Strongly recommneded: MATH 280 or COSC 200; Prerequisite: Math 270.

Math 330 Differential Equations (4)
Study of ordinary differential equations. Methods of solutions to differential equations are presented and applied in detail. Topics include the general solution to a linear differential equation, linear homogeneous and nonhomogeneous differential equations of higher order with constant coefficients, Laplace transforms, infinite series methods, Legendre Polynomials, Bessel Functions, and linear systems of differential equations. Strongly recommended: Math 280 and/or COSC 200; Prerequisite: Math 270. Offered: Spring only.

Math 340 Linear Algebra (4)
Fields, systems of linear equations, matrices, vector spaces, subspaces, bases and dimension, linear transformations, isomorphism, representation of transformations by matrices, linear functionals, determinants, eigenvalues and eigenvectors, invariant subspaces, inner product spaces, stochastic matrices, matrix exponentials, and numerical methods. Strongly recommended: MATH 280 and/or COSC 200; Prerequisite: Math 270. Offered: Fall only.

Math 350 Vector Calculus (4)
Vector algebra in two and three dimensions, equations of lines in space, scalar products, orientation, vector products, triple scalar products, vector identities, tensors, vector valued functions, velocity, tangent vectors, acceleration, vector fields, gradients, divergence, curl, the Laplacian, line integrals, potentials, conservative fields, irrotational fields, surface integrals, volume integrals, divergence theorem, Green's formula, Stoke's theorem. Applications to electrostatics, force fields, potential theory, fluid flow, heat flow, gravitation, wave equations. Strongly recommended: PHYS 203 and PHYS 204; MATH 280 and/or COSC 200; Prerequisite: Math 270.

Math 360 Complex Variables (4)
Study of functions of a complex variable. Topics include analytic and harmonic functions, transformation and mapping, complex integration, power series, residues and poles, conformal mapping, and additional theory of functions. Strongly recommended: MATH 280 and/or COSC 200; Prerequisite: Math 270.

Math 370 Mathematical Statistics (4)
Introduction to calculus-based probability theory and statistical inference. Topics include: Probability measures, independence and conditional probability, discrete random variables, continuous random variables, distribution functions, expectations, multivariate distributions, correlations, binomial, Poisson, gamma, chi-square, and normal distributions, sampling distributions, order statistics, moment-generating functions, functions of random variables, convergence of distributions, central limit theorem, point estimators, maximum likelihood, confidence intervals, hypothesis testing, sufficient statistics, Bayesian estimation, likelihood ratio tests, analysis of variance, linear regression, and nonparametric statistics. Strongly recommended: MATH 280 and/or COSC 200; Prerequisite: Math 270.

Math 410W Number Theory (4)
Introduction to the theory of numbers. Divisibility, factorization, prime numbers, congruencies, arithmetic functions, quadratic residues, and Diophantine equations. Additional topics could be chosen from primitive roots, continued fractions, cryptography, Fibonacci numbers, and numerical techniques. Prerequisite: Math 280.

Math 420 College Geometry (4)
Axiomatic, proof-oriented treatment of different geometries. This includes synthetic, metric, absolute, and euclidean geometries. Other topics can include finite geometries, fractals, constructions, and specific non-euclidean geometries. Prerequisite: Math 280.

Math 430 Abstract Algebra (4)
Introduction to abstract algebra: groups, rings, and fields. Binary operations, groups, subgroups, cyclic groups, groups of permutations, cosets, finitely generated groups, homomorphisms, isomorphisms, factor groups, rings, fields, and integral domains. Additional topics could include fields of quotients, rings of polynomials, factor rings, ideals, unique factorization domains, and the Sylow Theorems. Prerequisite: Math 340 or Math 410.

Math 440 Introductory Real Analysis (4)
Proof-oriented course covering an introduction to topics in mathematical analysis. Topics include: Field axioms of the real numbers, completeness axiom, set theory, relations and functions, infinite sets, countable sets, open and closed sets, closure, limit points, Bolzano-Weierstrass theorem, limits and partial limits of sequences, monotone sequences, Cauchy sequences, limits of functions, continuity, extreme value theorem, intermediate value theorem, uniform continuity, differentiation, chain rule, mean value theorem, L'Hopital's rule, convergent series, tests for convergence of series, rearrangement of series, Riemann sums, Riemann integrability, Fundamental theorem of Calculus, change of variables, sequences of functions, uniform convergence, and power series. Prerequisite: MATH 280.

Math 450 General Topology (4)
Survey of the fundamental concepts of general topology which depend upon the elementary properties of sets and functions. This course will cover topological spaces, subspaces, continuity, homeomorphisms, product spaces, connectedness, compactness, separation properties, and metric spaces. Prerequisite: Math 280.

Math 480 Topics in Mathematics (1-4)
Various topics in Mathematics to be covered primarily through an independent study set up between a student (or students) and a faculty member. May be repeated for credit. Prerequisite: At least one upper-level mathematics course.

Math 490W Senior Seminar (4)
Course consists of three components: 1) A topic will be selected by the instructor to be presented in the "Moore style", i.e. a list of results will be handed out to the students, and the students will be responsible for proving these results in class. Topics in the past have included fractals, game theory, wavelets, cryptography, combinatorics, and graph theory. 2) Students will be required to write a paper surveying a major area in mathematics. 3) Students will be required to turn in a term project in the form of a Mathematica notebook. The project will involve extensive writing introducing and developing a topic, programming in Mathematica, and numerical/graphical examples using Mathematica. Students will also be required to present their project in class. Also, students will be required to take the MFT. Prerequisite: At least one 400-level mathematics course. Offered: Fall and Spring only.