MATHEMATICAL TECHNOLOGY

4 credits

Powers

The use of technology as a tool for solving problems in mathematics, learning mathematics and building mathematical conjectures; electronic spreadsheets, a Computer Algebra System (CAS), and a graphing calculator; the use of these tools, programming within all three environments, including spreadsheet macros, structured CAS programming, and calculator programming. A TI-89 calculator is required for mathematics majors; a TI graphing calculator is required for other majors.

INTERMEDIATE ALGEBRA

3 credits

Algebraic operations; linear and quadratic equations; exponents and radicals; elementary functions; graphs; and systems of linear equations. Students who have other college credits in mathematics must obtain permission of the department chair to enroll in this course. NOTE: Not to be taken to fulfill major requirements.

ALGEBRA AND TRIGONOMETRY

4 credits

Review of algebra; simultaneous equations; trigonometry; functions and graphs; properties of logarithmic, exponential, and trigonometric functions; problem-solving and modeling. A TI graphing calculator is required.

APPLIED BUSINESS CALCULUS

4 credits

Powers

Introduction to functions and modeling; differentiation. There will be a particular focus on mathematical modeling and business applications. Applications include: break-even analysis; compound interest; elasticity; inventory and lot size; income streams; and supply and demand curves. The course will include the frequent use of Microsoft Excel. A TI-84 or TI-83 graphing calculator is required. Co-requisite: CSC 151. Prerequisite: MTH 101 or its equivalent.

CALCULUS AND ANALYTIC GEOMETRY I

4 credits

Powers

Functions of various types: rational, trigonometric, exponential, logarithmic; limits and continuity; the derivative of a function and its interpretation; applications of derivatives including maxima and minima and curve sketching; antiderivatives, the definite integral and approximations; the fundamental theorem of calculus; integration using substitution. A TI-89 calculator is required for mathematics majors; a TI graphing calculator is required for other majors. Prerequisite: MTH 113 or its equivalent.

MATHEMATICS: MYTHS AND REALITIES

3 credits

Powers

Overview of mathematical concepts that are essential tools in navigating life as an informed and contributing citizen; logical reasoning, uses and abuses of percentages, interpreting statistical studies and graphs, the basics of probability, descriptive statistics, and exponential growth. Applications of these topics include population statistics, opinion polling, voting and apportionment, statistics in disease diagnoses and health care, lotteries and games of chance, and financial mathematics.

CALCULUS AND ANALYTIC GEOMETRY II

4 credits

Differentiation and integration of inverse trigonometric and hyperbolic functions; applications of integration, including area, volume, and arc length; techniques of integration, including integration by parts, partial fraction decomposition, and trigonometric substitution; L’Hopital’s Rule; improper integrals; infinite series and convergence tests; Taylor series; parametric equations; polar coordinates; and conic sections. A TI graphing calculator is required for other majors. Prerequisite: MTH 120.

CALCULUS AND ANALYTIC GEOMETRY III

4 credits

Three-dimensional geometry including equations of lines and planes in space, vectors. An introduction to multi-variable calculus including vector-valued functions, partial differentiation, optimization, and multiple integration. Applications of partial differentiation and multiple integration. A TI-89 calculator is required. Prerequisite: MTH 221.

LINEAR ALGEBRA AND APPLICATIONS

4 credits

Systems of linear equations; matrices; determinants; real vector spaces; basis and dimension; linear transformations; eigenvalues and eigenvectors; orthogonality; applications in mathematics, computer science, the natural sciences, and economics. Prerequisite: MTH 221.

DISCRETE STRUCTURES I

3 credits

This course is the first half of a two-semester course in discrete mathematics. The intended audience of the course consists of computer science majors (both B.A. and B.S.) and IT majors. Topics in the course include logic, sets, functions, relations and equivalence relations, graphs, and trees. There will be an emphasis on applications to computer science.

DISCRETE STRUCTURES II

3 credits

This course is the second half of a two-semester course in discrete mathematics. The intended audience of the course consists of computer science majors (both B.A. and B.S.) and IT majors. Topics in the course include number theory, matrix arithmetic, induction, counting, discrete probability, recurrence relations, and Boolean algebra. There will be an emphasis on applications to computer science. Prerequisite: MTH 260.

FOUNDATIONS OF MATHEMATICS

3 credits

Propositional logic; methods of proof; sets and cardinality; basic properties of integers; elementary number theory; structure of the real numbers; sequences; functions and relations. Prerequisite: MTH 221.

REAL ANALYSIS

3 credits

Theory behind calculus topics such as continuity, differentiation, integration, and sequences and series (both of numbers and of functions); basic topology, Fourier Series. Prerequisites: MTH 222 and 302

DIFFERENTIAL EQUATIONS

4 credits

Analytical, graphical, and numerical techniques for first and higher order differential equations; Laplace transform methods; systems of coupled linear differential equations; phase portraits and stability; applications in the natural and social sciences. Prerequisite: MTH 221.

MODERN GEOMETRIES

3 credits

Topics from Euclidean geometry including motions and similarities, collinearity and concurrence theorems, compass and straightedge constructions; the classical non-Euclidean geometries; finite geometries. Prerequisite: MTH 240.

ABSTRACT ALGEBRA

3 credits

Sets and mappings; groups, rings, fields, and integral domains; substructures and quotient structures; homomorphisms and isomorphisms; abelian and cyclic groups; symmetric and alternating groups; polynomial rings. Prerequisite: MTH 302.

COMBINATORICS

3 credits

Permutations and combinations; generating functions; recurrence relations and difference equations; inclusion/exclusion principle; derangements; other counting techniques, including cycle indexing and Polya’s method of enumeration. Prerequisite: MTH 221.

SELECTED TOPICS IN MATHEMATICS

3 credits

An introduction to specialized areas of mathematics. The subject matter will vary from term to term. Prerequisite: junior Mathematics standing.

HISTORY OF MATHEMATICS

3 credits

In-depth historical development of arithmetic, algebra, geometry, trigonometry, and calculus in Western mathematics (Europe and Near East) from ancient times into the 1700s; highlights from the mathematical work of such figures as Hippocrates, Euclid, Archimedes, Heron, Diophantus, Fibonacci, Cardano, Napier, Descartes, Fermat, Newton, and Leibniz; non-Euclidean geometry (1800s); important contributions of Euler and Gauss; the advent of computers. Prerequisite: MTH 302.

PROBABILITY AND STATISTICS I

3 credits

Sample spaces and probability measures; descriptive statistics; combinatorics, conditional probability and independence; random variables, joint densities and distributions; conditional distributions; functions of a random variable; expected value and variance; Chebyshev’s inequality; correlation coefficient; laws of large numbers; the Central Limit Theorem; various distribution models; introduction to confidence intervals. Prerequisite: MTH 222.

PROBABILITY AND STATISTICS II

3 credits

Measures of central tendency and variability; random sampling from normal and non-normal populations; estimation of parameters; maximum likelihood estimates; confidence intervals and hypothesis testing; normal, chi-square, Student’s t and F distributions; analysis of variance; randomized block design; correlation and regression; goodness of fit; contingency tables. Prerequisite: MTH 410.

NUMERICAL ANALYSIS

4 credits

Basic concepts; interpolation and approximations; summation and finite differences; numerical differentiation and integration; roots of equations. Prerequisite: MTH 222

COMPLEX VARIABLES

3 credits

Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem; power series; infinite series; calculus of residues; contour integration; conformal mapping. Prerequisite: MTH 222 or permission of the instructor.

MATHEMATICAL MODELING

3 credits

Uses of mathematical methods to model real-world situations, including energy management, assembly-line control, inventory problems, population growth, predator-prey models. Other topics include: least squares, optimization methods interpolation, interactive dynamic systems, and simulation modeling. Prerequisite: MTH 221.

TOPOLOGY

3 credits

Topological spaces; subspaces; product spaces, quotient spaces; connectedness; compactness; metric spaces; applications to analysis. Prerequisite: MTH 302.

SELECTED TOPICS IN MATHEMATICS

3 credits

An introduction to specialized research, concentrating on one particular aspect of mathematics. The subject matter will vary from term to term. Prerequisite: senior Mathematics standing.