CSM 154: MATHEMATICAL TECHNOLOGY (S)
4 credits/ Powers
This course focuses on 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 graphing calculator is required.
MTH 101: INTERMEDIATE ALGEBRA (F)
This course addresses 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.
MTH 113: ALGEBRA AND TRIGONOMETRY (F)
This course provides a 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.
MTH 114: APPLIED BUSINESS CALCULUS (F, S)
4 credits/ Powers
This course is an introduction to functions and modeling and 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 155. Prerequisite: MTH 101 or its equivalent.
MTH 120: CALCULUS AND ANALYTIC GEOMETRY I (F, S)
4 credits/ Powers
Topics in this course include 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; and integration using substitution. A TI graphing calculator is required. Prerequisite: MTH 113 or its equivalent
MTH 150: MATHEMATICS: MYTHS AND REALITIES (F, S)
3 credits/ Powers
This course offers an overview of mathematical concepts that are essential tools in navigat- ing 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.
MTH 221: CALCULUS AND ANALYTIC GEOMETRY II (S)
This course addresses 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. Prerequisite: MTH 120
MTH 222: CALCULUS AND ANALYTIC GEOMETRY III (F)
This course addresses three-dimensional geometry including equations of lines and planes in space, vectors. It offers 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.
MTH 240: LINEAR ALGEBRA AND APPLICATIONS (F)
This course includes 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.
MTH 260: DISCRETE STRUCTURES I (F)
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.
MTH 261: DISCRETE STRUCTURES II (S)
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.
MTH 302: FOUNDATIONS OF MATHEMATICS (S)
Topics in this course include 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.
MTH 321: REAL ANALYSIS
This is a course that emphasizes the 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
MTH 322: DIFFERENTIAL EQUATIONS (S, Even Years)
This course focuses on 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.
MTH 330: MODERN GEOMETRIES (F, Even Years)
Topics from Euclidean geometry including motions and similarities, collinearity and concurrence theorems, compass and straightedge constructions; the classical non-Euclidean geometries; finite geometries are presented in this course. Prerequisite: MTH 240.
MTH 341: ABSTRACT ALGEBRA (F, Even Years)
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 are topics of discussion in this course. Prerequisite: MTH 302.
MTH 345: COMBINATORICS
This course addresses permutations and combinations, generating functions, recurrence relations and difference equations, inclusion/exclusion principle, derangements, and other counting techniques, including cycle indexing and Polya’s method of enumeration. Prerequisite: MTH 221
MTH 370-379: SELECTED TOPICS IN MATHEMATICS
This is an introducory course to specialized areas of mathematics. The subject matter will vary from term to term. Prerequisite: junior mathematics standing
MTH 405: HISTORY OF MATHEMATICS (F, Odd Years)
This course is an 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.
MTH 410: PROBABILITY AND STATISTICS I (F, Odd Years)
Topics in this course include 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.
MTH 411: PROBABILITY AND STATISTICS II (S, Even Years)
Topics in this course include 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.
MTH 421: NUMERICAL ANALYSIS
This course addresses basic concepts, interpolation and approximations, summation and finite differences, numerical differentiation and integration, and roots of equations. Prerequisite: MTH 222
MTH 424: COMPLEX VARIABLES (F, Odd Years)
This course examines 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.
MTH 425: MATHEMATICAL MODELING (F, even years)
This course addresses the 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.
MTH 430: TOPOLOGY (S, Odd Years)
Topics in the course include topological spaces; subspaces; product spaces, quotient spaces; connectedness; compactness; metric spaces; applications to analysis. Prerequisite: MTH 302.
MTH 470-479: SELECTED TOPICS IN MATHEMATICS
This course is 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