# Course Descriptions

CSM 154: MATHEMATICAL TECHNOLOGY

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)

3 credits

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)

4 credits

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. 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 navigating life as an informed and contributing citizen, including logical reasoning, uses and abuses of percentages, financial mathematics (compound interest, annuities), linear and exponential models, fundamentals of probability, and descriptive statistics. Applications include such topics as population growth models, opinion polling, voting and apportionment, health care statistics, and lotteries and games of chance.

MTH 221: CALCULUS AND ANALYTIC GEOMETRY II (S)

4 credits

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)

4 credits

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 graphing calculator is required. Prerequisite: MTH 221.

MTH 240: LINEAR ALGEBRA AND APPLICATIONS (F)

4 credits

This course includes vectors and matrices, systems of linear equations, determinants, real vector spaces, spanning and linear independence, basis and dimension, linear transformations, eigenvalues and eigenvectors, and orthogonality. Applications in mathematics, computer science, the natural sciences, and economics are treated. Prerequisite: MTH 221.

MTH 260: DISCRETE STRUCTURES I (F)

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.

MTH 261: DISCRETE STRUCTURES II (S)

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.

MTH 302: FOUNDATIONS OF MATHEMATICS (S)

3 credits

Topics in this course include propositional logic, methods of proof, sets, fundamental properties of integers, elementary number theory, functions and relations, cardinality, and the structure of the real numbers. Prerequisite: MTH 221.

MTH 321: REAL ANALYSIS

3 credits

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

4 credits

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)

3 credits

Topics from Euclidean geometry including: planar and spatial motions and similarities, collinearity and concurrence theorems for triangles, the nine-point circle and Euler line of a triangle, cyclic quadrilaterals, compass and straightedge constructions. In addition, finite geometries and the classical non-Euclidean geometries are introduced. Prerequisite: MTH 240.

MTH 341: ABSTRACT ALGEBRA (F, Even Years)

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 are topics of discussion in this course. Prerequisite: MTH 302.

MTH 345: COMBINATORICS

3 credits

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

3 credits

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)

3 credits

This course is an in-depth historical study of the development of arithmetic, algebra, geometry, trigonometry, and calculus in Western mathematics (Europe and the Near East) from ancient times up through the 19th century, including highlights from the mathematical works of such figures as Euclid, Archimedes, Diophantus, Fibonacci, Cardano, Napier, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, and Gauss. A term paper on some aspect of the history of mathematics is required. Prerequisite: MTH 302.

MTH 410: PROBABILITY AND STATISTICS I (F, Odd Years)

3 credits

Topics in this course include sample spaces and probability measures, descriptive statistics, combinatorics, conditional probability, independence, random variables, joint densities and distributions, conditional distributions, functions of a random variable, expected value, variance, various continuous and discrete distribution functions, and the Central Limit Theorem. Prerequisite: MTH 222.

MTH 411: PROBABILITY AND STATISTICS II (S, Even Years)

3 credits

Topics in this course include measures of central tendency and variability, random sampling from normal and non-normal populations, estimation of parameters, properties of estimators, maximum likelihood and method of moments estimators, confidence intervals, hypothesis testing, a variety of standard statistical distributions (normal, chi-square, Student’s t, and F), analysis of variance, randomized block design, correlation, regression, goodness of fit, and contingency tables. Prerequisite: MTH 410.

MTH 421: NUMERICAL ANALYSIS

4 credits

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)

3 credits

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

3 credits

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)

3 credits

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

3 credits

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