Mathematics CoursesMATH 110 Mathematics in our World 4 hours Quantitative literacy plays an important role in an increasing number of professional fields, as well as in the daily decisionmaking of informed citizens in our changing society. This course is designed to improve students' quantitative reasoning and problem-solving skills by acquainting them with various real-world applications of mathematical reasoning, such as fair division, voting and apportionment, graph theory, probability, statistics, the mathematics of finance, check digits and coding, and geometry. This course is recommended for students who wish to take a non-calculus-based mathematics class as they prepare for their lives as informed members of a larger world. Prerequisite: high school algebra. (Quant) MATH 115 Introduction to Statistics 4 hours The course uses data sets from the social and natural sciences to help students understand and interpret statistical information. Computer software is used to study data from graphical and numerical perspectives. Topics covered include measures of central tendency and dispersion ("descriptive statistics"), probability distributions, sampling methods, point and interval estimation ("confidence intervals"), correlation, regression, contingency tables and tests of hypotheses. This class does not count towards the mathematics major or minor or the mathematics/statistics major. Prerequisite: high school algebra. (Quant) MATH 123 Mathematics for Elementary School Teachers 4 hours This course provides pre-service K–8 teachers a strong foundation in the mathematics content areas as described in the NCTM's Principles and Standards for School Mathematics. The content standards include: Numbers and Operations, Algebra, Geometry, Measurement, Statistics and Probability. This course will engage students in standards-based mathematics learning to prepare them for the pedagogical practices they will learn in EDUC 325. Prerequisite: one year of high school algebra, one year of high school geometry and admission into the teacher education program. Corequisite: EDUC 325. (Quant) MATH 139, 239, 339, 439 Special Topics Credit arr. MATH 140 Precalculus with Derivatives 4 hours Algebraic and graphical representations of functions including: polynomial, rational, exponential, logarithmic, and trigonometric; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change: limits, derivatives; continuity; applications of derivatives. Graphing calculator use is required. (Quant) MATH 141 Calculus I with Algebra and Trigonometry 4 hours Continuation of topics of MATH 140: functions and their derivatives, chain rule, the mean value theorem, Riemann sum approximation for integrals, definite integrals, antiderivatives, and applications. Graphing calculator use is required. (Students who earn credit for MATH 141 may not earn credit for MATH 151.) Prerequisite: MATH 140 or consent of instructor. (Quant) MATH 151 Calculus I 4 hours Topics related to instantaneous rates of change: functions, limits, continuity, derivatives, mean value theorem and applications; antiderivatives and definite integrals. Graphing calculator use is required. (Students who earn credit for MATH 151 may not earn credit for MATH 140, or MATH 141.) Prerequisites: a minimum of one and one-half years of algebra, one-half year of trigonometry, and one year of geometry. (Quant) MATH 152 Calculus II 4 hours Applications of the definite integral, techniques of integration, differential equations, power series, Taylor series, and an introduction to computer algebra systems. Prerequisite: MATH 141 or MATH 151 or consent of instructor. (Quant) MATH 185 First-year Seminar 4 hours A variety of seminars for first-year students offered each January term. MATH 220 Discrete Structures 4 hours Propositional and predicate logic, methods of proof, induction, recursion and recurrence relations, sets and combinatorics, binary relations (including equivalence relations and partial orderings), functions, Boolean algebra and computer logic, and finite state machines. Prerequisite: MATH 152 or above; or CS 150, 151, or 200; or consent of instructor. (Same as CS 220.) (Quant) MATH 235 Operations Research 4 hours Model building. Analytic tools useful to management chosen from linear programming, simplex algorithm, sensitivity analysis, duality; integer linear programming; goal programming; dynamic programming; networks, PERT-CPM, maximum flow, shortest path; simulation; nonlinear programming. Offered alternate years. Prerequisite: MATH 140 or MATH 151. (Quant) MATH 240 Linear Algebra 4 hours Matrices, abstract vector spaces, subspaces, spanning sets, linear independence, bases, linear transformations, isomorphisms, eigenvalues and eigenvectors, inner product spaces. Prerequisite: MATH 152, or consent of instructor. (Quant) MATH 253 Multivariable Calculus 4 hours Vector valued functions: limits, continuity, derivatives, and integrals. Length of space curves, tangents and normals to curves. Functions of several variables: limits, continuity, partial derivatives, directional derivatives, the gradient, tangent plane approximation and differentials, extreme value, multiple integrals, vector fields, line integrals, Green's theorem, surface integrals, Stokes' theorem, the divergence theorem. Prerequisite: MATH 240. (Quant) MATH 260 Elementary Number Theory 4 hours Divisibility theory in the integers, prime numbers, Euclidean algorithm, Diophantine equations, congruences, divisibility tests, Euler's theorem, public key cryptography, primitive roots, quadratic reciprocity law. Usually offered in alternate years. Prerequisites: MATH 220 or MATH 240. (Quant) MATH 285/295 Directed Study 2, 4 hours An opportunity to pursue individualized or experiential learning with a faculty member, at the sophomore level or above, either within or outside the major. MATH 285 can be taken only during January term, MATH 295 can be taken during the fall, spring, or summer terms. MATH 321 Probability and Statistics I 4 hours Axioms and laws of probability, independence, conditional probability, combinatorics, discrete and continuous random variables, mathematical expectation, central limit theorem, descriptive statistics, confidence intervals. Only two of MATH 321, 322, 327, and MATH 328 may apply toward the math major. Prerequisite: MATH 152. (Quant) MATH 322 Probability and Statistics II 4 hours Sampling distribution theory, theory of estimation and hypothesis testing, confidence intervals, inferences for means and proportions, correlation and regression, chi-square tests. Only two of MATH 321, 322, 327, and MATH 328 may apply toward the math major. Prerequisite: MATH 321. (Quant) MATH 327 Applied Statistics I 4 hours Regression Analysis: Least square estimates, simple linear regression, multiple linear regression, hypothesis testing and confidence intervals for linear regression models, prediction intervals, and ANOVA. Model diagnostics including tests of constant variance assumptions, serial correlation, and multicollinearity. Time series: Linear time series, moving average, autoregressive and ARIMA models. Estimation and forecasting. Forecast errors and confidence intervals. Prerequisite: college-level statistics course. (Quant) MATH 328 Applied Statistics II 4 hours Design and analysis of experiments; analysis of variance techniques; fixed, random, and mixed models; repeated measures. Only two of MATH 321, 322, 327, and MATH 328 may apply toward the math major. Prerequisite: MATH 327. (Quant) MATH 351 Ordinary Differential Equations 4 hours An introduction to first and second order differential equations, existence and uniqueness theorems, higher order linear differential equations, Laplace transforms, power series solutions, boundary value problems, systems of linear differential equations, and applications in the physical, biological, and social sciences. Prerequisite: MATH 240. (Quant) MATH 358 Chaotic Dynamical Systems 4 hours This course will focus on discrete dynamical systems and iterated functions. Topological and geometric methods will be used to gain qualitative understanding of solutions to systems of nonlinear differential equations. Topics will include phase portraits, bifurcations, symbolic dynamics, chaos, fractals, Julia sets, and the Mandelbrot set. Prerequisites: MATH 240. (Quant) MATH 365 Geometry 4 hours Elements of Euclidean and non-Euclidean geometries: incidence, betweenness, separation, congruence, and parallel postulates. Geometry of physical space. Historical development. A proof oriented course. Prerequisites: MATH 220, 240. (Quant) MATH 380 Internship Credit arr. On-the-job learning experience. The plan must be presented for departmental approval before the experience begins. MATH 385 Seminar Credit arr. MATH 395 Independent Study 1, 2 or 4 hours MATH 452 Partial Differential Equations 4 hours An introduction to initial and boundary value problems associated with certain linear partial differential equations (e.g., Laplace, heat, and wave equations). Fourier series methods, including the study of best approximation in the mean and convergence, will be a focus. Sturm-Liouville problems and associated eigenfunctions will be included. Numerical methods, such as finite difference, finite element, and finite analytic, may be introduced, including the topics of stability and convergence of numerical algorithms. Extensive use of a computer algebra system (CAS). Prerequisites: MATH 351 or consent of instructor. (Quant) MATH 454 Principles of Real Analysis 4 hours The mathematics of real functions, emphasizing rigorous analytical proofs. Sets, real number properties, cardinality, topology of the reals, limits of a function, continuity, differentiation, integration, sequences, series. Prerequisites: MATH 220, 240. (Quant) MATH 456 Functions of a Complex Variable 4 hours Extending calculus to functions of a complex variable. Complex numbers, limits, derivatives, Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formula. Taylor series, Laurent series, residues, conformal mappings, and applications. Offered in alternate years. Prerequisite: MATH 253. (Quant) MATH 459 Topology 4 hours An introduction to general, or point-set, topology. Topological spaces and continuous functions. Order, metric, product, and subspace topologies. Limit points, connectedness, compactness, countability axioms, separation axioms, Urysohn lemma and metrization theorem. Usually offered in alternate January terms. Prerequisite: MATH 220, 240. (Quant) MATH 462 Numerical Analysis 4 hours Roots of equations and solutions of systems of linear equations, interpolation and approximation, differences and numerical integration, and numerical solutions of ordinary differential equations. Offered in alternate years. Prerequisites: MATH 240, CS 150. (Same as CS 462.) (Quant) MATH 471 Abstract Algebra I 4 hours Introduction to the basic structures of abstract algebra: groups, subgroups, cosets, isomorphisms, factor groups, homomorphisms, rings, integral domains, fields, ideals, and polynomial rings. Prerequisites: MATH 220, 240. (Quant) MATH 472 Abstract Algebra II 1, 2, or 4 hours Topics may include simple groups, Sylow theorems, divisibility in integral domains, generators and relations, field extensions, splitting fields, solvability by radicals, Galois theory, symmetry, and geometric constructions. Offered on demand. Prerequisite: MATH 471. (Quant) MATH 485 Seminar Credit arr. MATH 490 Senior Project 1, 2, or 4 hours MATH 493 Senior Honors Project 4 hours A yearlong independent research project. Applications are completed on the "Honors Program" form available at the registrar's office, requiring the signatures of a faculty supervisor, the department head, the honors program director, and the registrar. Interdisciplinary projects require the signatures of two faculty supervisors. The project must be completed by the due date for senior projects. The completed project is evaluated by a review committee consisting of the faculty supervisor, another faculty member from the major department, and a faculty member from outside the major department. All projects must be presented publicly. Only projects awarded an "A-" or "A" qualify for "department honors" designation. The honors project fulfills the all-college senior project requirement. |