College of Integrated Science and Technology College of Science and Mathematics

Mathematics Department of
Mathematics *MATH 103. The Nature of Mathematics. 3 credits. Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think. MATH 107*108. Fundamentals of Mathematics III. 3 credits each semester. Sets, logic, numeration systems, number theory, probability and statistics, measurement, geometry and an introduction to computers. This course will fulfill the requirements for licensure of prospective early childhood and middle school teachers, as well as provide a general introduction to mathematics for students in other majors. Prerequisite for MATH 108: MATH 107. MATH 135. Elementary Functions. 4 credits. Algebraic, exponential, logarithmic and trigonometric functions; matrices and matrix solutions to systems of linear equations; vectors. Not open to students who have previously earned credit in MATH 125, 145, 155, 156, 205 or 235, except with the consent of the department head. MATH 155. College Algebra. 3 credits. Polynomial, rational, exponential and logarithmic functions and applications, systems of equations and inequalities, sequences. Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or MATH 156. Not open to students who have previously earned credit in MATH 125, 135, 145, 156, 205, 220 or 235. MATH 156. College Algebra. 3 credits. Covers same topics as MATH 155. MATH 156 will meet five times a week for students requiring more instructional time. Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or 156. Not open to students who have previously earned credit in MATH 125, 135, 145, 155, 205, 220 or MATH 235. MATH 167. Topics in Mathematics. 13 credits. Topics or projects in mathematics which are of interest to the lowerdivision student. May be repeated for credit when course content changes. Topics or projects selected may dictate prerequisites. Students should consult the instructor prior to enrolling for this course. *MATH 205. Introductory Calculus I. 3 credits. Topics from differential calculus with applications to the social, behavioral or life sciences and business or management. Prerequisite: Demonstration of strong preparation in algebra. Not open to mathematics or physics majors or to students who have already earned credit in MATH 235. Not recommended for chemistry majors. *MATH 205E. Introductory Calculus I with Laboratory. 4 credits. Topics from differential calculus, including a laboratory component stressing data collection, data analysis, and applications to environmental issues. Prerequisite: Demonstration of strong preparation in algebra. MATH 206. Introductory Calculus II. 3 credits. Topics from integral calculus with applications to the social, behavioral or life sciences and business or management. Prerequisite: MATH 205. Not open to mathematics or physics majors or to students who have already earned credit in MATH 236. Not recommended for chemistry majors. *MATH 220. Elementary Statistics. 3 credits. Descriptive statistics, frequency distributions, sampling, estimation and testing of hypotheses, regression, correlation and an introduction to statistical analysis using computers. Prerequisite: Demonstration of strong preparation in algebra. Not open to majors in mathematics. MATH 235*236. Calculus III. 4 credits each semester. Differential and integral calculus of functions of one variable. Sequences and infinite series. Prerequisite for MATH 235: MATH 135 or equivalent. Prerequisite for MATH 236: MATH 235 with grade of “C” or better. MATH 237. Calculus III. 4 credits. Vectors.
Multivariate calculus. Prerequisite: MATH 236 with grade of “C”
or better. MATH 238. Linear Algebra with Differential Equations. 4 credits. Matrices; determinants; vector spaces; linear transformations; eigenvalues and eigenvectors; separable, exact and linear differential equations; and systems of linear differential equations. Prerequisite: MATH 236. Not open to students with credit in MATH 300 or MATH 336 without departmental permission. MATH 248. Computers and Numerical Algorithms. (3, 2). 4 credits. Programming in a highlevel computer language. Applications of numerical algorithms to problems basic to areas such as mathematics, the sciences and economics and finance. Prerequisite or corequisite: MATH 206 or MATH 236. This course is not open to students who have previously earned credit in MATH/CS 448. MATH/PHYS 265. Introduction to Fluid Mechanics. 4 credits. Introduces the student to the application of vector calculus to the description of fluids. The Euler equation, viscosity and the NavierStokes equation will be covered. Prerequisites: MATH 237 and PHYS 260. MATH 280. SAS Programming and Data Management. 3 credits. Use of statistical software to manage, process and analyze data. Writing of statistical programs to perform simulation experiments. Prerequisites: MATH 220 or MATH 318. MATH 285. Data Analysis. 4 credits. Topics include experimental and survey design, distributions, variation, chance, sampling variation, computer simulation, bootstrapping, estimation and hypothesis testing using real data generated from classroom experiments and large databases. Prerequisite: MATH 206 or MATH 236 or permission of instructor. Not open to students who have already earned credit in MATH 220 or MATH 318. MATH 300. Linear Algebra. 3 credits. Vector spaces, linear transformations, matrices, determinants, systems of linear equations and eigenvalues and eigenvectors. Prerequisite or corequisite: MATH 237 or consent of the instructor. MATH 310. Elementary Theory of Numbers. 3 credits. Properties of integers and prime numbers, divisibility, congruence, residues and selected topics. Prerequisite or corequisite: MATH 237 or consent of the instructor. MATH 312. Discrete Mathematics. 3 credits. Logic, set theory, relations and functions,
mathematical induction and equivalent forms, recurrence relations,
counting techniques. Prerequisite: MATH 237 or consent of the
instructor. MATH 315. The Real Number System. 3 credits. A development of the real number system through a systematic approach to the natural numbers, integers, rationals and irrationals. Prerequisite or corequisite: MATH 237 or consent of the instructor. MATH 318. Introduction to Probability and Statistics. 4 credits. Counting, probability axioms, discrete and continuous random variables, method of moments and maximum likelihood estimation, descriptive statistics, central limit theorem, single and twosample inference, blocking and dependent sample inference, simple linear regression and correlation. Prerequisite: MATH 236. MATH 321. Analysis of Variance and Experimental Design. 3 credits. Introduction to basic concepts in statistics with applications of statistical techniques including estimation, test of hypothesis, analysis of variance and topics in experimental design. Prerequisite: MATH 220, MATH 318 or equivalent. MATH 322. Applied Linear Regression. 3 credits. Introduction to basic concepts and methods in regression analysis and the application of these models to reallife situations. Prerequisite: MATH 220, MATH 318 or equivalent. MATH 324. Applied Nonparametric Statistics. 3 credits. Methods of analyzing data from nonnormal populations including binomial tests, contingency tables, use of ranks, KolmogorovSmirnov type statistics and selected topics. Prerequisite: MATH 220, MATH 318 or equivalent. MATH 325. Survey Sampling Methods. 3 credits. Theory and practice of sampling including stratified random samples, discussion of simple random samples, cluster sampling, estimating sample size, ratio estimates, subsampling, twostate sampling and analysis of sampling error. Prerequisite: MATH 220 or MATH 318. MATH 326. Statistical Quality Control. 3 credits. Uses and concepts of probability and sampling procedures. Acceptance sampling by attributes and variables, Shewhart concepts of process control, control chart process capability studies, reliability and life testing. Design of sampling plans. Prerequisite: MATH 318. MATH 327. Categorical Data Analysis. 3 credits. Exact inference for population proportions, comparison of population proportions for independent and dependent samples, two and threeway contingency tables, Chisquare tests of independence and homogeneity, Chisquare goodnessoffit tests and Poisson and logistic regression. Prerequisites: MATH 220 or MATH 318. MATH/FIN 328. Time Series Analysis. 3 credits. Regression and exponential smoothing methods for forecasting nonseasonal and seasonal time series, stochastic processes, BoxJenkins’ autoregressive and moving average models. Prerequisites: MATH 238 and MATH 318. MATH 336. Elementary Differential Equations. 3 credits. Development of techniques for obtaining, analyzing and graphing solutions to differential equations, with emphasis on first and second order equations. Prerequisite: MATH 237. MATH 337. Methods of Applied Calculus. 4 credits. Laplace transforms, power series and their application to differential equations. Vector differential and integral calculus; parametric curves; coordinate systems; line, surface and volume integrals; and gradient, divergence and curl including the theorems of Green, Stokes and Gauss. Prerequisite: MATH 237 and MATH 238. MATH 340. Mathematical Modeling I – Optimization. 3 credits. Linear and nonlinear optimization with an emphasis on applications in the sciences, economics and social sciences. Techniques studied include the simplex, Newton and Lagrange methods and KuhnTucker theory. Software packages will be used to implement these methods. Prerequisite: MATH 248. MATH 341. Mathematical Modeling II – Dynamical Systems. 3 credits. Discrete and continuous dynamical systems with an emphasis on applications in the sciences, economics and social sciences. Topics include stability, chaos, phase portraits, strange attractors and fractals. Software packages will be used to model the dynamical systems. Prerequisite: MATH 340; or MATH 238 and MATH 248. MATH 353. Graph Theory. 3 credits. Graphs and their applications. Possible topics include trees, Euler paths and Hamiltonian circuits, planar graphs, digraphs, adjacency matrices, connectivity and coloring problems. Prerequisite: One of MATH 310, MATH 312 or MATH 315 or consent of instructor. MATH 360. Complex Variables with Applications. 3 credits. Introduction to algebraic properties of complex numbers, analytic functions, harmonic functions, mappings of elementary functions, contour integration, series, residues and poles and conformal mappings. Emphasis on computations and applications to fluid and heat flow. Prerequisite: MATH 237. MATH/PHYS 365. Computational Fluid Dynamics. 3 credits. Applications of computer models to the understanding of both compressible and incompressible fluid flows. Prerequisites: MATH 248, either MATH 238 or MATH 336, MATH/PHYS 265 and PHYS 340. MATH/PHYS 366E. Computational Solid Mechanics. 3 credits. Development and application of mathematical
models and computer simulations to investigate problems in solid
mechanics, with emphasis on
numerical solution of associated boundary value
problems. Prerequisites:
MATH/PHYS 266, MATH 238 and MATH 248, or consent of instructor. MATH 387. Fourier Analysis and Partial Differential Equations. 3 credits. Elementary applied partial differential equations, the heat equation, Laplace’s equation, the wave equation; Fourier series and boundary value problems. Both theory and problemsolving will be included. Prerequisite: MATH 238 or MATH 336. MATH/FIN 395. Mathematical Finance. 3 credits. An overview of the role of mathematical concepts in financial applications. Topics include continuous time finance, optimization, numerical analysis and applications in asset pricing. Prerequisite: MATH 237 and FIN 380. MATH/FIN 405. Securities Pricing. 3 credits. A quantitative treatment of the theory and method of financial securities pricing to include an examination of closed form pricing models such as the BlackScholes and its various derivatives as well as numerical solution techniques such as binomial methods. Prerequisite: MATH/FIN 395. MATH 410411. Advanced Calculus. 3 credits each semester. Limits, continuity, differentiation, sequences, series, integration and selected topics. Prerequisite for MATH 410: MATH 238 or MATH 300 and one of MATH 310, MATH 312 or MATH 315 or consent of the instructor. Prerequisite for MATH 411: MATH 410. MATH 415. History of Mathematics. 3 credits. Topics in the history of mathematics spanning ancient times to the present. Prerequisite: One of MATH 310, MATH 312 or MATH 315 or consent of the instructor. MATH 421. Applied Multivariate Statistical Analysis. 3 credits. Multivariate statistical methods with applications. Topics include canonical correlation, clustering, discriminant analysis, factor analysis, multivariate analysis of variance, multiple regression, multidimensional scaling and principal component analysis. Prerequisites: MATH 300 or MATH 238; and MATH 321 or MATH 322. MATH 423. Stochastic Processes. 3 credits. Sequences and classes of random variables. Applications to physical, biological, social and management sciences. Topics include Markov chains, branching processes, the Poisson process, queuing systems and renewal processes. Prerequisites: MATH 238 or MATH 300 or equivalent and MATH 318. MATH 424. Statistical Decision Theory. 3 credits. Development and use of probability and statistics for strategic decision making with applications. Topics include decision flow diagrams, analysis of risk and risk aversion, utility theory, Bayesian statistical methods, the economics of sampling, sensitivity analysis and collective decision making. Prerequisite: MATH 318. MATH 426. Probability and Mathematical Statistics I. 3 credits. Probability spaces, random variables, discrete and continuous probability distributions, mathematical expectation, moment generating functions, moments of linear combinations of random variables and sampling distributions. Prerequisite: MATH 318. MATH 427. Probability and Mathematical Statistics II. 3 credits. Sampling theory and distributions, theory and applications of estimation and hypothesis testing, regression and correlation and analysis of variance. Prerequisite: MATH 426. MATH 429. Research Project in Statistics. 13 credits. Experience in the design, data collection and analysis for a survey or experiment. MATH 429 should be taken concurrently with one of the following statistics courses: MATH 321, 322, 324, 325, 327. Corequisite: One of MATH 321, MATH 322, MATH 324, MATH 325, or MATH 327. Prerequisite: Six hours of statistics courses at the 300 or 400 level. MATH 430431. Abstract Algebra. 3 credits each semester. An introduction to groups, rings and fields. Prerequisite for MATH 430: MATH 238 or MATH 300 and one of MATH 310, 312 or 315 or consent of the instructor. Prerequisite for MATH 431: MATH 430. MATH 435. Introduction to Topology. 3 credits. Metric spaces, limits, continuous maps and homeomorphisms, connectedness, compact topological spaces and applications. Prerequisites: MATH 238 or MATH 300 and one of MATH 310, MATH 312 or MATH 315 or consent of the instructor. Formerly MATH 335. MATH/CS 448. Numerical Analysis. 3 credits . Study and analysis of algoriothms used to solve nonlinear equations and systems of linear and nonlinear equations. Iterative methods for matrices and Newtontype methods. Numerical differential and integral calculus. Programming using a highlevel language and/or software packages. Prerequisites: MATH 237, MATH 238 and MATH 248. Formerly MATH 448449. MATH/CS 449. Numerical Analysis For Differential Equations. 3 credits. Study and analysis of numerical techniques to solve ordinary and partial differential equations, including Euler, RungeKutta, Picard, finitedifference and finiteelement methods. Programming using a highlevel language and/or software packages. Prerequisite: MATH/CS 448. Formerly MATH 448449. MATH 450. Analysis and Dynamics of Differential Equations. 3 credits. Analysis of qualitative properties and dynamics of linear and nonlinear ordinary differential equations, including topics such as existence, uniqueness, phase portraits, stability and chaos, with applications to the sciences. Prerequisites: MATH 238; and either MATH 310, 312, 315, 387 or consent of instructor. MATH/FIN 465. Seminar in Actuarial Science I. 3 credits. Theory and application of contingency mathematics in the areas of life and health insurance and of annuities from both a probabilistic and deterministic approach. This class, together with MATH/FIN 466, helps students prepare for the professional actuarial examinations. Offered fall, oddnumbered years. Prerequisite: MATH/FIN 395 or consent of the instructor. Prerequisite or corequisite: MATH 426. MATH/FIN 466. Seminar in Actuarial Science II. 3 credits. A continuation of MATH/FIN 465. Additional coverage of contingency mathematics in the areas of life and health insurance, annuities, pensions and risk theory from both probabilistic and deterministic approaches. The twocourse sequence helps to prepare the student for the professional actuarial examinations. Prerequisite: MATH/FIN 465. Prerequisite or corequisite: MATH 427. MATH 467. Selected Topics in Mathematics. 13 credits each semester. Topics in advanced mathematics which are of special interest to the student but not covered in the regularly offered courses. Offered only with approval of the department head; may be repeated for credit when course content changes. MATH 475. Fundamental Concepts of Geometry. 3 credits. Origin and development of Euclidean and other geometries including axiomatic systems, mathematical proof and special topics from incidence geometry. Prerequisite: MATH 310, MATH 312 or MATH 315 or consent of the instructor. MATH 483. Selected Topics in Applied Mathematics. 3 credits. Topics in applied mathematics not covered in the regularly offered courses. Offered only with the approval of the department head; may be repeated for credit when course content changes. Prerequisites: Junior standing and consent of the instructor. MATH 485. Selected Topics in Statistics. 13 credits. Topics in statistics which are of interest but not otherwise covered in the regular statistics offerings of the department. Offered only with approval of the department head; may be repeated for credit when course content changes. Prerequisites: Junior standing and consent of the instructor. MATH 497498. Independent Study. 13 credits each semester. Independent study in mathematics under faculty supervision. Offered only with consent of the department head. MATH 499. Honors. 6 credits. Year course. 
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