Mathematical Sciences continued

UG 401 Mathematics with Technology for Teachers 3 cr. Prereq., Math 305. Discrete and continuous mathematical models from a variety of diciplines using appropriate technology.

UG 406 History of Mathematics 3 cr. Prereq., Math 305. Offered alternate years. Historical study of the development of mathematics from the Egyptian and Babylonian eras to the 20th century.

UG 414 Deterministic Models 3 cr. Prereq., Math 158 or 311 or consent of instr. Linear and nonlinear difference and differential equations: stability, phase-plane analysis, oscillatory behavior, limit cycles, and chaos. Eigenvalues and eigenfunctions. Emphasis on models in biology.

UG 421 Abstract Algebra 4 cr. Prereq., Math 251 and one of 305, 324 or 325. An introduction to modern ideas of algebra. Groups, rings, fields, vector spaces, matrix theory and linear groups.

UG 422 Abstract Algebra 4 cr. Prereq., Math 421. Continuation of 421.

UG 431 Euclidean and Non-Euclidean Geometry 3 cr. Prereq., Math 305. Euclidean geometry from a rigorous, axiomatic viewpoint and Non-Euclidean geometries including Lobachevskian, projective, finite and Riemannian.

UG 435 Introduction to General Topology 3 cr. Prereq., Math 251, 305. Offered alternate years. Topological spaces, continuity, connectedness, compactness, convergence, separation axioms, metric spaces.

UG 441 Mathematical Statistics 3 cr. Prereq., Math 251 and 341 or consent of instr. An introduction to probability, random variables and their probability distributions, estimation and hypothesis testing. This course is the foundation on which more advanced statistics courses build.

UG 442 Mathematical Statistics 3 cr. Prereq., Math 441. Continuation of 441.

UG 443 Applied Nonparametric Statistics 3 cr. Prereq., Math 341 or 345 or consent of instr. Offered alternate years. Nonparametric methods using ranks and elementary counting methods to develop statistical estimation and testing techniques. Applications to a variety of situations including one- and two-sample, correlation, regression, analysis of variance and goodness-of-fit problems. For majors and non-majors.

UG 444 Applied Linear Models 3 cr. Prereq., Math 341 or 345 or consent of instr. Offered alternate years. Simple linear and multiple regression and analysis of variance, including estimation, inference and residual analysis. Use of the computer and real data sets integrated throughout. For majors and non-majors.

UG 445 Applied Time Series 3 cr. Prereq., Math 345 or coreq., 442 or consent of instr. Offered alternate years. Introduction to time series and applications. Approach is that of Box-Jenkins ARIMA models. Use of the computer and real data sets integrated throughout. For majors and non-majors.

UG 451 Introduction to Real Analysis 4 cr. Prereq., Math 251, 305. Offered alternate years. Theory of metric spaces and point set topology, Riemann-Stieltjes integral, sequences and series of functions. Stone-Weierstrass theorem, theorem of Arzela-Ascoli, introduction to Lebesgue integration.

UG 452 Complex Variables 4 cr. Prereq., Math 251, 305. Offered alternate years. Analytic functions, complex integration, singularities and application to contour integration, harmonic functions, spaces of analytic functions.

UG 471 Numerical Analysis 4 cr. Prereq., Math 305, 311, one computer language. Error analysis; approximation and interpolation, numerical solution of linear and non-linear equations, numerical integration of ordinary and partial differential equations.

UG 481 Mathematical Operations Research: Mathematical Programming 3 cr. Prereq., Math 221, 251 and 305; Math 381 and 382 recommended. The mathematical development of topics in operations research, including linear and nonlinear programming, duality theory and sensitivity analysis.

UG 482 Mathematical Operations Research: Stochastic Optimization 3 cr. Prereq., Math 251, 305 and 341; Math 381 and 382 recommended. The mathematical development of topics in operations research including stochastic decision theory, inventory theory, queuing theory, simulation, stochastic programming.

U 494 Seminar Variable cr. (R-9) Prereq., consent of instr. Guidance in special work for advanced students.

UG 495 Special Topics Variable cr. (R-9) Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one-time offerings of current topics.

U 496 Independent Study Variable cr. (R-9) Prereq., consent of instr. Guidance of an individual student in doing independent study on material not offered in a regular course.

U 498 Cooperative Education Experience Variable cr. (R-9) Prereq., consent of instr. Extended classroom experience which provides practical application of classroom learning during placements off campus. Prior approval must be obtained from the faculty supervisor and the Cooperative Education Office.

U 499 Senior Thesis Variable cr. (R-12) Prereq., consent of instr. Senior thesis for mathematics majors and/or Watkins Scholars.

G 500 Current Mathematical Curricula 3 cr. Prereq., undergraduate major or minor in mathematics. Offered alternate years. Analysis of contemporary materials for secondary school mathematics: the goals, the mathematical content, alternative methodologies, and curriculum evaluation.

G 501 Technology in Mathematics for Teachers 3 cr. Prereq., undergraduate mathematics major or minor. Offered alternate years. Technology usage_when it is appropriate and when it is not. Experience is provided with scientific calculators, graphing utilities, computers, and identification of exemplary software.

G 510 Problem Solving for Teachers 3 cr. Prereq., undergraduate major or minor in mathematics. Offered alternate years. Strategies for problem solving, problem posing in a variety of situations, modeling and applications. Problems are selected from various areas of mathematics.

G 511 Advanced Mathematical Methods 3 cr. Prereq., Math 311-312 or 414. Offered alternate years. Methods in applied mathematics related to the qualitative and quantitative solution of nonlinear and differential integral equations, dynamical systems, and perturbation methods. Applications of these methods to other sciences.

G 512 Advanced Mathematical Methods 3 cr. Prereq., Math 511. Offered alternate years. Continuation of 511.

G 514 Topics in Applied Mathematics Variable cr. (R-12) Prereq., consent of instr. or Math 511- 512. Offered alternate years. Topics of current interest in applied mathematics, mathematical modeling, dynamic modeling, and optimal management in stochastic or deterministic environments.

G 520 Algebra for Teachers 3 cr. Prereq., Math 324 or equiv. Offered alternate years. Topics include algebraic number fields, linear algebra topics, and applications appropriate for secondary teachers.

G 521 Advanced Algebra 3 cr. Prereq., Math 422 or consent of instr. Offered alternate years. General topics from groups, rings, modules, commutative algebra, fields and categories.

G 522 Advanced Algebra 3 cr. Prereq., Math 521 or consent of instr. Offered alternate years. Continuation of 521.

G 524 Special Topics in Algebra Variable cr. (R-6) Prereq., Math 422 or consent of instr. Offered alternate years. Topics of modern research interest in algebra.

G 525 Special Topics in Algebra Variable cr. (R-6) Prereq., Math 524. Offered alternate years. Continuation of 524.

G 526 Discrete Mathematics for Teachers 3 cr. Prereq., Math 305 or consent of instr. Offered alternate years. Elements and operations of finite structures, combinatorics, recursion, graph theory, matrix representations, and finite state transition models.

G 530 Geometries for Teachers 3 cr. Prereq., Math 431 or equiv. Offered alternate years. Comparison of synthetic, analytic, vector, and transformational approaches to geometry. Includes classification of geometries, geometric representations, axiomatics, and the applications of modern geometries.

G 531 Topology 3 cr. Prereq., Math 451 or consent of instr. Offered alternate years. Set theory, topological spaces, metrizability, continuous mappings and selected topics.

G 532 Topology 3 cr. Prereq., Math 531 or consent of instr. Offered alternate years. Continuation of 531.

G 540 Probability and Statistics for Teachers 3 cr. Prereq., Math 341 or equiv. Offered alternate years. A survey of modern topics in probability and statistics. Emphasis will be on applications of statistics in real situations.

G 541 Advanced Mathematical Statistics 3 cr. Prereq., Math 442. Offered alternate years. Generating functions, limit theorems, sufficient statistics, maximum likelihood, estimation, uniformly most powerful tests, decision theory, sequential procedures, stochastic models, and other current topics in statistics.

G 542 Advanced Mathematical Statistics 3 cr. Prereq., Math 541. Offered alternate years. Continuation of 541.

G 543 Applied Multivariate Statistical Analysis 4 cr. Prereq., Math 345 or coreq., Math 442, or consent of instr. Offered alternate years. Introduction to multivariate statistical analyses and applications. Appropriate linear algebra, random vectors, multivariate normal, multivariate ANOVA, principal components, factor analysis, discrimination and classification, clustering, canonical correlations. For majors and non-majors.

G 544 Topics in Probability and/or Statistics 3 cr. Prereq., Math 442 and consent of instructor. Topics chosen from those listed under 541.

G 545 Statistical Inference 3 cr. Prereq., Math 442. Offered alternate years. One of the topics chosen from multivariate analysis, linear models, design of experiments, sampling theory, nonparametric theory.

G 546 Statistical Inference 3 cr. Prereq., Math 442; Math 545 may be a prerequisite depending on topics chosen in a given year. Offered alternate years. Topics chosen from those listed under Math 545 or other current topics in statistics.

G 547 Advanced Computer Data Analysis 1 cr. Prereq. or coreq., Math 344 or equiv. Computing techniques in probability and statistics intended primarily for students in Math 344. Graduate students register for Math 547 and one credit of Math 347. Main frames, Macintosh, and or PC usage.

G 548 Advanced Computer Data Analysis 1 cr. Prereq., Math 547 or equiv. Coreq., Math 345 or equiv. Continuation of Math 547. An introduction to selected large statistical packages. Graduate students register for Math 548 and one credit of Math 348.

G 549 Statistics and Research Methods 3 cr. Prereq., one course in college mathematics. Introduction to modern statistics. Exploratory data analysis, sampling and experimental designs, probability, confidence intervals, hypothesis testing, and regression analysis. Topics from research methods; may include literature search techniques, analysis of primary and secondary data courses, and questionnaire design. Credit not allowed toward graduate degree in mathematics.

G 550 Analysis for Teachers 3 cr. Prereq., Math 251 or equiv. Offered alternate years. Notions of limits, continuity, differentiation, and integration in Rn.

G 551 Real Analysis 3 cr. Prereq., Math 451 or 452 or consent of instr. Measure theory, abstract integration theory, theory of Lp_spaces.

G 555 Functional Analysis 3 cr. Prereq., Math 451 or 452 or consent of instr. Normed linear spaces, linear functionals, separation theorems, topological linear spaces, weak topologies, dualities.

G 564 Topics in Analysis 3 cr. (R-12) Prereq., consent of instr. Research projects or topics in analysis. May include but not restricted to Banach algebras, Fourier analysis, Harmonic analysis, Hilbert space theory, integral equations, or operator theory.

G 581 Operations Research 3 cr. Prereq., Math 421, 451, or consent of instr. Offered alternate years. Introduction to the mathematical techniques in operations research. Topics from discrete optimization theory, graphs and network theory, linear and non-linear programming, stochastic optimization theory, queuing theory, inventory theory, decision theory, and simulation.

G 582 Operations Research 3 cr. Prereq., Math 581. Offered alternate years. Continuation of Math 581.

G 584 Topics in Optimization 3 cr. (R-12) Prereq., Math 582 or consent of instr. Offered alternate years. Topics may include but are not limited to, Karmarkar's algorithm and other interior point methods, nonlinear optimization, multiple objective optimization, dynamic programming, combinatorial optimization.

G 593 Professional Project Variable cr. (R-6) Prereq., consent of advisor.

G 595 Special Topics Variable cr. (R-12) Prereq., consent of instr. Experimental offerings of visiting professors, experimental offerings of new courses, or one-time offerings of current topics.

G 596 Independent Study Variable cr. (R-12) Prereq., consent of instr.

G 597 Research Variable cr. (R-12) Prereq., consent of instr.

G 598 Cooperative Education Experience Variable cr. (R-12) Prereq., consent of department. Extended classroom experience which provides practical application of classroom learning during placements off campus. Prior approval must be obtained from the faculty supervisor and the Cooperative Education Office.

G 599 Thesis Variable cr. (R-6) Prereq., consent of instr.

G 600 Mathematics Colloquium 1 cr. (R-3) Prereq., consent of advisor.

G 610 Graduate Seminar in Applied Mathematics Variable cr. (R-12) Prereq., consent of instr.

G 620 Graduate Seminar in Algebra Variable cr. (R-12) Prereq., consent of instr.

G 630 Graduate Seminar in Geometry/Topology Variable cr. (R-12) Prereq., consent of instr.

G 640 Graduate Seminar in Probability and Statistics Variable cr. (R-12) Prereq., consent of instr.

G 650 Graduate Seminar in Analysis Variable cr. (R-12) Prereq., consent of instr.

G 670 Graduate Seminar in Numerical Analysis Variable cr. (R-12) Prereq., consent of instr.

G 680 Graduate Seminar in Operations Research Variable cr. (R-12) Prereq., consent of instr.

G 694 Seminar Variable cr. (R-12) Prereq., consent of instr.

G 699 Dissertation Variable cr. (R-9)

Faculty

Professors