Mathematics
continued
Graduate Courses
The faculty has approval to offer the following courses in the academic years 20012002 and 20022003; however, not all courses are taught each semester or summer session. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.
Unless otherwise stated below, each course meets for three lecture hours a week for one semester.
380C. Algebra.
A survey of algebraic structures, including groups, fields, rings, and modules. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
380D. Algebra.
Continuation of Mathematics 380C. Prerequisite: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 380C.
381C. Real Analysis.
Same as Computational and Applied Mathematics 381R. Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
381D. Complex Analysis.
Same as Computational and Applied Mathematics 381D. Introduction to complex analysis. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
381E. Functional Analysis.
Same as Computational and Applied Mathematics 381S. Introduction to functional analysis. Prerequisite: Graduate standing, consent of instructor or the graduate adviser, and Computational and Applied Mathematics 381R or Mathematics 381C.
382C. Algebraic Topology.
Surfaces, covering spaces, fundamental group, and homology. Prerequisite: Graduate standing, an undergraduate course in topology, and consent of instructor or the graduate adviser.
382D. Differential Topology.
Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory. Prerequisite: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 382C.
382E. Algebraic Topology.
Continuation of Mathematics 382C. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
382F. Algebraic Topology.
Continuation of Mathematics 382E. Prerequisite: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 382E.
382G. Differential Geometry.
Continuation of Mathematics 382D. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
383C. Methods of Applied Mathematics.
Same as Computational and Applied Mathematics 385C. Topics include basic normed linear space theory; fixedpoint theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to SturmLiouville problems; approximation and computational methods such as the Galerkin, RayleighRitz, and Newton procedures. Only one of the following may be counted: Computational and Applied Mathematics 385, 393C (Topic: Methods of Applied Mathematics I), Mathematics 383C. Prerequisite: Graduate standing.
383D. Methods of Applied Mathematics.
Same as Computational and Applied Mathematics 385D. Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems. Prerequisite: Graduate standing and Mathematics 383C.
383E. Numerical Analysis: Linear Algebra.
Same as Computational and Applied Mathematics 383C and Computer Sciences 383C. Survey of numerical methods in linear algebra: floatingpoint computation, solution of linear equations, least squares problems, algebraic eigenvalue problems. Prerequisite: Graduate standing, either consent of instructor or Mathematics 341 (or 311) or 340L, and either Mathematics 368K or Computer Sciences 367.
383F. Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations.
Same as Computational and Applied Mathematics 383D and Computer Sciences 383D. Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations. Prerequisite: Graduate standing; either consent of instructor or Mathematics 427K and 365C; and Computational and Applied Mathematics 383C, Computer Sciences 383C, or Mathematics 383E.
383G. Numerical Treatment of Differential Equations.
Same as Computational and Applied Mathematics 386K and Computer Sciences 386K. The analysis of numerical methods for solving ordinary and partial differential equations. Prerequisite: Graduate standing; and Computational and Applied Mathematics 383D, Computer Sciences 383D, Mathematics 368K, 383F, or consent of instructor.
384C. Mathematical Statistics.
Same as Computational and Applied Mathematics 384R. General theory of mathematical statistics. Hypothesis testing, estimation, decision theory. Prerequisite: Graduate standing, and Mathematics 378K or consent of instructor or the graduate adviser in mathematical statistics.
384D. Mathematical Statistics.
Same as Computational and Applied Mathematics 384S. Continuation of Mathematics 384C. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 384R or Mathematics 384C.
384E. Analysis of Variance.
Analysis of variance, including one and twoway layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; split plot designs. Prerequisite: Graduate standing, and Mathematics 378K or the equivalent or consent of instructor.
384F. Design of Experiments.
Design of experiments, including 2^{n} and 3^{n} factorial experiments, confounding, fractional factorials, sequential experimentation, orthogonal arrays, Doptimal experiments, and response surface methodology. Prerequisite: Graduate standing, and Mathematics 378K or the equivalent or consent of instructor.
384G. Regression Analysis.
Fitting linear models to data by the method of least squares, choosing best subsets of predictors, and related materials. Prerequisite: Graduate standing and consent of instructor.
384H. Multivariate Statistical Analysis.
Introduction to the general multivariate linear model; a selection of techniques, such as principle component, factor, and discriminant analysis. Prerequisite: Graduate standing and consent of instructor.
385C. Theory of Probability.
Same as Computational and Applied Mathematics 384K. Prerequisite: Graduate standing and consent of instructor.
385D. Theory of Probability.
Same as Computational and Applied Mathematics 384L. Continuation of Mathematics 385C. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 384K or Mathematics 385C.
389J. Probability Models with Actuarial Applications. Probability models with actuarial applications, including Markov chains, Brownian motion, the BlackScholes formula, frequencyofloss and severityofloss random variables, compound distributions, and ruin theory. With Mathematics 389U and 389V, covers the syllabus for exam #3 of the Society of Actuaries and the Casualty Actuarial Society. Four lecture hours a week for one semester. Prerequisite: Graduate standing and Mathematics 362K; either Mathematics 341 or 340L is recommended.
389P. Actuarial Statistical Estimates.
Statistical estimates for frequencyofloss and severityofloss random variables; credibility theory; statistics of simulation. Covers 40 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society. Prerequisite: Graduate standing, Mathematics 389J or 439J, and Mathematics 358K or 378K.
389T. Time Series and SurvivalModel Estimation.
Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society. Prerequisite: Graduate standing, Mathematics 358K or 378K, and Mathematics 389U.
389U. Actuarial Contingent Payments I.
Simulation of random samples, singlestatus survival models, presentvalue random variables for life insurance and annuities. With Mathematics 389J and 389V, covers the syllabus for exam #3 of the Society of Actuaries and the Casualty Actuarial Society. Prerequisite: Graduate standing and Mathematics 362K. Actuarial Foundations 309 is recommended.
389V. Actuarial Contingent Payments II.
Mathematical analysis of insurance premiums, reserves, multiplestatus survival models, multipledecrement survival models; applications to such areas as life insurance and property/casualty insurance. With Mathematics 389J and 389U, covers the syllabus for exam #3 of the Society of Actuaries and the Casualty Actuarial Society. Four lecture hours a week for one semester. Prerequisite: Graduate standing, and Mathematics 389U or 339U.
390C. Topics in Algebra.
Recent topics have included algebraic geometry, number theory, algebraic curves, algebraic number theory, algebraic functions, rational curves on varieties, homological algebra. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
391C. Topics in Analysis.
Same as Computational and Applied Mathematics 391C. Recent topics have included measure and integration, real variables, complex analysis, functional analysis, ordinary differential equations, partial differential equations, integral transforms, operator theory, approximation theory, abstract harmonic analysis. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
392C. Topics in Topology.
Recent topics have included algebraic topology, differential topology, geometric topology, Lie groups. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393C. Topics in Applied Mathematics.
Same as Computational and Applied Mathematics 393C. Recent topics have included quantum mechanics, statistical physics, ergodic theory, group representations, statistical mechanics, quantum field theory, introductory partial differential equations, monotone operators and partial differential equations, Hilbert space methods for partial differential equations, Hamiltonian dynamics, nonlinear functional analysis, Euler and NavierStokes equations, microlocal calculus and spectral asymptotics, calculus of variations. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393D. Topics in Numerical Analysis.
Same as Computational and Applied Mathematics 393D and Computer Sciences 393D. Recent topics have included numerical methods in ordinary differential equations, numerical methods in partial differential equations, computational problems in linear algebra, numerical solution of systems of equations, numerical methods in functional approximation, numerical integration. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393N. Numerical Solution of Elliptic Partial Differential Equations.
Same as Computational and Applied Mathematics 393M and Computer Sciences 393N. The numerical solution of large systems of linear algebraic equations arising in the solution of elliptic partial differential equations by discretization methods. Prerequisite: Graduate standing; and Computational and Applied Mathematics 386K, Computer Sciences 386K, Mathematics 383G, or consent of instructor.
394C. Topics in Probability and Statistics.
Same as Computational and Applied Mathematics 394C. Recent topics have included nonparametric statistics, advanced probability. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
395C. Topics in Logic and Foundations.
Recent topics have included set theory, model theory, proof theory, axiomatic theorem proving, automatic theorem proving, foundations of mathematics, recursion theory. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
396C. Topics in Mathematics.
Recent topics have included set theory, history of mathematics. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
197S, 397S. Seminar in Mathematics.
One or three lecture hours a week for one semester. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
698. Thesis.
The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in mathematics and consent of the graduate adviser; for 698B, Mathematics 698A.
398R. Master's Report.
Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in mathematics and consent of the supervising professor and the graduate adviser.
398T. Supervised Teaching in Mathematics.
Offered on the credit/no credit basis only. Prerequisite: Graduate standing and appointment as a teaching assistant.
399R, 699R, 999R. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.
399W, 699W, 999W. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Mathematics 399R, 699R, or 999R.
