Topics will include numerical methods for determinants, systems of linear equations (direct and iterative methods), matrix inversions, eigenvalues, eigenvectors, techniques to minimize error propagation, splittings, rates of convergence of methods. 4 lectures/problem-solving. Prerequisites: C or better in MAT 208; MAT 315 and MAT 401 or consent of instructor.

Topics will include sources of error, types of error, error propagation, techniques for minimizing error, backward error analysis, approximation of functions, error analysis of iterative methods for non-linear equations. 4  lectures/problem-solving. Prerequisites: C or better in MAT 401 and MAT 402 or consent of instructor.

Properties of Lebesgue measure and integration, Borel Sets, monotone functions and functions of bounded variation, classical Banach spaces, metric spaces, measure spaces and measurable functions, the Radon-Nykodym theorem, the Fubini theorems, Daniel integrals, applications. 4 lectures/problem-solving. Prerequisite: C or better in MAT 315 or consent of instructor.

Groups, Sylow theorems, rings and modules, chain conditions, morphism theorems, principal ideal domains, field extensions and finite fields, Galois theory. 4 lectures/problem-solving. Prerequisite: C or better in MAT 418 or consent of instructor.

Topological spaces, connectedness, compactness, continuity, separation and countability axioms, metric spaces, product spaces, function spaces and quotient spaces, uniform spaces, paracompactness. 4 lecture discussions. Prerequisite: consent of instructor.

General form of Cauchy's theorem, conformal mappings, normal families. Riemann mapping theorem, theorems of Mittag-Leffler and Weierstrass, analytic continuation.  Picard's theorem, gamma and zeta functions. 4 lecture discussions. Prerequisite: MAT 314 or MAT 428 or consent of instructor.

Historical development of selected mathematical topics drawn generally from the body of 18th century and later mathematics. Topics to be covered announced by the professor prior to registration. 4 lecture discussions. Prerequisite: consent of instructor.

Discrete- and continuous-time Kalman Filter. Design, simulation, and implementation; the extended Kalman Filter.  Application to radar tracking, communcation networks, space navigation, social and environmental systems. 4 lectures/problem-solving. Prerequisites: CS 128 or CS 125, MAT 208, MAT 216, STA 241, or STA326, or consent of instructor.

Modeling of deterministic systems and random processes using ordinary and partial differential equations. Fourier methods, general modeling principles and techniques, perturbation theory and sensitivity analysis, applications. 4 lectures/problem-solving. Prerequisite: consent of instructor.

Topics in advanced mathematics chosen according to the interests and needs of the students enrolled.  Each seminar will have a subtitle according to the nature of the content.  May be repeated for a maximum of 8 units. 1-4 seminars. Prerequisite: consent of instructor.

Matching theory in graphs and network flows in capacity-constrained networks.  Major topics include the Konig-Egervary Theorem for bipartite graphs and the Maximal Flow Algorithm for networks, along with a wide variety of applications.  4 lectures/problem-solving. Prerequisite: MAT 370 or consent of instructor.

Topics will include convex sets, extrema of functions, convex functions, non-linear convex, quadratic and dynamic programming, applications, primal-dual methods for solving constrained problems, applications to large scale mathematical programming problems. 4 lectures/problem-solving. Prerequisite: C or better in MAT 480 or consent of instructor.

Group study of a selected topic, the title to be specified in advance. Total credit limited to 8 units with a maximum of 4 units per quarter.  Lecture/Activity/Laboratory or combination of these. Prerequisite: consent of instructor.

Individual reading program in an area chosen by the student under the direction and supervision of the faculty.  Maximum of 4 units credit.  Students must obtain the written permission of the graduate coordinator in order to register for this course.  Unconditional standing required.

Independent research and study under supervision of a faculty advisor.  Research results must be reported in an acceptable form.  Require 3 units credit for thesis.  Students must obtain the written permission of the graduate coordinator in order to register for this course. Advancement to Candidacy required.

Preparation for the comprehensive examination.  Students must obtain the written permission of the graduate coordinator in order to register for this course.  May be taken no more than twice.  Failure to complete exam satisfactorily the second time will result in termination from the program.  Only applicable with Pure Mathematics Emphasis.  Advancement to Candidacy required.

Registration or an approved leave of absence is required for any quarter following the final assignment of the grade RP until the completion of thesis.  The candidate must be enrolled in the university during the quarter in which he/she graduates.  Students must obtain the written permission of the graduate coordinator in order to register for this course. Advancement to Candidacy required.

Stationary and non-stationary models.  Autocorrelation and partial autocorrelation functions.  Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA), and Autoregressive Integrated Moving Average (ARIMA) models.  Models for seasonal time series.  Identification, estimation, diagnostic checking and forecasting.  Use of computer package such as SAS or Minitab.  4 lecture/problem-solving.  Prerequisite: C or better in STA 341 or STA 326 or consent of instructor.

Topics will include second order stationary processes, mean and covariance properties, Gaussian processes, Wiener process and white noise, counting and renewal processes. 4 lectures/problem-solving. Prerequisite: C or better in STA 241 or STA 326, or consent of instructor.

Introduction to general linear models, distribution of quadratic forms, the Gauss-Markov theorem, estimation, testing the general linear hypothesis.  Computer package SAS will be used.  4 lectures/problem-solving. Prerequisite: C or better in STA 432 or consent of instructor.

Fixed and random components models, balanced and unbalanced cases, analysis of covariance, components of variance. Computer package SAS will be used.  4 lectures/problem-solving.  Prerequisite: C or better in STA 533 or consent of instructor.

Advanced topics in probability theory with and/or without measure theoretic approaches.  4 lectures/problems. Prerequisite: consent of instructor.

Incomplete block designs, fractional factorial designs, multifactor experiments with randomization restrictions, response surface methods and designs. 4 lectures/problems. Prerequisite: STA 435 or consent of instructor.

Multivariate distribution.  Variance-covariance matrices.  Multivariate Normal distribution, Hotelling's T² distribution.  Inference about a mean vector.  Discriminant analysis, Principal components, Factor analysis and Clustering.  Use of computer package such as SAS or Minitab.  4 lecture/problem-solving.  Prerequisite: C or better in STA 341or STA 326, and MAT 208 or consent of instructor.

Analysis of queueing systems, discrete and continuous time Markov processes, birth and death processes, equilibrium results for single and multiple server queues, method of stages, priority queues.  4 lectures/problems. Prerequisites: C or better in STA 430, STA 241 or STA 441, or consent of instructor.

Use of statistical computer packages and spreadsheets, Formulation of statistical/probabilistic models, Planning of surveys and experiments, Data analysis, Report writing and presentation, Oral communication with clients, Role-playing and group discussions. 2 lectures/problem-solving. Prerequisites: C or better in STA 432 or STA 435 or consent of instructor.  May be repeated for a maximum of 4 units of credit.

Group study of a selected topic, the title to be specified in advance.  Total credit limited to 8 units with a maximum of 4 units per quarter.  Lecture/Activity/Laboratory or combination of these. Prerequisite: consent of instructor.