F, W, Sp, Su notations indicate the quarter(s) each course is normally
offered. Unless otherwise specified, the course is offered during the indicated
quarter(s). Any course listed as a prerequisite must be passed with a C or better
grade.
MAT
508: Numerical Linear Algebra (4) W
(even years)
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 lecture/problems. Prerequisites: C or better
in MAT 208, MAT 315 and MAT 401 or consent of instructor.
|
MAT
509: Error Analysis (4) Sp
(even years)
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 lecture/problems. Prerequisites: C or better in MAT 401 and 402 or consent
of instructor.
|
MAT
511, 512: Real Analysis (4) (4) F, W
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-Nikodym theorem, the Fubini theorems, Daniel integrals, applications.
4 lecture/discussions. Prerequisite: C or better in MAT 315 or consent of
instructor.
|
MAT
517, 518: Abstract Algebra (4) (4) W, Sp
(odd years)
Groups, Sylow theorems, rings and modules, chain conditions, morphism theorems,
principal ideal domains, field extensions and finite fields, Galois theory.
4 lecture/discussions. Prerequisite: C or better in MAT 418 or consent of
instructor.
|
MAT
521: Topology (4) F (even years)
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.
|
MAT
528, 529: Complex analysis (4) (4) F (odd years) W (even years)
General form of Cauchy's theorem, conformal mappings, normal families. Riemann
mapping theorem, theorems of Mittag-Leffler and Weierstrass, analytic continuation.
Picard's theorem. Selected topics such as Dirichlet's problem, generalization
of Picard's theorem, gamma and zeta functions. 4 lecture/discussions. Prerequisite:
MAT 314 or 428, or consent of instructor.
|
MAT
535: History of Mathematics (4)
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.
|
MAT
540: Kalman Filter (4) F
(odd years)
Discrete- and continuous-time Kalman Filter. Design, simulation, a nd implementation;
the extended Kalman Filter. Applications to radar, tracking, communication
networks, space navigation, social and environmental systems. 4 lecture/problems.
Prerequisites: CS 120 or CS 125, MAT 208, MAT 216, STA 241 or STA 326, or
consent of instructor.
|
MAT
545, 546: Modeling (4) (4) W, Sp
(odd
years)
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 lecture/problems. Prerequisite: Consent of instructor.
|
MAT
550: Seminar in Mathematics (1-4)
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 seminar/discussions. Prerequisite: Consent of instructor.
|
MAT
570: Graphs and Network Flows (4) Sp
(even
years)
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 lecture/problems. Prerequisite: MAT 370 or consent of the instructor.
|
MAT
580: Optimization Theory and Applications (4) F
(odd years)
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 lecture/problems. Prerequisite: C or better in MAT
480 or consent of instructor.
|
MAT
599/599A/599L: Special Topics for Graduate Students (1-4)
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/Lab.
Prerequisite: Consent of Instructor.
|
MAT
691: Directed Study (1)
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.
|
MAT
696: Master's Degree Thesis (1)
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.
|
MAT
697: Comprehensive Examination (1) Credit/no Credit
Preparation for the comprehensive examination. Students must obtain
the written permission of the graduate coordinator in order to register
for this course. Only applicable with Pure Math option. Advancement to Candidacy
required.
|
MAT
699: Master's Degree
Continuation (0)
Registration or an approved leave of absence is required
for any quarter following the final assignment of the grade SP 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.
|
STA
525: Time Series Analysis (4) F (odd years)
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.
|
STA
530: Random Processes (4) Sp (odd years)
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.
|
STA
533: Linear Statistical Models I (4) W (even years)
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 lecture/problems. Prerequisite: C or
better in STA 432 or consent of instructor.
|
STA
534: Linear Statistical Models II (4) Sp (even years)
Fixed and random components models, balanced and unbalanced cases, analysis
of covariance, components of variance. Computer package SAS will be used.
4 lecture/problems. Prerequisite: C or better in STA 533 or consent of instructor.
|
STA
550: Probability Theory (4)
Independence, zero-one laws, laws of large numbers, convergence theorems,
characteristic functions, and basic limit theorems. Prerequisite: C or
better
in STA 440 or consent of instructor.
|
STA
565: Applied Multivariate Data Analysis (4) W (odd years)
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.
|
STA
584: Queueing Theory (4) F (even years)
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. Prerequisites: C or better in
MAT 382 or STA 430, and STA 341 or STA 441, or consent of instructor.
|
STA
590: Supervised Statistical Consulting (2) Sp
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 seminar/discussions.
Prerequisite: C or better in
STA 432 or STA 435 or consent of instructor. May be repeated for a
maximum of 4 units of credit. |
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