Open elective credit also is required to meet the minimum graduation requirement of 192 hours.
Additional Recommended Courses:
Students interested in graduate study in mathematical statistics are encouraged to take the following:
PROBABILITY AND STATISTICS I
Probability spaces, combinatorial probability methods, discrete and continuous random variables and distributions, moment generating functions, development and applications of the classical discrete and continuous distributions.
MAT 261 is a prerequisite for this class.
PROBABILITY AND STATISTICS II
Joint probability distributions and correlation; law of large numbers and the central limit theorem; sampling distributions and theory of estimation.
MAT 351 is a prerequisite for this class.
PROBABILITY AND STATISTICS III
Principles of hypothesis testing; most powerful tests and likelihood ratio tests; linear regression; one-way analysis of variance; categorical data analysis, nonparametric statistics.
MAT 352 is a prerequisite for this class.
STATISTICAL METHODS USING SAS
The SAS programming language. Data exploration, description and presentation. Inference based on continuous and categorical data. Analysis of variance models and regression procedures including logistic regression. Cross-listed with MAT 448.
APPLIED REGRESSION ANALYSIS
Simple linear, multiple, polynomial and general regression models. Selection of best regression equation and examination of residuals for homoscedasticity and other diagnostic. Use of statistical software. Cross-listed with MAT 456.
MAT 353 and (MAT 220 or MAT 262) is a prerequisite for this class.
SAMPLE SURVEY METHODS
Simple random, stratified, systematic and cluster sampling. Multistage and area sampling. Random-response and capture-release models.
MAT 349 or MAT 353 is a prerequisite for this class.
DESIGN OF EXPERIMENTS
Linear models and quadratic forms. Single, two and several-factor experiments, incomplete designs, confounding and fractional factorial experiments. Response surfaces and partially balanced incomplete block designs.
MAT 349 or MAT 353 is a prerequisite for this class,.
APPLIED STATISTICAL METHODS
Introduction to statistical software (which will be used throughout the course). Descriptive statistics; elementary probability theory; discrete and continuous probability models; principles of statistical inference; Simple linear regression and correlation analysis. PREREQUISITE(S): MAT 148 or 151 or 161 or 171.
MAT 148 or MAT 151 or MAT 161 or MAT 171 is a prerequisite for this class.
APPLIED STATISTICAL METHODS II
A continuation of Mathematics 348. Multiple regression; analysis of frequency data, ANOVA and some experimental designs; nonparametric inference and time series analysis. Use of statistical software. PREREQUISITE(S): MAT 348.
MAT 348 is a prerequisite for this class.
MULTIVARIATE STATISTICS (CROSS-LISTED WITH MAT 454)
The multivariate normal distribution. Hypothesis tests on means and variances including the multivariate linear model. Classification using the linear discriminant function. Principal components and factor analysis.
MAT 262 and MAT 353 are a prerequisite for this class.
Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes. Cross-listed with MAT 455.
MAT 353 is a prerequisite for this class.
Inference concerning location and scale parameters, goodness of fit tests, association analysis and tests of randomness using distribution free procedures. Bootstrap techniques. Smoothing methodologies. Cross-listed with MAT 457.
PREREQUISITE: MAT 349 or 353
APPLIED TIME SERIES AND FORECASTING
Development of the Box-Jenkins methodology for the identification, estimation, and fitting of ARIMA, and transfer-function stochastic models for the purpose of analyzing and forecasting stationary, non-stationary, and seasonal time series data. The course emphasizes practical time-series data analysis using computer packages and includes applications to economic, business, and industrial forecasting. Cross-listed with MAT 512.
MAT 341 and MAT 353 are a prerequisite for this class.
REAL ANALYSIS I
Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.
(MAT 149 or MAT 152 or MAT 162 or MAT 172) and (MAT 141 or MAT 215) are a prerequisite for this class.
REAL ANALYSIS II
Properties of continuous functions, uniform continuity, sequences of functions, differentiation, integration. To follow 335 in the Winter Quarter.
MAT 335 is a prerequisite for this class.
ADVANCED LINEAR ALGEBRA
Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces; diagonalization of symmetric linear operators, principal-axis theorem, and applications. Cross-listed MAT 470.
MAT 262 and (MAT 141 or MAT 215) are a prerequisite for this class.
NUMERICAL ANALYSIS I
Use of a digital computer for numerical computation. Error analysis, Gaussian elimination and Gauss-Seidel method, solution of non-linear equations, function evaluation, cubic splines, approximation of integrals and derivatives, Monte Carlo methods. Cross-listed with MAT 485.
(MAT 220 or MAT 262) and (MAT 149 or MAT 152 or MAT 162 or MAT 172) is a prerequisite for this class.
NUMERICAL ANALYSIS II (CROSS-LISTED WITH MAT 486 & CSC 386/486)
Theory and algorithms for efficient computation, including the Fast Fourier transform, numerical solution of non-linear systems of equations. Minimization of functions of several variables. Sparse systems of equations and corresponding eigenvalue problems.
MAT 385 is a prerequisite for this class.