Mathematics and Statistics

Degrees and Certificates

DEPARTMENTAL PROGRAMS

The Department of Mathematics and Statistics offers two Master’s programs: Master of Arts in Mathematics and Master of Science in Applied Statistics and Data Science. Courses offered in these programs normally meet weekday evenings. Each program has a core of required courses. However, within each program there are several options available, and students are encouraged to take courses from other programs when those courses fit well with their overall goals. In addition to these Master’s programs, there are several certificate programs available: Certificate of Graduate Study in the Teaching of Secondary Mathematics, Post-Master’s Certificate in Mathematics, and Certificate in Applied Statistics and Data Science.

Classes

MAT 7110 : Quantitative Literacy

Workshop format is ued to present content and predagogy for statistical methods in the K-12 curriculum. Topics include data analysis, probability, simulation, surveys, and measurements. Emphasis is on understanding of statistics through discovery and non-formula orientation to material. Restricted to graduate students & qualified undergraduates.

Credits

3

MAT 7290 : Geometry

Topics selected from affine, finite, hyperbolic, spherical, elliptic, Euclidean or projective geometry.

Credits

3

MAT 7300 : History of Math

The development of mathematics from ancient times to the birth of calculus in the seventeenth century. Independent work on a topic in the history of mathematics since 1700.

Credits

3

MAT 7305 : Technology in Teaching of Math

Applications of technology to topics selected from algebra, geometry, calculus, statistics and programming. Technologies used may include computer algebra systems, e.g., Maple, geometry software, e.g., Sketchpad, and statistics software, e.g., Fathom.

Credits

3

MAT 7600 : Advanced Calculus

Real numbers, completeness, sequences, limits, continuous functions, the derivative, sequences of functions, pointwise and uniform convergence, power series.

Credits

3

MAT 7605 : Topics in Analysis

Advanced topics selected from real analysis, complex analysis, or higher analysis. Prerequisite: Determined by instructor.

Credits

3

Prerequisites

MAT 7600 :C

MAT 7610 : Complex Analysis

Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral theorem and Cauchy integral formulae, power series, Taylor and Laurent series, singularities, residue theorem, harmonic functions.

Credits

3

MAT 7660 : Linear Algebra

Vector spaces, linear transformations, eigenvalues and eigenvectors, invariant subspaces, decomposition theorem, Jordan forms, bilinear forms, selfadjoint operators, functions of operators, differential systems.

Credits

3

MAT 7670 : Mathematical Logic

The sentential calculus, truth functions, analytic tableaux, natural deduction, first order logic, models, consistency, completeness. Applications to computer science including the P-NP problem.

Credits

3

MAT 7750 : Numerical Analysis I

Error generation and propagation, root finding, approximation of functions by polynomials and cubic splines, direct and iterative solutions of linear systems, operations count, numerical differentiation and integration.

Credits

3

MAT 7755 : Numerical Analysis II

Topics selected from: calculation of eigenvalues and eigenvectors, finite difference techniques, numerical methods for solving initial and boundary value problems, convergence, stability.

Credits

3

Prerequisites

MAT 7750 :C

MAT 7770 : Number Theory

Divisibility; Euclidean algorithm; prime numbers; Fundamental Theorem of Arithmetic; congruences; arithmetic functions; Diophantine equations, additional topics, which may vary by semester, include cryptography, law of quadratic reciprocity, continued fractions.

Credits

3

MAT 7780 : Financial Mathematics

Basic tools of financial markets; annuities; options; asset price random walks; estimation of parameters; Black-Scholes Model; implied volatility; portfolio-engineering; hedging; discrete models.

Credits

3

MAT 7790 : Dynamical Systems & Chaos

Topics selected from: iteration of real and complex functions, population models, qualitative theory of differential equations, fractals and dimension, topological and metric properties of systems, and applications.

Credits

3

MAT 7990 : Seminar in Biomathematics

Supervised study and research project incorporating mathematical and computational models for topics such as: pattern detection and pattern matching in DNA sequences; population growth and the dynamics of epidemics.

Credits

3

MAT 8010 : Biomath Pedagogy Seminar

Supervised study to develop, test, and implement an interdisciplinary instructional module for use in a high school curriculum. Module incorporates mathematical and computational models for topics such as: pattern detection and pattern matching in DNA sequences; population growth and the dynamics of epidemics.

Credits

3

MAT 8430 : Operations Research

Deterministic mathematical models, including linear programming, integer programming, inventory, transportation and assignment problems, networks and flows, nonlinear programming and dynamic programming with an emphasis on principles and techniques.

Credits

3

MAT 8435 : Mathematical Modeling

Model construction, Markov chains, game theory, networks and flows, growth processes and models for epidemics and queues with an emphasis on model construction.

Credits

3

MAT 8600 : Real Analysis

General theory of measure and integration, Lebesgue measure, Lebesgue integral.

Credits

3

Prerequisites

MAT 7605 :C

MAT 8655 : Topics in Algebra

Possible topics include Boolean algebras, graph theory, coding theory, Galois theory.

Credits

3

Prerequisites

MAT 8650 :C

MAT 8740 : Applied Math I

Symmetric linear systems, eigenvalue and dynamical systems, Lagrange multipliers, equilibrium and minimum principles, least squares estimation and Kalman filter, equilibrium of fluids and solids, calculus of variations.

Credits

3

Prerequisites

MAT 7660 :C

MAT 8790 : Selected Topics I

Particular topics of study determined on a year to year basis to suit the desire and prepartion of students.

Credits

3

MAT 9000 : Graduate Math Seminar

Supervised study of selected topics in mathematics with presentations by individual students. Content may be chosen by the instructor or may be tailored to interests of students.

Credits

3

Prerequisites

MAT 7660 :C

STAT 7111 : AP Statistics Workshop

Workshop for teachers of the Advanced Placement (AP) Statistics course. Inference, design of experiments, exploratory data analysis, simulation, probability, investigative tasks, and AP Statistics exam overview.

Credits

3

STAT 7120 : Intro to Stats for HS Teachers

A brief overview of statistical reasoning using both descriptive and inferential statistical methods. Special focus on the Advanced Placement statistics course.

Credits

1

STAT 7125 : Intermed Stats for HS Teachers

Workshop for teachers of introductory statistics. Overview of material just beyond the AP / introductory statistics curriculum, including simulation-based inference, multiple regression, ANOVA, statistical programming, and selected topics.

Credits

1

STAT 7130 : Teaching Intro. Statistics

For current or future teachers of statistics. Combines theoretical framework and hands-on experience in understanding and developing statistical reasoning and thinking necessary for teaching an introductory statistics course. Ideas for addressing common student misconceptions will be addressed.

Credits

3

Prerequisites

STAT 1230 or STAT 1250 or STAT 1313 or STAT 1430 or STAT 4310 or STAT 7404

STAT 7200 : Data Science for Professionals

Reading and scraping data, data wrangling, data visualization, and predictive analytics from a variety of sources. Knowledge of statistics and programming experience (any language) strongly recommended.

Credits

2

STAT 7404 : Statistical Methods

Data summarization and display, distributions; binomial, Poisson, normal, t, chi-square and F, estimation, hypothesis testing, linear regression, correlation, statistical software packages.

Credits

3

STAT 7500 : Statistical Programming

Use SAS and R for data manipulation, presentation, and summarization. Topics include inputting/importing/exporting data cleaning and manipulation, and numerical and graphical summaries/analyses. Students will be introduced to simulations, SAS macro programming, and R functions.

Credits

3

Prerequisites

MAT 4310 :Y or STAT 4310 :Y or MAT 7404 :Y or STAT 7404 :Y

STAT 8400 : Statistical Theory I

Probability, random variables, univariate and multivariate distributions, mathematical expectation, Central Limit Theorem, Law of Large Numbers.

Credits

3

STAT 8401 : Statistical Theory II

Sampling, estimation, hypothesis testing, decision theory, least squares, regression, analysis of variance, Bayesian statistics.

Credits

3

Prerequisites

MAT 5700 or STAT 5700 or MAT 8400 or STAT 8400

STAT 8406 : Regression Methods

Linear regression, correlation, multiple regression, weighted least squares, residuals and influence diagnostics, model building, variable selection, nonlinear regression.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8408 : Multivariate Methods

Multivariate normal distribution, principal component analysis, Hotelling T2 test, discriminant function analysis, multivariate analysis of variance, covariance and repeated measurements, canonical correlation analysis, factor analysis, claffication and cluster analysis.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8410 : Bayesian Statistics

Prior distributions, Posterior distributions, Conjugate priors, the Metropolis-Hastings algorithm, the Gibbs sampler, Markov chain Monte Carlo, Convergence diagnostics, Credible Intervals Hierarchical modeling, Differences between Bayesian and frequentist inference.

Credits

3

Prerequisites

(MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404) and (MAT 5700 or STAT 5700 or MAT 8400 or STAT 8400)

STAT 8412 : Linear Models

Analysis of general linear models, fixed and random effects, variance components, unbalanced data.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8414 : Categorical Data Anal

Estimation, maximum likelihood, weighted least squares, log- linear models, logistic regression.

Credits

3

Prerequisites

MAT 8406 or STAT 8406 :Y

STAT 8416 : Design of Experiments

Completely randomized, randomized block, latin square, nested, split plot, balanced incomplete block and crossover designs, factorials, systems of confounding, fractional factorials and response surface designs.

Credits

3

Prerequisites

MAT 8412 or STAT 8412

STAT 8440 : Statistics Quality Control

Industrial applications of statistical techniques, Deming's 14 points, Ishikawa's charting techniques, control charts for attributes and variables, acceptance sampling, military standards, process capability studies, introduction to Taguchi designs.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8446 : Survival Data Analysis

Analysis of survival or lifetime data; life tables and Kaplan-Meier estimation; survival analysis with covariates; Cox proportional hazard models.

Credits

3

Prerequisites

(MAT 5700 or STAT 5700 or MAT 8400 or STAT 8400) and (MAT 8406 :Y or STAT 8406 :Y)

STAT 8448 : Clinical Trials

Basic principles of clinical trials, rationale, history, organization and planning, randomization and ethical issues, sample size determination, study designs: parallel, crossover, repeated measurements, statistical analysis of clinical trials data, interim analyses.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8450 : Longitudinal Data Analysis

Longitudinal data plots, univariate and multivariate repeated measures ANOVA, generalized linear models, response profile models, linear mixed models, generalized linear mixed models, residual diagnostics, missing data, clinical trials applications, analysis in SAS.

Credits

3

Prerequisites

(MAT 8406 or STAT 8406) and (MAT 5700 or STAT 5700 or MAT 8400 or STAT 8400)

STAT 8452 : Nonparametric Statistics

One sample rank tests, estimates and confidence intervals, paired replicates, two sample rank tests, nonparametric correlation and regression techniques.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8454 : Sampling Methods

Sampling and survey methodology, basic sampling theory, random and stratified sampling, systematic sampling errors, estimation procedures.

Credits

3

Prerequisites

MAT 4310 or STAT 4310 or MAT 7404 or STAT 7404

STAT 8462 : Stochastic Modeling

Monte Carlo Simulation, Markov chains, generating functions, random walk models, gambler's ruin problem, queuing processes, Poisson processes, Gaussian processes.

Credits

3

Prerequisites

MAT 5700 or STAT 5700 or MAT 8400 or STAT 8400

STAT 8480 : Data Mining & Predictive Analy

Data preparation, Predictive modeling via decision trees, regression models and neural network, Model assessment and implementation, Pattern discovery, Association rule discovery, Text mining.

Credits

3

Prerequisites

MAT 8406 or STAT 8406

STAT 8790 : Selected Topics I

Particular topics of study determined on a year to year basis to suit the desire and prepartion of students.

Credits

3