GRAD > MATH

## Mathematics Courses

#### MATH 545 Probability & Statistics I for Secondary Teachers +

**Description:**

This course presents the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. Topics also include basic ideas and techniques of statistical analysis. More Info

**Offered in:**#### MATH 570 History of Mathematics for Secondary Teachers +

**Description:**

This course traces the development of mathematics from ancient times up to and including 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problems solving. Attention will also be paid to the relevance of history to mathematics teaching as well as investigation into the origins of non-Euclidean geometry even though this comes well after Newton and Leibniz, because of its relatively elementary character and fascinating nature. More Info

**Offered in:**#### MATH 597 Special Topics +

**Description:**

An advanced course offering intensive study of selected topics in mathematics. More Info

**Offered in:**- TBA

#### MATH 625 Numerical Analysis +

**Description:**

This course provides an introduction to numerical analysis and its applications in practical problems in applied mathematics and engineering. In most scientific modeling projects, investigators have to deal with very large systems of linear and nonlinear equations, understanding of which requires powerful computers and a firm understanding of the vast number of existing pertinent algorithms. The main goal of the course is to provide an introduction to algorithmic and mathematical foundations of high-performance scientific computations. Introductory topics of the course include root finding, fixed point methods, interpolation methods, initial value problems and optimization. Particular emphasis will be on optimization methods, including steepest descent, line search methods, newton methods, quasi-Newton methods, trust regions, theory of constraint optimization and linear programming. More Info

**Offered in:**#### MATH 626 Numerical Linear Algebra +

**Description:**

This course introduces the essential ideas and computational techniques that modern scientists or engineers will need in order to carry out their work. In most scientific modeling projects, investigators have to deal with very large systems of linear equations, understanding of which requires powerful computers, and a firm understanding of the vast number of existing pertinent algorithms. The main goal of the course is to provide an introduction to algorithmic and mathematical foundations of high-performance matrix computations. Topics include linear algebraic systems, the singular value decomposition (SVD) of a matrix and some of its modern applications. We will discuss Principal Component Analysis (PCA) and its applications to data analysis. We will study linear transformations and change of basis. We will discuss complex vector spaces and the Jordan canonical form of Matrices. We will discuss non-negative matrices and Perron-Frobenius Theory. We will explain multiple matrix factorizations, such as LU, QR, NMF. For each of these topics we will discuss numerical computer algorithms and their implementations. In particular we will discuss in detail eigenvalue estimation, including iterative and direct methods, such as Hausholder methods, tri-diagonalization, power methods, and power methods with shifts. We will explain concepts of numerical analysis that are important to consider when we talk about the implementation of algorithms, such as stability and convergence. We will discuss iterative methods as well as direct ones, their advantages and disadvantages. The methods and their applications will be illustrated using a common programming language such as python and/or R. The course will emphasize mathematical and software engineering methods that will allow students to fully participate at all levels of algorithm design and implementation. More Info

**Offered in:**#### MATH 647 Probability Models +

**Description:**

This is a graduate course on probability models with a strong emphasis on stochastic processes. The aim is to enable students to approach real-world phenomena probabilistically and build effective models. Topics include probability spaces, random variables, conditional probability, Markov chains, Poisson processes, Browian motion, probabilistic simulations. More Info

**Offered in:**#### MATH 648 Computational Statistics +

**Description:**

This course is an introduction to the fundamental ideas and techniques of statistical inference. The course demonstrates how and when to use statistical methods, explains the mathematical background behind them and illustrates them with case studies. Topics covered include the Central Limit Theorem, parameter estimation, confidence intervals, hypothesis testing, type I and II errors, power, significance level, p-value, likelihood ratiotests, t-test, paired and 2-population t-test, goodness-of-fit tests, contingency tables, exact tests, nonparametric tests, ANOVA and regression models. Statistical software such as R, Matlab, or Python, will be used to analyze real-world data. More Info

**Offered in:**#### MATH 655 An Introduction to Statistical Machine Learning +

**Description:**

This course will provide an introduction to methods in statistical machine learning that are commonly used to extract important patterns and information from data. Topics include: supervised and unsupervised learning algorithms such as generalized linear models for regression and classification, support vector machines, random forests, k-means clustering, principal component analysis, and the basics of neural networks. Model selection, cross-validation, regularization, and statistical model assessment will also be discussed. The topics and their applications will be illustrated using the statistical programming language R in a practical, example/project oriented manner. More Info

**Offered in:**#### MATH 696 Independent Study +

**Description:**

Study of a particular area of this subject under the supervision of a faculty member. More Info

**Offered in:**#### MATH 697 Special Topics +

**Description:**

An advanced course offering intensive study of selected topics in mathematics. Course content varies each semester and will be announced prior to registration. More Info

**Offered in:**- TBA