Fall 2019, Winter 2020 and Summer 2020

Fall 2019

Math 504: Dynamical Systems [T 6:00-8:45pm, Prof. Mike Dakowski]

This course will be a survey of methods, both analytic and numerical, used to study discrete time and continuous time dynamical systems. Dynamical systems are states which evolve over time and can be modeled by differential equations. This course will study these linear and nonlinear systems in one dimension and higher. It will begin with an analysis of the solutions of linear dynamical systems and the phase plane together with applications. Nonlinear systems will be studied through a variety of techniques including the Lyapunov method, LaSalle's Invariance Principle, and Poincare recurrence. There will be a particular focus on gradient flows and Hamiltonian systems. The course will conclude with a study of chaotic systems and fractal sets.  

Satisfies: Modeling Specialization Area B: Differential Models

Offered: Occasionally

Math 551: Advanced Calculus I [TR 9:30-10:45am, Prof. John Clifford]

Advanced Calculus is the rigorous study of the concepts of limit, differentiation, and integration. In this course, we dig deeper into the historical developments of these concepts and deduce many principles from basic axioms. Students will practice a serious application of logic and proof techniques in the course. The basic ideas develop in this course constitute a strong foundation for any further course in mathematics. Previous experience in first-year calculus and proof methods will be helpful.

Satisfies: Core A: Analysis

Offered: Every fall

Math 562: Math Modeling [M 6:00-8:45 PM, Prof. Hyejin Kim]

The processes of constructing, implementing, and evaluating mathematical models of "real world" phenomena are investigated. Optimization models, dynamic models, and probability models are considered. The goal is to learn how to model phenomena arising in biology, social sciences, physics etc. and rigorously study them using mathematics. Matlab will be used extensively to solve problems that are not tractable by hand.

Satisfies: Core C: Modeling 

Offered: every Fall

Math 572: Numerical Analysis [TR 4:30-5:45 PM, Prof. Aditya Viswanathan]

Numerical Analysis is the study of algorithms that approximate solutions to many problems in mathematics. In this course, we study how computers approximate and store numbers and how round off error can affect computations. We develop and analyze algorithms to approximate solutions to mathematical problems including finding roots of functions, solving definite integrals, interpolating data by polynomials and splines, numerical differentiation, solving systems of linear equations, and solving differential equations. Some programming experience will be helpful.

Satisfies: Core B: Numerical Methods

Offered: every fall

Stat 530:  Applied Regression Analysis [TR 2:00-3:15 PM, Prof. Keshav Pokhrel ]

Topics include single variable linear regression, multiple linear regression and polynomial regression. Model checking techniques based on analysis of residuals will be emphasized. Remedies to model inadequacies such as transformations will be covered. Basic time series analysis and forecasting using moving averages and autoregressive models with prediction errors are covered. Statistical packages will be used.

 Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization: Statistics Models (students admitted Fall 16 or later)

Offered: Every fall

Winter 2020

Math 525: Mathematical Statistics II [MW 2:00 - 3:15 PM, Prof. Hyejin Kim]

Statistical inference is the process of drawing conclusions about a given population based on observed data from random samples. There are many approaches to perform inference, which enables us to argue from the particular observations in a sample to the general case.  The two main classes of inference problems are estimation of parameters and testing hypotheses about the value of the parameters. In this course we will study the fundamentals of statistical inference and we expect that students will be able to use them for more complex inferential challenges.

Satisfies:  Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization C: Statistical Models (students admitted Fall 16 or later)

Offered: Every other year

Prerequisite: Math 325 (or previous introductory stats class)

Math 555: Complex Variables [MW 4:30 - 5:45 PM, Prof. Yulia Hristova]

This course presents the mathematical structure that underlies many aspects in science and engineering.  One needs a broader outlook than the real number system provides to properly describe electric phenomenon, fluid flow, and thermal flow.  All these phenomena are related to potentials, and have identical basic mathematical underpinnings.  To begin, the complex number system is introduced and concepts of calculus are explored in depth as they relate to this new system.  The theory of derivatives (analytic functions) and especially integrals turns out to be a much cleaner and richer environment than with real variables.  Power Series and Laurent Series are explored, leading to residues and poles.  Towards the end of the course, applications are presented.   Conformal maps also play a significant role.

Satisfies: Core A: Analysis

Offered: Every winter

Math 573: Matrix Computations  [TR 6:00 - 7:15 PM, Prof. Joan Remski]

Matrix Computations is concerned with the solution of real world problems that involve calculations with matrices.  One aspect of the course is the translation of real world problems into matrix theoretic terms.  Another is identifying the matrix operations involved in their solution and a third is implementing matrix operations in various computer environments.  In particular, the course is concerned with computational aspects of the solution of systems of equations, optimization, eigenvalues and eigenvectors and their application to difference and differential equations, orthogonal expansions, and singular value decompositions.  It also considers the time, space, and round-off error problems that arise when the number of variables is large.  (Left: plot of the norm of (zI - A)-1 in the complex plane for 2x2 matrix A)

Satisfies: Core B: Numerical Methods

Offered: Every other winter

Stat 560: Time Series Analysis [TR 4:30 - 5:45 PM, Prof. Gengxin Li]

Time series Analysis is an important aid in the efficient panning and allocating of resources. In this course, we will we study different methods to analyze time series data. We develop predictive models including simple regression, multiple regression, ARMA, ARIMA, simple smoothing, exponential smoothing, seasonal variation, time series decomposition, and neural network models. We use software called "R" to visualize and analyze the data.  This course is a useful tool if you are interested in predictive modeling and data science.

Satisfies: Modeling Specialization C: Statistical Models

Offered: Occasionally 

Summer 2020

Math 520: Stochastic Processes  [Online, Prof. Hyejin Kim]

Review of distribution theory. Introduction to stochastic processes, Markov chains and Markov processes, counting, and Poisson and Gaussian processes. Applications to queuing theory. 

Satisfies: Modeling Specialization: Stochastic Models (students admitted before Fall 16) or Modeling Specialization C: Statistical Models (students admitted Fall 16 or later) 

Offered:  Occasionally