Fall 2018, Winter 2019 and Summer 2019

Fall 2018

Math 554: Fourier Series and Boundary Value Problems [MW 4:30 - 5:45 PM, Prof. Yulia Hristova]

 Fourier series and integrals. Their use in solving boundary value problems of mathematical physics by the method of separation of variables. Sturm-Liouville theory and generalized Fourier series, including those involving Bessel functions and Legendre polynomials, with applications.  

Satisfies: Core A: Analysis, and Modeling Specialization B: Differential Models

Offered: Every year

Math 551: Advanced Calculus [MTR 12:00 - 12:50 PM, Prof. Yunus Zeytuncu]

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 [MW 2:00 - 3:15 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 6:00 - 7:15 PM, Prof. Joan Remski]

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 C: Statistics Models (students admitted Fall 16 or later)

Offered: Every fall

Winter 2019

Math 548: Introduction to Wavelets  [TR 4:30-5:45pm]

In this course we develop the mathematical theory of discrete wavelet transforms and pay particular attention to how they are used in digital image processing. Specific topics include a review of matrix algebra, an introduction to digital images, complex numbers, discrete Fourier series, filters, convolution, Haar wavelet transforms, Daubechies wavelet transforms, wavelet shrinkage, denoising, compression, and bi-orthogonal wavelet transforms. Graduate students will be required to complete a project on a topic of their choice. A programming course will be helpful.  

 Figure 1: Original image of Abe Lincoln is shown at the left. The middle and right images have been compressed using a discrete Daubechies wavelet transform. In the middle, 52% of the data from the original image was removed. At right, 25% of the data was removed.

Satisfies: 

Offered: Occasionally

Math 523: Linear Algebra with Applications [MW 6-7:15pm]

This course is an introduction to linear algebra with applications to engineering and the sciences. Topics include: matrices, vector spaces, inner products and projections, eigenvalues and eigenvectors, and norms and condition numbers. Applications include networks and incidence matrices, the fast Fourier transform, solutions to systems of differential equations, and the finite element method. If time permits, we will also discuss iterative methods for solving linear systems, linear programming and game theory.

Satisfies:  Modeling Specialization: Linear Models (students admitted before Fall 16) or Modeling Specialization: Linear and Discrete Models (students admitted Fall 16 or later)

Offered: every other year

Summer 2019

Stat 535: Data Analysis and Modeling [MW 4:30-7pm]

This course is an introduction to programming in R and Python for data analysis. The target audience is masters level students in math or engineering with little or no background in statistics or computer programming. Advanced undergraduates are also welcome. For students without much previous knowledge, this course can serve as an en

Topics in R include: the working environment of RStudio and RMarkdown, data structures (vectors, matrices, lists, data frames), loops, control statements, user-defined functions, reading and writing try point to other statistics and mathematics courses that use R or Python. On the other hand, for students who already have some previous knowledge, this course can serve as a methodical study of R and Python.

functions, reading and writing files, plotting using ggplot2, cleaning and reshaping data with dplyr, and debugging. Statistical content in R will include linear models with mixed effects, as well as the machine learning technique of k-nearest neighbors with application to classification of scanned handwritten digits.

The second half of the course will introduce Python, which is a popular programming language in the machine learning community. Python is also an open-source alternative to MATLAB. Topics in Python include the working environments of Spyder and Jupyter notebooks in Anaconda, data structures (lists, dictionaries, tuples), loops, control statements, user-defined functions, reading files, pickling Python objects to files, and debugging. We will also introduce the packages NumPy, SciPy, matplotlib, and Pandas for matrix computation, scientific computing, plotting, and dataframes respectively.

The only prerequisite is graduate standing in a technical field such as mathematics or engineering, however exceptions can be made for advanced undergraduates with a high degree of perseverance. We will code in class, so a personal laptop computer is recommended but not required, since class will meet in a computer lab

Figure: Job trends for Python and R, from the article “The Popularity of Data Science Software” by Robert A. Muenchen, http://r4stats.com/articles/popularity/

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

Offered: Occasionally