Department of Mathematics

Special Mathematics Classes: Capstones

MTH 396 Prerequisites:

MTH 396 Prerequisites: Completion of Tier I Writing Requirement, MTH 309, MTH 310, and MTH 320 (or the honors equivalents, or approval of department) and approval of the department. Typically the department expects a cumulative GPA of at least 2.0 and an average of at least 2.0 across MTH 309, MTH 310 and MTH 320. Note: Email notification will be given once your override has been issued.

MTH 496 Prerequisites:

Completion of Tier I Writing Requirement and approval of the department. Typically the department expects students to have completed MTH 309, MTH 310, and MTH 320 (or the honors equivalents) with cumulative GPA of at least 2.0 and an average of at least 2.0 across MTH 309, MTH 310 and MTH 320. Additional prerequisite courses may be required and can be found in the descriptions below. Note: Email notification will be given once your override has been issued.

Fall Semester 2020: MTH 496 Section 1 - Machine Learning

Instructor: Jiahui Chen

This is an introductory course to Machine Learning (ML). ML is a powerful technique widely used in data-driven areas such as language processing, face recognition, image segmentation, banking, nance, insurance, drug discovery, engineering, etc. In this course, we will discuss theoretical background of ML algorithms and architectures, and focus on programming skills. Ultimately, each student is able to implement ML algorithm for practical applications. This course includes an introduction of Python, which covers popular Python packages and standard datasets, and ML algorithms, which are linear regression, logistic regression, k-means, k-nearest neighbors (KNN), support vector machine (SVM), Naïve Bayes, and Hop eld Network. If time allows, more advanced methods such as random forests, gradient boosting trees and deep neural networks will be introduced.

Prerequisites: Approval of Department. Suggested Background: CSE 231, MTH 235/340, STT 441, & STT 442

Fall Semester 2020: MTH 496 Section 2 - Fourier Analysis and Applications

Instructor: Farhan Abedin

Fourier analysis originated from the investigation of vibrating strings and heat flow. The ensuing mathematical theory now has myriad applications in areas like differential equations and signal processing. The goal of this course will be to develop the basic theory of Fourier series and the Fourier transform in order to understand and appreciate some of these applications. Our main reference will be the book "Fourier Analysis" by Stein and Shakarchi.

Prerequisites: MTH 309 and MTH 320

Spring Semester 2021: MTH 496 Section 1 - Fourier Analysis and Applications

Instructor: Farhan Abedin

Fourier analysis originated from the investigation of vibrating strings and heat flow. The ensuing mathematical theory now has myriad applications in areas like differential equations and signal processing. The goal of this course will be to develop the basic theory of Fourier series and the Fourier transform in order to understand and appreciate some of these applications. Our main reference will be the book "Fourier Analysis" by Stein and Shakarchi.

Prerequisites: MTH 309 and MTH 320

Spring Semester 2021: MTH 496 Section 2 - Introduction to Machine Learning

Instructor: Ekaterina Rapunchik

This course provides a broad introduction to machine learning. Topics include supervised learning ( support vector machines, kernels, neural networks) and unsupervised learning (clustering, dimensionality reduction, etc.). We will also discuss the different tasks of machine learning: classification, regression, clustering, density estimation and dimensionality reduction. During the last part of the course, we will discuss some of the recent approaches to machine learning, including those involving the graphical framework.

Prerequisites: MTH 309 and department approval

Spring Semester 2021: MTH 496 Section 3 - From Archimedes to Donald Knuth - Mathematical Masterpieces

Instructor: Nikolai Ivanov

The goal of the course is to experience the discovery of mathematics by reading the original works of some of the greatest minds throughout history. We will focus on a story starting with a discovery of Archimedes, leading to the Bernoulli numbers, the work of Euler on one of the most important problems of his time, and continued up to this day.

Prerequisites: department approval