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 2019: MTH 496 Section 1 - Machine Learning

Instructor: Duc Nguyen

This is an introductory course to Machine Learning (ML). ML is a powerful technique widely used in many big data areas such as insurance, economics, bioinformatics, medicine, face recognition etc. In this course, we will not only discuss theoretical framework of ML algorithms and architectures, but also put an emphasis on programing skills so that each student is able to implement ML algorithms for real-world problems. The tentative topics will cover linear regression, logistic regressions, decision trees, SVM and KNN. If time allows, more advanced methodologies such as random forests, gradient boosting trees and deep neural networks will be discussed.

Prerequisites: Approval of the department; though helpful courses will be CSE 231, MTH 235 or MTH340, STT 441 and STT 442.

Fall Semester 2019: 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

Fall Semester 2019: MTH 496 Section 3 - Grid Homology for Knots and Links

Instructor: Matt Hedden

In recent years significant advances have been made in the mathematical theory of knots using a collection of newly discovered techniques called "link homology theories". These techniques assign algebraic invariants, known as homology groups, to knots and links. They have led to new insights in knot and link theory, and have proved long-standing conjectures. This course will begin with an introduction to the mathematical theory of knots, a subfield of topology, and then move on to study some of these recently discovered homology theories.

Prerequisites: MTH 411 or concurrently

Spring Semester 2020: MTH 496 Section 1 - Machine Learning

Instructor: Duc Nguyen

This is an introductory course to Machine Learning (ML). ML is a powerful technique widely used in many big data areas such as insurance, economics, bioinformatics, medicine, face recognition etc. In this course, we will not only discuss theoretical framework of ML algorithms and architectures, but also put an emphasis on programing skills so that each student is able to implement ML algorithms for real-world problems. The tentative topics will cover linear regression, logistic regressions, decision trees, SVM and KNN. If time allows, more advanced methodologies such as random forests, gradient boosting trees and deep neural networks will be discussed.

Prerequisites: Approval of the department; though helpful courses will be CSE 231, MTH 235 or MTH 340, STT 441 and STT 442.

Spring 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