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 Note: Email notification will be given once your override has been issued.

Spring Semester 2017: MTH 496 - An elementary Introduction to Knot Theory

An elementary Introduction to Knot Theory Description: This course will be an elementary introduction to the mathematical theory of knots with emphasis in some developments that occurred in the last 30 years. We will describe the different classifcations of knots, their properties, various ways for measuring their complexity and some applications of knot theory to biology and physics. Since some open problems in this area can be explained at an elementary level, students will also have the opportunity to get a taste of what it is like to do research in mathematics. We expect to cover material from the first eight chapters of the textbook.

Spring Semester 2017: MTH 496 Section 3 - Capstone for Actuarial Majors

Introduction to Corporate Finance and Accounting, GAAP Financial Statements, Insurer Statutory Accounting, Cash Flow Valuation, Bonds and Stocks, Insurer Investment Portfolio Management, Insurer Capital Needs and Sources, Capital Management, Mergers and Acquisitions, and The Underwriting Cycle.

Fall Semester 2017: MTH 496 Section 2 - Capstone for Actuarial Majors

Introduction to Risk Management, Risk Assessment, Risk Financing, and Enterprise Risk Management. An Overview of Insurance Operations, Insurance Regulation, Insurance Marketing and Distribution, the Underwriting Function, Underwriting Property and Liability Insurance, The Claim Function, Adjusting Property and Liability Claims, Actuarial Operations, and Reinsurance.

Fall Semester 2017: MTH 496 Knot theory, and low dimensional manifolds

Instructor: S Akbulut

We will discuss knots in 3-space, show how to use them to build and visualize low dimensional manifolds. Recommended books "Knot theory" by C. Livingston, The Carus Math. Monoghraphs (MAA) ISBN 0-88385-027-3; and "4-manifolds" by S. Akbulut, Oxford University Press, ISBN-13: 978-0198784869.

Spring Semester 2018: MTH 496 Section 1 - Machine Learning

Instructor: E Merkurjev

Almost everyone encounters email spam on a daily basis. Some email engines, like Gmail, run an algorithm that automatically classifies email as “spam” or “not spam”. This is a classification problem, one of main applications of machine learning, that occurs in other numerous applications, such as medical or genomics data, face recognition, financial predictions and text mining. This course will focus on optimization techniques for the classification application of machine learning. We will give examples of fast algorithms to classify images, hyper spectral data, 3D point clouds, text, etc. The major concepts of machine learning will also be covered. We will distinguish supervised learning, unsupervised learning and reinforcement learning. In addition to classification, we will discuss the following applications of machine learning: clustering, density estimation, dimensionality reduction and regression.

Spring Semester 2018: MTH 496 Section 2 - Mathematics Masterpieces

Instructor: N Ivanov

Experience the discovery of mathematics by reading original works of some of the greatest minds throughout history. This is writing course and will involve homework problems requiring extensive written out solutions. Additionally, there will be group projects administered under the guidance of the instructor. Textbook: Knoebel, Laubenbacher, Lodder, Pengelley, Mathematical Masterpieces. Further Chronicles by the Explorers, Springer-Verlag, 2007.