Teaching Undergraduate Topology

"Advanced Kindergarten" - An Inquiry-Based First Course in Topology // Using Oral Assessment in Undergraduate Topology

1) This talk gives an overview of the introductory topology course that I taught last spring at Kenyon College, with focus on the inquiry-based and collaborative approach to course structure.

2) In the second talk I focus specifically on the use of an oral exam format as a component of the cumulative course final, including details of how the assessment was presented to the students, the prompts used, how it was graded, and some pros and cons of this approach.

Teaching topology without a course

The math departments at many small colleges and universities do not offer a topology course but may want to find other means to include topology in the curriculum to help expose their students to it and prepare them for graduate school. In the first talk, we discuss five such strategies: topology talks in an undergraduate colloquium, mini-units in other courses, independent study, 1-credit classes, and undergraduate research. In the second talk we look particularly at teaching 1-credit special topics courses, arguing that this is a great way to supplement the primary math curriculum and detailing how one can design such a course. The presenter draws upon his experience from teaching such a 1-credit knot theory course and incorporating it into his mentoring of undergraduate research.

An Overview of an Introduction to Applied Algebraic Topology Course

This talk provides an overview for an introduction to applied algebraic topology course in the Department of Mathematics at The Ohio State University. In particular, I discuss the course's history, its positioning within the department, its prerequisites, and a road map of the topics covered in Talk 1. In talk 2 I focus on three components from when I taught the course in the Spring of 2021: Guest Speakers, Project Based Exams, and Weekly Online Discussion Boards.

Interdisciplinary Topology at a Liberal Arts College

We will examine how to craft a topology course that fits in a liberal arts curriculum with a strong applied math and data analytics focus. In the first talk, we will discuss how the mathematics curriculum and student interests have helped shape the topology course taught at Furman University. In the second talk, we will analyze how to inject interdisciplinary topics, such as geographic information systems, into a point-set topology course. 

Broader topology

Introductory topology courses often focus on point set topology, obscuring the variety of places where topology can crop up and how much geometry and algebra can be relevant in current research. I will describe a course that took place at Brandeis University in the fall semester of 2015, where the first half of the course covered the core topics of point set topology (basic definitions to compactness), while the latter half covered special topics voted on by the students (e.g. dynamical systems and game theory). 

The course syllabus and course evaluations are available at: http://people.mpim-bonn.mpg.de/aruray/documents/teaching/f15_104a_syllabus.pdf and http://people.mpim-bonn.mpg.de/aruray/documents/teaching/f15_104a_evaluation.pdf