Registration Deadline: January 20th, 2025

Instructor: Professor Anibal Medina-Mardones, Western University

Course Dates: January 7th - April 3rd, 2025
Mid-Semester Break: February 17th - 21st, 2025
Lecture Times: Tuesdays, 11:30 AM - 1:30 PM (ET) | Thursdays, 10:30 AM - 11:30 AM (ET)
Office Hours: Thursdays, 11:30 AM - 12:30 PM (ET)

Registration Fee: PSU Students - Free | Other Students - CAD$500

Capacity Limit: N/A

Format: Fully remote via Zoom

Course Description

This course offers an in-depth introduction to the dynamic field of Topological Data Analysis (TDA), a discipline that melds concepts from topology, data science, and machine learning.

Course Objectives:
In this course, students will:

1. Understand the Foundations: Grasp the fundamental principles of topology that underpin TDA, including simplicial complexes, persistent homology, and hyperharmonic analysis.
2. Explore Data Analysis Techniques: Learn how to apply topological methods to analyze and interpret complex, high-dimensional data. This includes studying various algorithms and tools used in TDA.
3. Develop Computational Skills: Gain hands-on experience with software and libraries (such as giotto-TDA and GUDHI) that are commonly used for topological data analysis.
4. Interdisciplinary Applications: Understand the application of TDA in diverse fields such as biology, sensor networks, and image analysis, illustrating the versatility and power of topological methods in solving real-world problems.
5. Research and Collaboration: Engage in research-oriented tasks and collaborative projects that encourage the practical application of TDA concepts and techniques.

Course Structure:
This course is structured to facilitate a deep understanding of both the theoretical and practical aspects of TDA. It will include:

1. Lectures: Introducing key concepts and theories.
2. Seminars: Featuring guest speakers and discussions on current TDA research and applications.
3. Practical Sessions: Hands-on labs for implementing TDA techniques on real datasets.
4. Project Work: Opportunities to work on individual or group projects, fostering research and collaboration skills.

Prerequisites: No specific prerequisites are required beyond enrollment in a Master’s or Ph.D. program in Mathematics. However, a basic understanding of programming would be beneficial.

Who Should Enroll: This course is ideal for graduate students in mathematics who are interested in the intersection of topology and data science, and who are keen on exploring new, innovative methods to study complex data. Whether they aim to apply their skills in academia or industry, this course will provide a solid foundation in one of the most exciting frontiers of modern mathematics.