Topological Data Analysis

Program Overview

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The program combines theoretical knowledge with practical applications, allowing participants to confidently utilize TDA methods in their chosen fields. Graduates are well-positioned for careers in data analysis, data engineering, data science, artificial intelligence, machine learning, and scientific research.

Program Outline

This program caters to professionals seeking to advance their careers in various fields, including technology, finance, insurance, and scientific research.

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Objectives:

• To provide participants with a strong foundation in the mathematical principles of TDA.
• To equip participants with the ability to select and apply appropriate TDA software tools for specific projects.
• To offer participants hands-on experience in applying TDA methods to real-world data analysis problems.
• To prepare participants for careers utilizing TDA in artificial intelligence, machine learning, and statistical analysis.

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Program Description:

The TDA CGS program combines theoretical knowledge with practical applications, allowing participants to confidently utilize TDA methods in their chosen fields. The program features a comprehensive curriculum covering topics such as:

• Graph theory: Introduces the fundamentals of graph structures and their applications in TDA.
• Homological algebra: Explores the abstract algebraic structures underlying TDA methods.
• Persistent homology: Introduces the core tool of TDA, enabling the analysis of topological features across different scales of data.
• Discrete Morse theory: Provides the theoretical framework for implementing persistent homology in large-scale data analysis.
• The Mapper algorithm: Covers a powerful tool for feature selection and generation in machine learning and deep learning applications.
The program can be completed as a standalone credential or can be used to gain elective credits towards the Master's program in Data Science. The program covers the following key areas:
• Mathematical foundations: This includes topics such as linear algebra, graph theory, and homological algebra, providing a solid understanding of the underlying mathematical concepts.
• Persistent homology: This core tool of TDA allows for the analysis of topological features in data across different scales.
• Discrete Morse theory: This theoretical framework provides the foundation for implementing persistent homology in large-scale data analysis.
• The Mapper algorithm: This powerful tool is used for feature selection and generation in machine learning and deep learning applications.
• Applications of TDA: The program explores the use of TDA in various fields, including technology, finance, insurance, and scientific research.

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Program Structure:

The TDA CGS program consists of three required courses:

• Linear Algebra for Applications
• Topological Data Analysis II
These courses provide a comprehensive understanding of the theoretical foundations and practical applications of TDA.

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Course Schedule:

The TDA CGS program is offered online, allowing participants to study at their own pace. It also covers the implementation of persistent homology in software tools.

• Topological Data Analysis II: This module explores advanced topics in TDA, including multi-scale analysis, topological simplification, and applications of TDA in machine learning and deep learning.

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Assessment:

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Assessment methods:

The TDA CGS program utilizes various assessment methods to evaluate student learning, including:

• Homework assignments: Regular homework assignments provide opportunities for students to practice their understanding and application of TDA concepts.
• Exams: Midterm and final exams assess students' understanding of the theoretical foundations and practical applications of TDA.
• Project work: Students engage in individual or group projects that require them to apply TDA methods to real-world data analysis problems.

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Assessment criteria:

The assessment criteria for the TDA CGS program are based on the learning objectives of the program. These criteria include:

• Understanding of the theoretical foundations of TDA: Students should demonstrate a clear understanding of the mathematical concepts underlying TDA.
• Ability to apply TDA methods to real-world data: Students should be able to select and implement appropriate TDA methods for specific data analysis problems.
• Effective communication of results: Students should be able to effectively communicate their findings and insights from TDA analysis.

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Teaching:

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Teaching methods:

The TDA CGS program utilizes a variety of teaching methods, including:

• Lectures: Online lectures provide students with a comprehensive overview of the theoretical foundations and practical applications of TDA.
• Discussions: Online discussions allow students to engage with their peers and instructors, ask questions, and clarify concepts.
• Hands-on exercises: Students engage in hands-on exercises to gain practical experience in applying TDA methods to real-world data.
• Emphasis on real-world applications: The program emphasizes the use of TDA in various fields, providing students with practical skills that are relevant to their chosen careers.
• Online delivery: The online format allows students to study at their own pace and from anywhere in the world.
• Use of cutting-edge software: The program utilizes state-of-the-art TDA software tools, providing students with hands-on experience with the latest technologies.

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Careers:

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Potential career paths:

The TDA CGS program prepares graduates for a variety of career paths in fields such as:

• Data analysis
• Data engineering
• Data science
• Artificial intelligence
• Machine learning
• Scientific research
• Actuarial science
• Finance
• Insurance

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Career opportunities:

Graduates of the TDA CGS program are well-positioned for various career opportunities, including:

• Data analyst
• Data engineer
• Data research analyst
• Machine learning engineer
• Artificial intelligence specialist
• Research scientist
• Actuary
• Financial analyst
• Insurance analyst

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Career outcomes:

The TDA CGS program prepares graduates for successful careers in data-driven fields.

• The TDA CGS program is designated as a STEM program, making international students eligible for up to 12 months of Optional Practical Training (OPT) after graduation.
• The program is also eligible for the F-1 STEM OPT work authorization extension, allowing eligible students to extend their OPT for an additional 24 months.