Quantum Formalism (QF) Academy

Bridging Advanced Mathematics & Applications.

Topological Data Analysis with Applications

Learn the mathematical foundations of TDA and its applications to machine learning and quantum computing.

$$\emptyset = K^0 \subset K^1 \subset \cdots \subset K^m = K.$$

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Course Outline

Quantum Formalism Academy presents a course on TDA with Applications to Machine Learning. This course bridges advanced mathematical theory with practical applications in modern computing. The course now begins on June 27th, with limited spots available to ensure a small, focused cohort.

Topics Highlight:

  • Introduction to TDA:Motivation, basic topology concepts, simplicial complexes.
  • Simplicial Homology: Chains, cycles, homology groups, and computational tools.
  • Persistent Homology:Stability, filtrations, and persistence modules.
  • Computing Persistent Homology: Algorithms, persistence diagrams, and visualization techniques.
  • Topological Features in Data Analysis:Mapper algorithm, Reeb graphs, and topological signatures.
  • Statistical TDA:Statistical methods, kernel techniques, and hypothesis testing in persistence diagrams.
  • TDA in Machine Learning: Integration with ML models, topological neural networks, and graph-based learning.
  • TDA in Quantum Computing: topological approaches in quantum computing (e.g., topological quantum error correction, quantum state space analysis).
  • Advanced Topics:Multiparameter persistence, persistent cohomology, and category-theoretic approaches.

What This Course Offers:

  • Self-paced video lectures.
  • Quizzes to test your knowledge.
  • In-depth coverage of both theoretical and practical aspects of TDA.
  • Interactive Jupyter notebooks with visualizations.
  • Live office hour sessions with the instructor for clarifications and tutorials.
  • Project-based certification upon completion.

Who Should Take It?

  • Researchers and engineers in Machine Learning, and related fields.
  • Students and professionals eager to learn advanced mathematics for emerging technologies.

How to sign up (for free)?

You can get free automatic access to the course if sign up to one of the following plans:

Professional Plan OR Researcher Plan

How to sign up with a one off deal?

You can sign up without subscribing to our plans:

Early-bird for just $260

About Dr. Brian Hepler (Course Instructor)

Brian Hepler's Photo

Brian Hepler holds a Ph.D. in Mathematics and has over 12 years of experience in abstract modeling, relational structures, and algorithm design. His research spans singularity theory, algebraic geometry, and algebraic analysis.

Formerly a postdoctoral researcher at IMJ-PRG (Sorbonne Université) and a Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison, he brings deep expertise and a passion for making advanced mathematics accessible.

Where do our learners come from?

Meta G o o g l e NASA OpenAI