Quantum Formalism (QF) Academy

Quantum Formalism Academy presents a crash course on Group Theory, Topology and Manifolds. This course serves as an essential prerequisite for anyone planning to explore advanced topics in Lie Groups with applications to machine learning and quantum computing.

Topics Highlight:

• Introduction to Topology: Fundamental concepts like open and closed sets, continuous functions, compactness, and connectedness.
• Foundations of Smooth Manifolds: Introduce the structure of smooth manifolds, charts, and atlases.
• Tangent Spaces and Smooth Maps: Differential structure of manifolds, tangent spaces, and smooth maps. Derivations and tangent vectors at a point, the tangent space.
• Applications to Lie Groups: Bridge the material from topology and smooth manifolds directly to Lie theory.
• Fundamentals of Group Theory: Group axioms with geometric and algebraic interpretations. Subgroups, cosets, and quotient groups. Homomorphisms and Isomorphisms.
• Group Actions and Representations: Group actions, orbits and stabilizers. Cayley’s theorem and permutation representations. Linear representations of groups.
• Structure Theory and Matrix Groups: Normal subgroups and simple groups. Jordan-Hölder theorem and group decompositions. Special classes of groups (Abelian, nilpotent, solvable).

What This Course Offers:

• Self-paced video lectures.
• Quizzes to test your knowledge.
• Certificate of completion (after completing all the quizzes with a grade of 75% or more).

Who Should Take It?

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

How to sign up?

You can sign up with any of our plans. But if you are an industry professional or researcher, we recommend you the following plans:

Professional Plan OR Researcher Plan