Introduction to My Resource Collection

As an academic deeply immersed in the world of mathematics, I often find myself exploring and utilizing a wealth of online educational materials. Over time, I've curated a selection of resources that I believe are particularly valuable for students and fellow researchers alike.

These include lectures and courses by distinguished professors from renowned institutions, covering both foundational and advanced topics. Whether you are delving into combinatorics or seeking clarity in theoretical physics, I hope you find these resources beneficial.

Lectures on Combinatorics

One standout resource is Professor Timothy Gowers's lectures on Combinatorics from the University of Cambridge, Michaelmas 2020. These lectures combine rigor and clarity, making them invaluable for mastering combinatorial techniques.

Watch the full video lecture series here. Access the accompanying lecture notes here.

Lectures on Algebraic Topology

Algebraic Topology studies the deeper structure of topological spaces using algebraic methods. Two excellent lecture series provide thorough insights:

Prof. Siddhartha Gadgil (IISc Bangalore)

A well-structured course covering homotopy, homology, and cohomology, delivered in Fall 2020. Watch the playlist here.

Dr. Pierre Albin (UIUC)

A structured and visual companion to Hatcher’s classic text on Algebraic Topology. Watch the lectures here.

Geometric Anatomy of Theoretical Physics

Dr. Frederic P. Schuller's landmark lecture series builds up from basic logic to advanced topics in geometry, bridging mathematics and physics in a unified pedagogical flow.

These lectures cover foundational mathematical tools for physics, from bundle theory to mechanics and relativity. Watch the full playlist here.