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To self-study pure math, there are various resources available, such as books and videos. The video titled "How to self study pure math - a step-by-step guide" provides a collection of resources for self-studying pure math. The video covers different topics that one might encounter while studying pure math, including linear algebra, real analysis, point set topology, complex analysis, group theory, Galois theory, algebraic topology, and differential geometry.

For linear algebra, the recommended book is "Linear Algebra Done Right" by Sheldon Axler. The book introduces the concept of linear maps and provides concrete examples, making it suitable for self-study. It also includes plenty of exercises for practice.

For real analysis, the recommended book is "Understanding Analysis" by Stephen Abbott. The book covers topics such as real numbers, sequences and series, limits, derivatives, and integrals from a proofs perspective. The book is comprehensive and includes a YouTube playlist by Francis Su that explains concepts from the book.

For point set topology, online notes from the University of Toronto are recommended. These notes provide explanations, examples, and a list of problems for each concept, making them suitable for self-study. The notes are freely available on the internet.

For complex analysis, the video suggests the book "Visual Complex Functions: An Introduction with Phase Portraits" for an introduction to the topic. The book uses color and phase plots to illustrate complex analysis concepts. Another book recommended is "Complex Analysis" by Serge Lang, which provides a geometric intuition for the subject and includes numerous pictures.

For group theory, lectures by Professor Benedict Gross are highly recommended for their clarity and engaging explanations. Another recommended book is "Topics in Algebra" by Herstein. The book covers basic definitions, subgroups, quotients, theorems of group theory, and includes a large list of exercises.

For Galois theory, there is a video on the channel that gives an introduction to the subject. For more in-depth explanations, notes by Professor Tom Leinster are suggested. These notes are freely available on the internet, provide understandable explanations, and include exercises and examples.

For differential geometry, the book "Introduction to Differentiable Manifolds and Riemannian Geometry" is recommended. The book is rigorous and includes discussions, exercises, and examples. Additionally, the video creator has a video on differential geometry topics available for more detailed explanations.

For algebraic topology, the book "Algebraic Topology" by Allen Hatcher is highly recommended. The book covers homotopy, homology, and co-homology, which are the main pillars of the subject. Lectures by Professor Pierre Albin that closely follow the book are available on YouTube.

These recommendations are provided based on the information in the video transcript at the respective timestamps 1.