Master Pure Math on Your Own: Step-by-Step Self-Study Guide 📚

This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish. --- REAL ANALYSIS Book: “Understanding Analysis” by Stephen Abbott. Videos: Lectures by Francis Su (https://www.youtube.com/playlist?list=PL0E754696F72137EC) LINEAR ALGEBRA Book: “Linear Algebra Done Right” by Sheldon Axler Videos: Sheldon Axler’s Playlist (https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw) POINT SET TOPOLOGY Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat327/?resources) COMPLEX ANALYSIS Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert More Technical Book: “Complex Analysis” by Serge Lang Videos: Wesleyan University Playlist (https://www.youtube.com/playlist?list=PL_onPhFCkVQjdQTbG0eQk42eH0RaBoYJf) GROUP THEORY Book: “Topics in Algebra” by Herstein (Chapter 2) Videos: Lectures by Benedict Gross (https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5) GALOIS THEORY Notes by Tom Leinster: https://www.maths.ed.ac.uk/~tl/gt/gt.pdf DIFFERENTIAL GEOMETRY Book: Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby ALGEBRAIC TOPOLOGY Book: Algebraic Topology by Allen Hatcher (available for free on his website: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html) Videos: Lectures by Pierre Albin (https://www.youtube.com/playlist?list=PL41FDABC6AA085E78) Intro: (0:00) Linear Algebra: (0:36) Real Analysis: (2:20) Point Set Topology: (3:19) Complex Analysis: (4:09) Group Theory: (5:46) Galois Theory: (6:54) Differential Geometry: (7:23) Algebraic Topology: (8:44)