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.
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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)