Published On Dec 24, 2021
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 ( • Real Analysis: Lectures by Professor ... )
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
( • Linear Algebra Done Right )
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat3...)
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 ( • Playlist )
GROUP THEORY
Book: “Topics in Algebra” by Herstein (Chapter 2)
Videos: Lectures by Benedict Gross ( • Abstract Algebra )
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/...)
Videos: Lectures by Pierre Albin ( • Algebraic Topology: a beginner's cour... )
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)