How to self study pure math - a complete guide
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Published at : 27 Dec 2021
Published at : 27 Dec 2021
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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)
---
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)
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