I found this video particularly interesting and useful to me even though I am not a “pure math” person in the slightest. I am peering into a community for which I just barely qualify as educated in, but my enjoyment of the subject matter remains the same.
More importantly, I found some resources from this video to be quite useful for my field of study. I will not be using all the mentioned fields in the video, but Linear Algebra is one of the most vital concepts for machine learning and neuroscience alike. Practically everything seems to be represented by vectors, and this knowledge becomes all the more useful when dabbling in dynamical systems theory(very important in Computational Neuroscience, although more differential equations than linear algebra).
Beyond this, I am also someone who takes self-study to the extreme. For whatever reasons, I am rather poor in my ability to retain information when it is forced upon me through a class. I find that I excel in these same fields that I have classes for, but only when I seek that knowledge out on my own time. This will become more useful in graduate school, but has hindered my performance in many ways for my undergrad.
Resources from Video Description
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)