Applied Math
The Map of Mathematics - https://youtu.be/OmJ-4B-mS-Y
- Pure Mathmatics *
This video has a list of books, videos, and exercises that goes through the undergraduate pure mathematics curriculum from start to finish. ---
LINKS:
Watch this for a flavor of what pure mathematics is like: (Fredrich Schuller’s Lectures on Differential Geometry and Topology) https://www.youtube.com/watch?v=7G4Sq....
I watched these when I was a high-schooler, curious about what pure math was. Even though I understood very little, they fascinated me beyond measure!
REAL ANALYSIS
Open letter: http://assets.press.princeton.edu/cha... Book: “Understanding Analysis” by Stephen Abbott. Videos: MAT137 Playlist (https://www.youtube.com/channel/UCLzp...)
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler Problems: “Linear Algebra” by Insel, Freidberg, and Spence Videos: Sheldon Axler’s Playlist (https://www.youtube.com/playlist?list...)
TOPOLOGY
Book: “Topology through Inquiry” by Su and Starbird Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat3...) Videos: Point Set Topology Playlist (https://www.youtube.com/playlist?list...) and Algebraic Topology Playlist (https://www.youtube.com/playlist?list...)
DIFFERENTIAL EQUATIONS
Book: “Differential Equations with Boundary Value Problems” by Zill and Cullen
I recommend focusing on these sections: Chapter 1 (Introduction!) Chapter 4.1 (Preliminary Theory of Linear Equations) Chapter 4.3 (Homogeneous Linear Equations with Constant Coefficients) Chapter 7 (Laplace Transform) Chapter 8 (Systems of Linear Differential Equations) Chapter 9 (Numerical Methods) Chapters 11, 12, 13 (Fourier Series and Partial Differential Equations)
COMPLEX ANALYSIS
Books: “Visual Complex Analysis” by Tristan Needham Videos: Wesleyan University Playlist (https://www.youtube.com/playlist?list...)
EDIT: In hindsight, I think the best book to learn complex analysis is "A Friendly Approach to Complex Analysis" by Sara Maad and Amol Sasane. It's really friendly (as the title suggests!) and has tons of practice problems with solutions. I found this book a lot easier to go through than Needham's book.
ABSTRACT ALGEBRA
Book: “Contemporary Abstract Algebra” by Gallian Videos: Socratica Abstract Algebra Playlist (https://www.youtube.com/playlist?list...)
EDIT: For a more in-depth video series, check out these playlists below. They're by far the most comprehensive video series I've found so far.
(Group Theory) https://www.youtube.com/playlist?list... (Ring and Field Theory) https://www.youtube.com/playlist?list...
DIFFERENTIAL GEOMETRY
Book for Intuition: “A Geometric Approach to Differential Forms” by David Bachman Book for Rigor: “Introduction to Manifolds” by Loring Tu Videos: WhyBMaths (https://www.youtube.com/watch?v=RW5lJ...)
Proof centric START to FINISH https://youtu.be/pTnEG_WGd2Q
