Visual Complex Analysis

Loved that book ! Got me inspired to do this visualisation after reading it https://www.youtube.com/watch?v=CMMrEDIFPZY

- Linear Algebra: Gilbert Strang videos + book - Calculus and basics of Analysis: Spivak - Group Theory: Visual Group Theory - Complex Analysis: Visual Complex Analysis - Writing proofs: Proofs: A Long Form Textbook by Jay Cummings - Abstract Algebra: Dummit-Foote book. First few chapters if you like. ___ Pop-Sci: 1. The Joy of X by Steven Strogatz 2. Fermat's Enigma by Simon Singh (All this books except AA are very highly recommended by me)

A more traditional complex analysis textbook that's really good is Stewart and Tall's Complex Analysis. It's not necessarily a great complement to VCA; I used them both in my course and didn't find myself referring to VCA much, but then I had good lectures in my course and really got on with Stewart and Tall. The "standard" book was Churchill and Brown and, uh, I'd say that one is best avoided. It's awful enough that it may be responsible for a number of those courses being so badly taught....

Visual Complex Analysis. Partly because it's a brilliant book and partly because Complex Analysis is often really really badly taught. If you haven't read it, it teaches complex analysis in terms of transformations and pictures rather than solely algebra. It's very clever; Also touches on some concepts in physics and vector calculus. If you like the style 3Blue1Brown uses, he cites VCA as an inspiration for that style.

For mathematics, I would recommend: 1. "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures. 2. Strogatz's "Nonlinear Dynamics and Chaos" -- it's a bit narrow in scope (mostly dynamical systems with a little bit of chaos/fractals thrown in) but very good nonetheless. 3. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis. 4. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it. 5. Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e.g., why d/dx is not self-adjoint (i.e., Hermitian), whereas d^2/dx^2 is. For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated.

Focusing on mathematics, I think about two kinds of foundational books. 1. Historically foundational: books that brought important ideas, introduced a new branch, progressed the maths significantly. You can read them these days, but their content, proofs, language, etc. is not up to date. Examples: Elements by Euclid, Philosophiae Naturalis Principia Mathematica by Newton, Disquisitiones Arithmeticae by Gauss. 2. Modern foundational books: The ones that can be used for studying now. Books that are clearly written, popular, cover their subject well. Examples: Visual Complex Analysis, Spivak’s Calculus, Linear Algebra Done Right, Hardy’s An Introduction to the Theory of Numbers.

Visual Complex Analysis - Needham. A lot of great pictures, exerything is explained (and shown) geometrically. Complex differentiation/integration, non-Euclidean geometry, vector fields etc. Mathematics and its History - Stillwell. Wonderfully written. From the ancients to the 20th century, covers the mathematics (in a lot of detail) and lives of major mathematicians (potted bios). Concrete Mathematics - Knuth et al. Discrete maths, number theory, generating functions, covers most of the maths that pops up continually in programming. All You Wanted To Know About Mathematics But Were Afraid To Ask. Mathematics for Science Students 2 Vols. - Louis Lyons. Pretty basic, but covers all the mathematical basics for physics. (1st year uni level I guess) I learned a lot from this years ago, I still consult it as a reference. It's a pleasure to read. Also, all of Hamming's books.

I'm in a similar position as well - perhaps at just a wee bit higher level (am learning grad-level math by myself). Below is a list of books that I have enjoyed. Some might perhaps be at a slightly higher level than you might need right now though. 1. Analysis - The Elias Stein, Rami Shakarchi Analysis series, Meassure Theory by Terrence Tao, Lebesgue Integration on Euclidean Spaces by Frank Jones, A radical approach to Lebesgue Integration by Bressoud 2. Algebra - Can't do much better than the classic texts by Herstein & Artin here. I know Artin doesn't get much love but after a point, you really begin to appreciate it. 3. Complex Analysis - is there a better math book than Visual Complex Analysis by Needham? 4. Topology - i'm partial to a Dover book on Topology by Theodore Gamelin. I learnt the basics of point-set topology & homotopy form this book. Great exercises. 5. Number Theory - check out the 2 problem books on number theory by Ram Murty. Melvyn Nathanson's book is quite good as well. 6. Combinatorics - Combinatorics of Finite Sets by Ian Anderson. Extremal Combinatorics by Jukna. 7. Graph Theory - Diestel or Bondy/Murty. 8. Galois Theory - Rotman is great.

It's not at all like SICP (I've never met a math book that was similar), but it's a wonderful introduction and I don't see it mentioned in this thread yet: Needham's "Visual Complex Analysis".