Reading
Books and articles I recommend.
Books
Currently Reading
- Categories for the Working Mathematician
Review
The seminal work on category theory! Have read the first few chapters so far, and Mac Lane has, in my opinion, given enough motivation for the “abstract nonsense” that is category theory.
Read
- Linear Algebra Done Right, 4th ed
Review
Absolute fucking banger of a book, probably the best book in proof-based linear algebra. The exposition is as clean, satisfying, and engaging as f***. The exercises are also very well made, will make you spend hours doing them but they’re worth doing (I have a complete set of complementary notes as well as solutions to most exercises in my github, ill publish them sometime in the future).
- Algebra: Chapter 0
Review
A modern view of algebra from a categorical lens. Not nearly as dry as Dummit and Foote’s exposition. If I had to start over, I’d probably start with this book.
- How to Prove It: A Structured Approach
Review
Highly suggest for those who are getting into proof based mathematics. I started with this and you should too. There are many engaging exercises.
- Topology
Review
Blitzed through the core chapters (1-3, 9, 10, 13) within two months, was an enjoyable introduction to topology. It really did make undergraduate real analysis make sense!
- Computational Complexity: A Modern Approach (1st Edition)
Review
This was my first book in complexity theory. Lowk it was a little tough to get started on as a complete noob, but through enough head slamming, I kinda got the gist of it all. Very much worth reading and coming back to in the future. Overall, reads more like a reference book outside of the first two chapters. Probably not the best for those new to the field (learnt that the hard way).
- Introduction to Quantum Mechanics (3rd Edition)
Review
Very engaging exposition of quantum mechanics; its not nearly as boring or hard as popular media makes it out to be! The exercises are extensive, you don’t need to do all of them, a few for each chapter is sufficient. My main gripe is the lack of mathematical rigor, though tbf its a textbook for physicists!
- Abstract Algebra
Review
Very boring, very dry, but very thorough. I used this one as my primary material for both my undergraduate and graduate algebra courses. It is more than enough for most math undergraduates. The exercises are tough and the content is dense but you’ll learn all you need to know about groups, rings, and fields without all the categorical nonsense.
- Elementary Analysis
Review
My first introduction to real analysis. Very easy to get into, highly suggest trying this as an entry point if you’re just starting analysis. I don’t get why people dislike it; I think it’s a sufficient introduction to the topic.
- Introduction to Smooth Manifolds
Review
He yaps too much, though is very thorough in exposition. There are enough exercises and problems to keep you occupied for an entire year. Main gripe is how poorly exposited Sard’s Theorem is in this book.
- Differential Topology
Review
It’s a rather brief exposition on differential topology, treating all manifolds as just subsets of Euclidean space. I do appreciate their exposition of Sard’s theorem though.
- Algebra
Review
Absolutely horrible book, written in an era gone past. Though it has its merits as the holy reference book of algebra, it has the worst possible exposition out of any textbook I’ve ever read — only one to be in the same league is Spivak’s Calculus on Manifolds! A better title for this book would be Introduction to Algebra, but for Those who Already Know It. Use as a reference book — do NOT try to learn from this book. (I am aware it’s a graduate book and you should probably come into it already knowing algebra, don’t hate me).
- Calculus on Manifolds
Review
Worst fucking book ever written. Too terse to learn from as an introduction; this is better suited as a set of companion notes to a class on manifold calculus/diff top.
Want to Read
- Analysis Now
- Commutative Algebra: With a View Toward Algebraic Geometry
- A Comprehensive Introduction to Differential Geometry, Vol I–V
Review
Will read when I have the time, heard it’s good though.
- Real Analysis: Modern Techniques and Their Applications (2nd Edition)
- Real Mathematical Analysis