Recommended Readings
The following list contains books whose tone and language I personally liked. They may not suit everyone, so I recommend giving a few of them a read to find the ones you can follow easily. Every author writes from their own perspective, and needs vary from reader to reader—so be selective when choosing your textbooks.
How to Think Like a Mathematician
How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
This book is great for anyone being introduced to rigorous mathematics for the first time. It ignites curiosity, explains why math is important, and shows how to express thoughts mathematically. I strongly suggest reading at least the first chapter.
Logic
Mathematical Proofs: A Transition to Advanced Mathematics
I loved the simplicity of the language here—it felt as if someone were sitting beside me and explaining the concepts directly.
Analysis
Principles of Mathematical Analysis (often called Baby Rudin)
This is my personal favorite because of its clear and precise language.
People also frequently recommend Terence Tao’s analysis books:
Linear Algebra
Linear Algebra and Its Applications by Gilbert Strang
This is the main linear algebra textbook I have worked through.
Gilbert Strang’s full lecture series is available on YouTube:
Calculus
Thomas’ Calculus
A solid resource with a large collection of exercises.
Alternatively, you can pick up any standard economics mathematics textbook, such as:
- Mathematics for Economists by Simon & Blume
Note: I strongly recommend reading How to Think Like a Mathematician first. It will give you a better idea of how to select textbooks and navigate between topics effectively.
You can also find a broader curated list here: Awesome Math Series