Mathematics: From The Birth of Numbers—picked it out at a Barnes&Noble when I was a kid. It had so much in it. It didn’t go into depth but it had fantastic breadth. Reportedly the author spent ten years writing it. Feels like having a world atlas, but of mathematics.
The Art of Computer Programming—NOT for the reason you expect. The series is simultaneously fantastic and terrible. Being able to articulate why the series just plain sucks even though it’s also really good at the same time. 90% of the time, if there’s something I want to look up in TAOCP, I can just go for a walk, realize whatever I’m trying to do is unnecessary work, and come back and work on actual important stuff I care about. The other 10% of the time, I get better answers from digging through the citations on Wikipedia.
Exercises for the Feynman Lectures on Physics—Yes, the exercise book, not the lecture book. I know it’s not CS or math. The way that the problems build on each other is spellbinding. For example, there’s an early problem where you calculate the mean free path of air, but you’re not given a formula for it—you’re just given a series of problems which provoke you to think about the subject in a way that you can figure out a formula for it yourself.
I discovered Mathematics: From the Birth of Numbers in the summer of 2003 at my local library. At the time I was a high school student taking a summer Algebra 2 class in order to be able to take calculus my senior year for college admissions purposes. This book instilled in me a love for mathematics, even if I sometimes struggled with the topic.
Just a few hours ago my copy of Mathematics: Its Content, Methods and Meaning just arrived; I bought this book as a reference of undergraduate-level math concepts based on Hacker News recommendations since I'm right now in the process of reviewing undergraduate-level math to strengthen my understanding of deep learning fundamentals. I had the opportunity to glance through this book, and I wish I had discovered this book when I was in high school or during my undergraduate years; it appears to be an excellent, more technical companion to Mathematics: From the Birth of Numbers.
Given the direction in my career (I went from focusing on systems software to deep learning and data mining), I wish I had majored in mathematics as an undergraduate instead of computer science. I'm able to pick up computer science concepts rather quickly, but mathematics requires more effort for me. A part of me almost wants to do an online second bachelor's in math, but right now I use some of my spare time studying math.
They are extracted from my books, but can be used to support learning from any other book too. I find it helps a lot to think about the connections and parallels between concepts, and also use the concept maps as a "spec" to know when you've covered all the material.
The Art of Computer Programming—NOT for the reason you expect. The series is simultaneously fantastic and terrible. Being able to articulate why the series just plain sucks even though it’s also really good at the same time. 90% of the time, if there’s something I want to look up in TAOCP, I can just go for a walk, realize whatever I’m trying to do is unnecessary work, and come back and work on actual important stuff I care about. The other 10% of the time, I get better answers from digging through the citations on Wikipedia.
Exercises for the Feynman Lectures on Physics—Yes, the exercise book, not the lecture book. I know it’s not CS or math. The way that the problems build on each other is spellbinding. For example, there’s an early problem where you calculate the mean free path of air, but you’re not given a formula for it—you’re just given a series of problems which provoke you to think about the subject in a way that you can figure out a formula for it yourself.