Math books like Infite Powers or Calculus Made Easy but for other topics? I recently read the above because I wanted to refresh my calculus skills and they were exactly the level and depth for a busy software engineer. Do you have other examples of foundational math books that are readable for the interested layman, e.g. for linear algebra? |
What do you mean by "foundational"?
I love Calculus Made Easy, but in my opinion the reason it's so good is that it doesn't try to be foundational. It relies on quick and dirty tricks -- especially, treating dy/dx as a fraction when it can't be formally defined as such, but where doing so makes the subject much more intuitive and easy. It's not really a good foundation for further study, you need something that doesn't cut corners for that, but it's fantastic for what it is!
My favorite foundational book is Linear Algebra by Jim Hefferon:
https://hefferon.net/linearalgebra/
It is free, and I've seen the author on HN occasionally. It's foundational in the sense that it builds up the subject brick by brick, assuming the minimum realistic prerequisites needed, and it does an outstanding job of this.
But it's a slow read, essentially by design. If you want something quicker, you might try Interactive Linear Algebra by Margalit and Rabinoff:
https://textbooks.math.gatech.edu/ila/
Again free, with lots of widgets to play with.
Some other textbooks I really like:
Epp's Discrete Mathematics is fantastic. The newest edition is astronomically expensive, so go looking for used copies of previous editions.
Carter's Visual Group Theory is tremendous fun. Once again not foundational per se, but if you want to learn what group theory is all about without slogging through lots of formalities, that's a great choice. I'd say that roughly it's in the spirit of Calculus Made Easy.
Also, if you enjoy poker, check out Dan Harrington's books on the subject. In the course of explaining hold'em strategy, they will teach you lots about probability, counting, expected value, and game theory in an applied setting. They're fantastically written.
Easiest to start will be either Linear Algebra done right by Axler or Linear algebra done wrong by Treil - try both, they take very different approaches to introducing the subject, so one of them may be compatible with you.
After finishing either of these I heartily recommend you Finite-Dimensional Vector Spaces by Halmos - it's way more abstract, so I cannot recommend it as first introduction to LA, but it proves its results in very beautiful and a bit uncommon way. It's probably my favourite book from undergrad.
It’s a free download with additional material at:
Previously submitted: https://news.ycombinator.com/item?id=42999258
I interviewed Ivan and he shared five of his fav books on the subject.
Problems in it are a bit tough to chew through though.