Book of Proof

Category: Mathematics
Author: Richard H. Hammack
This Year Hacker News 2
This Month Hacker News 1


by Kagerjay   2018-05-19
Math is something that needs to be learned by rigorous practice

I find it helpful to first learn the theory via 3blue1brown

It goes into how to actually write mathmatical proofs / discrete math which I believe is extremely important to any math branches and computer-science in general.

I was lucky to have a great foundational math background in highschool, my calc 1/2 teacher was considered one of the best in my state. I practiced at least 30 problems every night in that class for 2 years

by dmix   2017-08-19
Reminds me of the MIT SICP lecture videos from the 80s. The concepts of black box abstraction and the simplicity of using LISP like lego building blocks blew my mind and made me switch from being a UX designer dabbling in Rails to a full blown programmer.

It was still entirely relevant to today even though it was a few decades old as the fundamentals of computer science are still fundamental.

by dmix   2017-08-19
A good entry point are one of these books which start from the very beginning of math in Egypt/Greece and teach the fundamentals of math through a narrative as humans discovered the various parts:

"Mathematics for the Nonmathematician"


"Mathematics for the Million"

Of the two I prefered Kline's book but they are both good, albeit a bit heavy on geometery as that was a big focus of early math research.

Another great starting point is "Book of Proofs" and "Introduction to Mathematical Reasoning" to give you a deeper sense of how to approach the subject.

From there I went down this path (the order of which is up to you, each has tons of good source material):

-> Proofs/Logic

-> Algebra

-> Linear Algebra

-> Calculus

-> Abstract Algebra

-> Set Theory

-> Group Theory

-> Category Theory

-> Statistics/Probability

-> Discrete Mathematics

I never did well with learning math in a classroom but I've grown to love math through this process. There are lots of applications in programming as well. It makes approaching the deeper parts of Haskell/FP, data science, and machine learning much more accessible. I particularly liked the higher level Abstract Algebra stuff over the more grinding equations of calculus/linear algebra as it was more similar to programming.