HN Books @HNBooksMonth

Math is something that needs to be learned by rigorous practice

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

https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

I'm currently working through the bookofproof math problems found here

https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...

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

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" https://www.amazon.com/Mathematics-Nonmathematician-Morris-K...

or

"Mathematics for the Million" https://www.amazon.com/Mathematics-Million-Master-Magic-Numb...

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.

https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...

https://www.amazon.com/Introduction-Mathematical-Reasoning-N...

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.

⬐ jnbiche

The author of Book of Proof referenced here also offers a free online Creative Commons-licensed version: http://www.people.vcu.edu/~rhammack/BookOfProof/

But the dead tree version is also very reasonably priced.

⬐ tnecniv

> 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.

Linear Algebra Done Right takes a more abstract approach so there is minimal computational pain.

⬐ dmix

Thanks, I'll check it out the book.

I prefer the more abstract stuff as I can do most of the computation via Sage (which is a great learning tool). Plus there are some amazing scientific calculator apps for Android and iOS these days which let you compose and calculate full complicated equations.

Of course it helps to work out equations to understand them but far too many math books push you towards rote memorization and test prep, meaning lots of exercises with endless equations, which is far from my goal here.

I'd say there is a market here for a math book/video series combined with Sage for teaching programmers and data scientists math. But there are so many math books already I'm afraid it would get lost in the noise.

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.

https://www.youtube.com/watch?v=2Op3QLzMgSY&list=PL8FE88AA54...

Hearing that intro music still brings a smile to my face.

I just happen to be relearning math right now as I dive deeper into data science and this is perfect timing. Going to watch this series once I get through my math proofs book ("Book of Proof" by Richard Hammack which I recommend to people getting into math https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...).

⬐ theoh

The Book of Proof is freely available online: http://www.people.vcu.edu/~rhammack/BookOfProof/

This stuff is usually rolled into courses called "abstract algebra". If a textbook is called "abstract algebra", it's usually designed for a first year undergraduate. If it's just called "algebra", it's usually aimed at a more mature audience. Herstein and Hungerford are the texts I learned from. This book seems more recent and popular:

http://www.amazon.com/Book-Proof-Richard-Hammack/dp/09894721...

The other big stream of basic undergraduate mathematics is analysis. For that I recommend Spivak's Calculus.

Keeping with the free theme, Book Of Proof by Richard Hammack is a nice introduction to proofs and formalism. It's available free from the author as a PDF[1], and also as a physical book on Amazon[2].

An alternative if you're willing to spend a little is How to Prove It by Daniel J. Velleman, also available from Amazon[3] and probably many other retailers. Both books cover roughly the same topics.

[1]: http://www.people.vcu.edu/~rhammack/BookOfProof/

[2]: http://www.amazon.com/Book-Proof-Richard-Hammack/dp/09894721...

[3]: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/05...