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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.




> 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.


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.


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.




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