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Ask HN: How do I learn mathematics starting from almost no knowledge?

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Ask HN: How do I learn mathematics starting from almost no knowledge?

#1

Post by Man_On_the_Moon »

Hi all -

In high school, I pretty much ignored math. I memorized everything without understanding anything. I got through AP calculus (and got a 5 on the exam but I honestly didn't really understand any of it). I didn't take any math in college. I can't help but feel like I missed out on great beauty. I was looking at an explanation of one of Euclid's proofs and this made me want to take action.

I have almost none of the building blocks. Can anyone refer me to a book that starts from the very building blocks of math (I assume things like prime numbers) and the simplest logic and builds off these first principles to create understanding?

I understand this probably doesn't exist, but is there anything close?

Re: Ask HN: How do I learn mathematics starting from almost no knowledge?

#3

Post by abbc »

Typical math undergrads study real numbers (real analysis), complex numbers (complex analysis), integers (number theory), structure(abstract algebra), linear maps & vector spaces(linear algebra), continuity(topology), discrete structures and systems (discrete math/analysis), counting (combinatorics), chance(probability) etc

Knowing how to program makes learning computer science that much more enjoyable. Similarly, coming into mathematical theory with a decent grasp of how math proofs work makes for a smooth(ish) journey through the math landscape. That said, consider the following FREE book that can introduce you to math from close to zero:

Book of Proof by Richard Hammack.

https://www.people.vcu.edu/~rhammack/BookOfProof/

Re: Ask HN: How do I learn mathematics starting from almost no knowledge?

#4

Post by throwawaybbqed »

What you are describing seems exactly like the text for first year math in school. Check out Spivak. I remember loling that it starts out explaining what is a number and why addition works the way it does. Heh .. I still lol a bit at that but if that is your cup of tea ..

My personal philosophy is to develop my mathematical intuition. I like applied problems. I really liked my high school math text: https://www.amazon.ca/Calculus-First-Course-James-Stewart/dp...

You can get old versions of these btw ... basic math has been the same since Newton :-p I also highly recommend the MIT course of Gilbert Strang on linear algebra.

Re: Ask HN: How do I learn mathematics starting from almost no knowledge?

#6

Post by probinso »

if you're doing it on your own, it helps to have a motivating story. there are a category of math book that is historically driven. you can pick a topic and typically find a really strong and well-written book on the history of that topic, or just pick up a book on the history of mathematics. these will give you solid examples that you can relate to, give you the motivating story of the persons who discovered the mathematics, and give you enough information to decide whether you want to explore that topic independently

Re: Ask HN: How do I learn mathematics starting from almost no knowledge?

#7

Post by sn9 »

bjourne wrote: post #5

Go to Khan Academy's math section and do ALL exercises from grade one and onwards.

This is the most effective route. BetterExplained can be a good supplement.

Make sure you know how to learn effectively: check out the Learning How to Learn course on Coursera.

If you want to go even deeper than Khan Academy, the Art of Problem Solving books are great.

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