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Ask HN: Math books that made you significantly better at math?

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Re: Ask HN: Math books that made you significantly better at math?

#91

Post by hosh »

salusinarduis wrote: post #74
enriquto wrote: post #49

The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds ) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * So…

I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?

I restarted with Kalid Azad’s Math, Better Explained. It approached math first by intuition, and then worked out to refine it with proofs.

Re: Ask HN: Math books that made you significantly better at math?

#92

Post by rcarr »

salusinarduis wrote: post #74
enriquto wrote: post #49

The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds ) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * So…

I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?

I’ve been doing a similar thing with Brilliant and really enjoying it. It feels like every course is orientated around teaching maths from a problem solving perspective so you actually get why you’re learning stuff rather than teachers just trying to brute force things into your head which unfortunately seems to be the default at schools nowadays.

Re: Ask HN: Math books that made you significantly better at math?

#93

Post by purpleblue »

salusinarduis wrote: post #74
enriquto wrote: post #49

The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds ) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * So…

I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?

What do you mean by basics? How far back do you want to go? Algebra? Art of Problem Solving is what my kids use, it's pretty good and thorough.

Re: Ask HN: Math books that made you significantly better at math?

#95

Post by haskellandchill »

I love math books with great exercises, I just wish I could code them up in a theorem prover and solve and store my proofs that way. I've tried a bunch of tools but haven't found a language or workflow that really meets the needs for computer assisted study of mathematics.

Re: Ask HN: Math books that made you significantly better at math?

#96

Post by orm »

salusinarduis wrote: post #74
enriquto wrote: post #49

The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds ) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * So…

I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?

3Blue1Brown videos seem like a good resource to use along any book. My experience as a math major (in the distant past) is that the kind of visualization the author shows you is also something you want to imitate in your head when you are learning new concepts. I find things I learned in this level tended to stick in my head 10+ years later, other stuff less.

Re: Ask HN: Math books that made you significantly better at math?

#97

Post by bombcar »

eddsh1994 wrote: post #90
bombcar wrote: post #12

Earlier quoted context omitted.

Reading Euclid's Elements and Newton's Principia really helped me get an intuitive feel for geometry and calculus. They may not be entirely easy (at least the second) without some commentary, but well worth the study.

This is sort of like recommending the art of computer programming as a way to learn how to code, isn’t it? Starting very far down the stack if you’re working through a 2000 year old book in Ancient Greek!

Perhaps, but the Elements is quite understandable, and surprisingly enough it's been translated - https://www.barnesandnoble.com/s/Euclid%20elements

Re: Ask HN: Math books that made you significantly better at math?

#98

Post by super256 »

For the German speakers:

Something that really helped me with my mathematic modules at university: Lothar Papula's "Mathematik für Ingenieure und Naturwissenschaftler" [1]. If you get the stuff in this book right, you're set for life.

[1] https://www.amazon.com/Mathematik-f%C3%BCr-Ingenieure-Naturw...

Re: Ask HN: Math books that made you significantly better at math?

#100

Post by ABeeSea »

Llamamoe wrote: post #87

A better question: What books made you significantly better at math that are also genuinely FUN to learn from? I find that my biggest barrier to learning math has always been how unengaging, excessively contrived, and unfun the learning material has been.

David Bressoud’s 4 books on calculus/analysis are the most engaging math books I’ve ever read. He uses the history of mathematics to drive the narrative and it’s an enlightening approach. However, this means certain theorems often taught in undergrad analysis are delayed until his “graduate” book and his graduate book would not be sufficient for passing many universities analysis quals. But the context and history he gives is fantastic.
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