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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?

#81

Post by friedman23 »

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'm doing this and am starting with Linear Algebra on MIT OCW (taught by Gilbert Strang). My current plan is to relearn Linear Algebra, Calculus, Probability, and Statistics and actually focus on retaining the knowledge in my memory using something like SRS learning. I think planning past that is pointless since by the time I'm done I will have a better ability to plan my future coursework.

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

#82

Post by michaericalribo »

In my experience, the best way to get better at math is to do a lot of it. Find some book that's "good enough" for some topic you're interested, and work many many problems from the book. You'll learn about the topic, but more importantly you'll learn problem solving skills. I recommend working the problem until you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct.

For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces.

Again, I recommend working nearly every problem.

[1] https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat...

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

#83

Post by yig »

fouronnes3 wrote: post #55
binarymax wrote: post #42

“Mathematical Notation: A Guide for Engineers and Scientists”[0] really changed my abilities with being able to read papers and decipher what was going on. I had university math experience but it was a long time ago. When I started reading papers for algorithms later in my career I couldn’t get past the notation. Once the symbols are explained, as a programmer, I was able to grok so much more. This should be on every…

As a programmer I really wish math notation was more rigorous: less ambiguity, more explicit typing, no implicit variables, etc. So much of it would never pass code review. We programmers figured out that code should be optimized for readability, not writtability ; I wish mathematicians did too.

Our project IHeartLA is a language with syntax designed to closely mimic conventionally-written linear algebra, while still ensuring an unambiguous, compilable interpretation: https://iheartla.github.io/

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

#84

Post by hyperific »

Calculus Made Easy (1910) simply for the quote at the beginning: "What one fool can do, another can."

I did horribly in math because I figured it was hard and just accepted I'd never be good at it. That quote somehow managed to dissolve my mental block.

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

#85

Post by larve »

fouronnes3 wrote: post #55
binarymax wrote: post #42

“Mathematical Notation: A Guide for Engineers and Scientists”[0] really changed my abilities with being able to read papers and decipher what was going on. I had university math experience but it was a long time ago. When I started reading papers for algorithms later in my career I couldn’t get past the notation. Once the symbols are explained, as a programmer, I was able to grok so much more. This should be on every…

As a programmer I really wish math notation was more rigorous: less ambiguity, more explicit typing, no implicit variables, etc. So much of it would never pass code review. We programmers figured out that code should be optimized for readability, not writtability ; I wish mathematicians did too.

Mathematics only clicked and became fun for me when I started using Wolfram Mathematica, because I could fairly easily mess around with the formulas I saw in books until I understood the types and arguments and what is an index vs a reference to some unnamed convention of the field.

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

#87

Post by Llamamoe »

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.

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

#89

Post by legends2k »

Not strictly math books but these three books turned me to live mathematics and appreciate for what it is:

[1]: 3D Math Prime for Games for Graphics and Game Development; https://www.gamemath.com/ (free to read online) [2]: Essential Mathematics for Games and Interactive Applications; https://www.essentialmath.com/book.htm [3]: Mathematics for 3D Game Programming and Computer Graphics; https://www.mathfor3dgameprogramming.com/

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

#90

Post by eddsh1994 »

bombcar wrote: post #12
keiferski wrote: post #6

I would not call myself great at math – I struggled with it in school, in fact – but in recent years I’ve begun “correcting” my lack of mathematical knowledge. The single best decision I’ve made is to first start with the philosophy of mathematics. Maybe it’s because my background is in philosophy, but I also think that for certain people like myself, understanding what math is makes me far more interested in underst…

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!
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