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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?

#101

Post by Philip-J-Fry »

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 had the same idea.

I bought myself a Remarkable 2 and signed up to Khan Academy. Now I'm revising algebra basics and I plan to go as advanced as Khan Academy lets me.

I was really bad at maths in school (UK A Levels). But I'm a successful software developer today. I felt like knowing more advanced maths could make me a better developer and not feel intimidated by a lot of the things I see.

I'm actually enjoying it as well. Maths isn't just something I have to do to get out of school, now it's something I want to do. And it gives me the same satisfaction as solving puzzles like sudoku.

I'd recommend it to anyone. The Remarkable 2 is actually really nice to write on too, since I want to store my notes digitally. And I make so many mistakes when writing, so undo is great.

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

#102

Post by bombcar »

krmboya wrote: post #63
pen2l wrote: post #16

Earlier quoted context omitted.

While it's laudable that you sought those texts and profited from them, I worry about what others might take away from this. When I was young I knew some geniuses who highly spoke of Principia and how it gave them great insights. And the teenager me said, okay cool, I'll have a go! The problem is that it's in Latin and quite impenetrable. We have some geniuses here and they would no doubt be able to take away a lot f…

I've been flirting with the idea of working through all of Leonard Euler's publications (as a life goal). Many of them are still not translated from Latin, so there's a possibility I may have to learn it. Anyone knows how long it would take to learn enough latin to undertake such a task?

If you're trying to understand a domain work (such as Euler's) you could probably get a working knowledge in a month of strong study, a year of off-and-on.

I bet you could start this week if you used machine translations as a crutch.

I'd start working with a publication that exists in Latin and a good translation, so you can compare your work.

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

#103

Post by _fullpint »

friedman23 wrote: post #81
salusinarduis wrote: post #74

Earlier quoted context omitted.

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.

Going back through Discrete would probably be a good idea as well.

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

#104

Post by mindcrime »

Maybe not "made me better at math" per-se, but definitely "made me more enthusiastic about math":

The Universe Speaks in Numbers[1] by Graham Farmelo

I found this very motivating and insightful, in terms of developing even more of an appreciation for how much math underpins other branches of science. Not that that is a novel insight by any means... but the details of the incidents where breakthroughs in mathematics allowed further advances in physics, etc. and looking at the "back and forth" between the domains, that was wildly interesting to me. Reading this book definitely helped motivate me to get serious about committing more time / focus to studying mathematics.

I also enjoyed the "counterpoint" book by Sabine Hosenfelder, Lost in Math[2]. I think these two books complement each other nicely.

Then the handful of additional (no pun intended) books that jump to mind would be:

- How Mathematicians Think by William Byers[3]

- How to Think Like a Mathematician by Kevin Houston[4]

- Discrete Mathematics with Applications[5] by Susanna Epp

- How Not To Be Wrong[6] by Jordan Ellenberg

- Introduction to Mathematical Thinking[7] by Keith Devlin

- How to Measure Anything[8] by Douglas Hubbard

[1]: https://www.amazon.com/Universe-Speaks-Numbers-Reveals-Natur...

[2]: https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/15...

[3]: https://www.amazon.com/How-Mathematicians-Think-Contradictio...

[4]: https://www.amazon.com/How-Think-Like-Mathematician-Undergra...

[5]: https://www.amazon.com/Susanna-S-Epp-Mathematics-Application...

[6]: https://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143...

[7]: https://www.amazon.com/Introduction-Mathematical-Thinking-Ke...

[8]: https://www.amazon.com/How-Measure-Anything-Intangibles-Busi...

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

#105

Post by TimTheTinker »

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…

Wow, I wish I had known about this book (and had a license to Mathematica) when I was in college. I always got hung up on the notation and my inability to visualize the concept.

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

#106

Post by orm »

orm wrote: post #96
salusinarduis wrote: post #74

Earlier quoted context omitted.

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.

I should mention focusing on doing a few interesting problems, rather than many not so interesting ones, is also one way to help yourself understand more deeply.

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

#108

Post by meken »

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 did this same exact thing back in 2010. I used khan academy for it. Started with positive and negative numbers, arithmetic, through trig and algebra.

I like khan academy back in 2010 because all the videos were in one place and you could see everything right there in front of you

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

#109

Post by VyseofArcadia »

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…

Seconding all of Spivak's books. My favorite treatment of differential geometry.

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

#110

Post by sfpotter »

Honestly, unless you're very gifted, a book on its own is not going to be enough to really develop your skills. You need to work interactively with a teacher. Getting a degree in math is a good start, but even then it will be limited if you don't work with other people, go to office hours, form relationships with professors---embed yourself in the culture, so to speak. I think getting engaged with an online community like MathOverflow or similar could be a substitute for this.

IMO, programming is "easier" to learn on your own for a few major reasons:

1) The sorts of things most people are interested in building just aren't unforgiving intellectually in the same way that math is.

2) You have a compiler to check if you're right, and your code will often still work even if it's "wrong" (not as efficient as it could be, has unwanted side effects, etc.). In some sense the compiler is a bit like a teacher this way.

3) With programming, you can upload and make it available for free, and whether it's legit or not is largely disconnected from your pedigree or how "correct" it is. This makes programming far more accessible. This makes sense considering that programming is primarily a practical tool. On the other hand, mathematics is primarily a field of scientific inquiry and is judged by different standards. If you learn a bit of math, try to write a paper, submit it to the arXiv... well, people will probably think you're a crank.

On the other hand, if you're just interested in math for the love of the game... you can certainly pick up a book and read it, maybe work some problems, but I think at this point it's quite easy to fool yourself into thinking you understand more than you actually do. I guess there's no real harm in being a charlatan, but probably the average person is interested in having some kind of real relationship with mathematics that they can be confident has a firm foundation. I'm very skeptical most people can truly pull this off by just reading books and not actually going to school.

---

As an aside, I think the fetishization of math in programming communities is very interesting...

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