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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?

#191

Post by mindcrime »

yodsanklai wrote: post #23

I wonder how good you can get at maths just by casually reading books. You need to work on problems for hours and hours to get a grasp on the theories. Programming is different in the sense that it's something people routinely do as a hobby because it's quite fun and addictive. But maths? maybe if you have already strong foundations you can pick up a new topic and develop your culture. But I doubt one can get these f…

I wonder how good you can get at maths just by casually reading books. You need to work on problems for hours and hours to get a grasp on the theories.

Maybe I'm unique in this regard, but I always took it as sort of implied that "reading a math book" entails "reading the book and working (at least some of) the exercises".

The tricky part is once you get to math where you can't trivially check your answer by "substituting back in" or "using a calculator" or whatever. Doing proofs, for example. Without a teacher, how do you know if your proof is correct? So far the only thing I've really found to do for that is to post on MathOverflow or one of the "learn math" related sub-reddits. I've often wondered if learning to use an automated theorem prover / proof assistant of some sort would be helpful, but that's such a huge undertaking in its own right...

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

#192

Post by strangattractor »

Philip-J-Fry wrote: post #157
DoingIsLearning wrote: post #139

Earlier quoted context omitted.

If you don't mind the question how is the Remarkable helping you in this. Just to avoid the clutter of paper? Or does it some how OCR you're handwriting?

I hate the clutter of paper and how hard to organise it is for me. Plus, how messy I am writing on paper and crossing things out all the time. The Remarkable, at least for me, is good because I can organise my notebooks into folders by certain math lessons or concepts. And I can undo any mistakes, so my notes are clean. Even if I am quickly working something out I am clean it up and make it a good note for future me.…

A similar solution might be https://getrocketbook.com/ RocketBook. It can be a $0 dollar solution if you download their app and then print out the free PDF pages that are pre-formatted.

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

#195

Post by matthewmorgan »

nhatcher wrote: post #75

Lot's of good books already here! In the same spirit as Polya's book "Thinking mathematically" by J. Mason, L. Burton and K. Stacey I learned a lot in the early days with Demidovich book on 5000 problems on mathematical analysis. Tom Apostol books on calculus, but for me his book on analytical number theory. Alongside alan baker's thin book on number theory. Gilbert Strang book(s) on linear algebra. Rudin book on fun…

Came here to recommend Thinking Mathematically (text only) by J. Mason. If only every high school maths teacher had this book, the world would be a better place

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

#196

Post by amai »

super256 wrote: post #98

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...

I recommend Lang: Mathematische Methoden der Physik

https://link.springer.com/book/10.1007/978-3-662-49313-7

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

#197

Post by Ishmaeli »

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?

Susan Fowler Rigetti posted a self-study curriculum last March: https://www.susanrigetti.com/math

I don't know how good it is, but her earlier entries on Physics and Philosophy were well-received.

HN thread: https://news.ycombinator.com/item?id=30591177&p=2

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

#198

Post by omershapira »

Donald Sarason's "Complex Function Theory". There are bigger more complete books on complex analysis. There are even ones that are more appealing, like "Visual Complex Functions" by Elias Wegert.

Sarason's book is only 160 pages long, with legible text and clear examples. It covers the length of an undergraduate university class, and explains Holomorphic functions perfectly. The proofs are crystal clear, and so are the motivations. I haven't seen a better introduction.

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

#199

Post by jldugger »

madcaptenor wrote: post #65
guhsnamih wrote: post #3

Statistics by Freedman, Pisani and Purves. Don't know if I got better but loved the real world examples and cartoons. Does not have too many pre-requisites. Each section presents a tiny concept which is followed by plenty of exercises that have answers at the end. The furthest I got in a book in recent days, Math or not.

I taught from this book (it wasn't my choice, it was the standard book where I was teaching). It's really good for intuition, but because it doesn't use standard notation I think it might have done a disservice to students who were going to go on to learn more.

My pandemic project in 2020 was to finally read through the used copy I bought a decade ago. I agree it was really useful at building foundational intuitions. And that it doesn't use professional jargon which sometimes makes Stats Wikipedia's "death by integrals" approach a dense barrier to entry.

For example, the book uses "the box model" all over the book but is not used anywhere else, and every else uses the phrase "i.i.d" which is not used in the book.

Still, it's been really useful at my job in reasoning about timeseries data from Prometheus, especially in canary analysis. Far more useful than the whirlwind tour of distributions my 1 semester "Statistics for Engineers" course in college undertook.

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

#200

Post by stormdennis »

K A Stroud Engineering Mathematics is probably the book that helped me most. 31 chapters each composed of about 60 problems. The problems are progressive and contain explanations of the new concepts that they contain. All the answers are at the back.
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