Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

news.ycombinator.com

Post reply on HN
Print view View original

61–70 of 323 posts

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

#61

Post by User23 »

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.

It can be made to be. Dijkstra came up with a nice and rigorous notation he used for his own proofs[1]. That page also includes some slightly spicy takes on why things are as they are. I agree that this is an area where the broader mathematical field has much to learn from computing science. The unforgiving nature of computing automata really drove that innovation. Meanwhile one can afford to be sloppy when one is trying to convince some other mathematician with a sky high IQ.

[1] https://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/E...

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

#62

Post by vippy »

Velleman's How to Prove It greatly helped my ability to construct set theoretic proofs, which better prepared me for Spivak's calculus and Baby Rudin. Hamkins' Proof and the Art of Mathematics is designed as a a good, less set-theory heavy, introduction to proof writing that leads more naturally to analysis. OpenStax books are FREE.

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

#63

Post by krmboya »

pen2l wrote: post #16
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.

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?

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

#65

Post by madcaptenor »

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.

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

#66

Post by breck »

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.

This is a project of mine that I take attempts at here and there.

Another great book on this topic is "History of Mathematical Notations" https://www.amazon.com/History-Mathematical-Notations-Dover-...

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

#67

Post by ag315 »

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 don't think you can get good at doing calculations without practicing the calculations, but reading books that discuss the higher-level aspects of math and the philosophical underpinnings can help you look at it in a different way that may inspire more interest as well as an easier time grasping the difficult parts.

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

#69

Post by rowanG077 »

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.

Couldn't agree more. Mathematician are masters at whipping up random notations and then not adhering to it rigorously. Higher level math would be an order of magnitude easier with machine checked syntax.
Post reply on HN