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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?

#281

Post by dysoco »

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.

Any suggestions for more conventional Statistics books? (Math-oriented, with proofs if possible). I'm reading Devore's one for Engineering and the Sciences and it's pretty good but I'm having a bit of hard time with p-values, hypothesis tests, etc. and wanted a second book as reference for those topics.

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

#282

Post by musictubes »

I read the first chapter of “Mathematics; Its Content, Form, and Meaning” (or something close to that) and it explained the entirety of my high school mathematics. If I had been given that to read back then I might have gone into mathematics in college. Instead I got burned out and quit doing any math for a decade or more. Sigh.

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

#284

Post by throwaway81523 »

sfpotter wrote: post #110

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…

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

I studied a fair amount of math in school, then worked for many years as a programmer without using one bit of it. More recently though, it has become important again. I try to make sense of the posts here about AI and generally find I don't know enough math, despite knowing more than most programmers do (though far less than actual mathematicians do). So I do feel like I have to study more math if I want to understand that stuff.

Similarly, trying to learn Haskell (a worthwhile endeavour for any programmer) sent me into a deep rabbit hole in mathematical logic. Maybe it wasn't necessary, but I do think it solidified my understanding of Haskell, such as it is. I still have no idea what a left Kan extension is though.

I'm not trying to humblebrag, I think maybe I'm just stupid, but I find it hard to trust my understanding of anything unless all those details are nailed down.

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

#285

Post by throwaway81523 »

dysoco wrote: post #281
madcaptenor wrote: post #65

Earlier quoted context omitted.

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.

Any suggestions for more conventional Statistics books? (Math-oriented, with proofs if possible). I'm reading Devore's one for Engineering and the Sciences and it's pretty good but I'm having a bit of hard time with p-values, hypothesis tests, etc. and wanted a second book as reference for those topics.

There is a list here that I saved the url from. I don't have recommendations from it, unfortunately.

https://mathoverflow.net/questions/31655/statistics-for-math...

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

#286

Post by dysoco »

sn9 wrote: post #261
boothby wrote: post #158

No specific book, but generic advise about how to use a math book. Homework, homework, homework. Read the whole thing, but focus on the exercises. Do every exercise as soon as you can manage: don't wait until you've read the whole chapter -- once you get confused and stumped, the lesson of the chapter becomes urgent and I find that sharpens my attention.

For a case study in how specifically to do this, see this post about how Cal Newport studied discrete mathematics in college: https://www.calnewport.com/blog/2008/11/25/case-study-how-i-...

I usually enjoy Newport but... this was rather underwhelming? It's basically "do a lot of proofs and study consistently not just 48hs before the exam".

Most if not all of my math and some comp-sci courses would require this, they were very proof-heavy, specially Algebra, Logic and Graph Theory, and there was no way you could even pass just studying for a week after let alone 48hs before.

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

#289

Post by bob_theslob646 »

nextos wrote: post #251
jsenn wrote: post #156

* The Art of Probability by Hamming. An opinionated, slightly quirky text on probability. Unlike the text used in my university course its explanations were clear and rigourous without being pedantic. The exercises were both interesting and enlightening. The only book in this list that taught skills I've actually used in the real world. * Calculus by Spivak. This was used in my intro calculus course in university. It…

These are good recommendations, but I think beginners tend to burn out due to the lack of a structured program and/or exercise solutions if they are trying to study on their own. The simplest structured program I can think of that satisfies both is: * Basic Mathematics by Lang. Covers basic algebra and geometry at high school level. Then one of these two, depending on your interests, or both: * Vector Calculus, Linea…

These are great. Thanks for sharing.

Do you happen to have any on probability or statistics and or both?

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