A Programmer's Introduction to Mathematics • Hacker News Board

Re: A Programmer's Introduction to Mathematics

#201

Post by nicoburns » Mon, Dec 03, 2018, 3:43 AM UTC

andrepd wrote: post #113

kccqzy wrote: post #100

Earlier quoted context omitted.

I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways with…

>the thing about math books I have read is that they overemphasize rigor at the expense of intuition I think these are not contradictory notions! Bad maths books lack rigour. Many books are like you say: rigorous but difficult to make sense of. But truly great books both explain the concepts in the simplest, most lucid and succinct way possible AND maintain the rigour necessary to do mathematics. I like this quote fr…

Agree, additionally I've found that the key to thw very best books is explaining how the intuition and rigour link. I have found that many books (and teachers) exaplin both seperately, but fail to adequately connect the two.

Re: A Programmer's Introduction to Mathematics

#202

Post by IOT_Apprentice » Mon, Dec 03, 2018, 4:04 AM UTC

mlejva wrote: post #139

I have a genuine question which might sound dumb but I really do wonder. How do you actually read math, physics and programming books? Reading them the same way as you'd read a novel doesn't seem right. I try to go chapter after chapter and make notes but I often get bored because I don't see the usage in my real life coding. Maybe I'm not working on problems that are challenging enough? Also after few chapters it of…

I'd add to that, how do you read programming language library documentation? Often I'll be reading along in the documentation for a function in say a python library and not really understand what the documentation is trying to say.

I was just as lost with the K & R C book.

Re: A Programmer's Introduction to Mathematics

#203

Post by Sniffnoy » Mon, Dec 03, 2018, 5:25 AM UTC

j2kun wrote: post #195

Sniffnoy wrote: post #143

Some comments/corrections on the first chapter, if you don't mind: 1. Theorem 2.4 is stated incorrectly. Given the context, I feel like this is worth correcting. Specifically, it says "degree n" rather than "degree at most n". Part of the proof purports to prove that the degree is indeed n but of course it doesn't because that needn't be true. There are other cases where you say "degree n" for "degree at most n". Aga…

Of course you're right about degree n vs. at most n, with many easy counterexamples (the list (1,1), (2,1), (3,1) being a simple one). If you'd like, please submit an erratum using the link at pimbook.org, and other readers can see it, and I will include the fix in the next version of the book and credit you. Thanks for reading! ^_^

OK, will do! Like I said, I think a lot of people will find this book quite helpful. :)

Re: A Programmer's Introduction to Mathematics

#204

Post by [deleted] » Mon, Dec 03, 2018, 5:47 AM UTC

necovek wrote: post #188

temo4ka wrote: post #169

Earlier quoted context omitted.

> How do you actually read math, physics and programming books? > Reading them the same way as you'd read a novel doesn't seem right. Indeed it doesn’t. As the author of the book in this post points out on his blog [1] in math you focus on learning the syntax first, just like in programming. Off the top of my head I can recommend pre-reading a chapter before reading it: go through theorems, bold/italic text, graphs,…

While I like most of your points, I've got to stand up for our brains (or mathematics, depending on who you think is getting shorthanded there :)). I would say the exact opposite of "our brains are not wired for [math]": mathematics is the simplest expression of our ultimate thought ("brain") processes. It is only hard because it is so abstract and builds on a large corpus of what has already been constructed, but it…

[deleted]

Re: A Programmer's Introduction to Mathematics

#205

Post by harias » Mon, Dec 03, 2018, 9:39 AM UTC

jamestimmins wrote: post #189

harias wrote: post #166

Earlier quoted context omitted.

I have completed all three courses in the series. It was a good supplement to other resources, especially 3blue1brown's Linear Algebra course on youtube[0] (mind-blowing, do check it out) but I wouldn't recommend it as a first course. The first two courses weren't rigorous enough for my taste (I am yet to find a rigorous course on Coursera), but the third was pretty good. You should take up books if you are serious.…

These are great insights! Thanks so much. Do you think it's worth going through pre-calc/calc deeply? I assumed I should do that first, but it would take quite a while (I haven't taken calc in ~8 years and barely remember more than the basics).

Essence of calculus[0] by 3blue1brown for the basics and the second course in the Coursera Mathematics for Machine Learning would let you get started. You would rarely need calculus more advanced than that covered in the above, and if need be you will be in a position to look it up quickly. If you can sustain your interest in ML over a long period of time and are in no hurry, I would recommend going through all the math mentioned. If you are a top-down learner, the fast.ai course on ML and deep learning for coders will get you started head-first. All the best!

[0] - https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53...

Re: A Programmer's Introduction to Mathematics

#206

Post by abhishekjha » Mon, Dec 03, 2018, 10:37 AM UTC

kccqzy wrote: post #100

amelius wrote: post #91

Earlier quoted context omitted.

> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.

I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways with…

>I think you aren't buying very good math books then.

Just to follow up. A comment[0] on the book `Discrete Mathematics and Its Applications by Kenneth H. Rosen`

`I'm convinced that math gurus are incapable of teaching math.

Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping that they'd profit from the thefts, but although their business plan included a Phase 1 ("Steal underwear") and a Phase 3 ("Make a profit"), Phase 2—the connective tissue—was just "?".

Rosen and others like him fail to grasp how much "?" connective tissue they're leaving out when they "teach" math. He'll describe a math concept using almost-but-not-quite human language, then—oh, there's always a "then" with these books—the math gymnastics begin. Math teachers can't resist the gymnastics, can they? No, they really can't. At some point they lose their ability to see how much they assume other people know, and when that happens they cease being effective at teaching. This describes almost every math teacher I've had, and it definitely describes almost every math textbook that I've read. Rosen's book isn't the worst math textbook that I've read, but it's still pretty awful.

Seriously, corner cases and extreme mind-bending problems don't help people learn math; giving students time to grasp concepts before baffling them with bullshit does. This is why math schools like Khan Academy are amazing and college/university level math courses are not. This stuff can be taught, but not like this.`

I strongly agree with this argument. I had this book in my undergrad and I felt barely learning anything and just kept getting drowned in the way the content was written. I switched to a different text in a few weeks and it became an easy subject. The difference was more intuitive examples and gradual difficulty in exercises and less of the proof is left for the reader as an exercise.

[0] https://www.goodreads.com/book/show/1800803.Discrete_Mathema...

Re: A Programmer's Introduction to Mathematics

#207

Post by ziont » Mon, Dec 03, 2018, 3:27 PM UTC

Ericson2314 wrote: post #43

ziont wrote: post #41

I am basically trying to understand the formulas in machine learning papers, will this book help achieve improvements in speed? I just realize I fear math because the educational system I grew up in was violent (like beating kids for getting a quiz wrong wtf). It was only through psilocybin mushrooms did I discover math and calculus again.

Plenty of cliffhangers in this comment

Sure, I grew up in South Korea much of my childhood, corporal punishments was the norm.

So I have this phobia of calculus and math. Anytime I'm faced with a formula I get this panic attack. Some may call it PTSD. But it explains why I had such problem with calculus and it really made me feel inferior.

it's still a cliff hanger, searching for my arc.

Re: A Programmer's Introduction to Mathematics

#208

Post by deadwanderer » Mon, Dec 03, 2018, 4:48 PM UTC

abhishekjha wrote: post #206

kccqzy wrote: post #100

Earlier quoted context omitted.

I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways with…

>I think you aren't buying very good math books then. Just to follow up. A comment[0] on the book `Discrete Mathematics and Its Applications by Kenneth H. Rosen` `I'm convinced that math gurus are incapable of teaching math. Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping tha…

May I ask what the "different text" was that you switched to? I have Rosen, and I'd like something more approachable and clear.

Re: A Programmer's Introduction to Mathematics

#209

Post by remind_me_again » Mon, Dec 03, 2018, 5:01 PM UTC

joaorico wrote: post #165

mlejva wrote: post #139

I have a genuine question which might sound dumb but I really do wonder. How do you actually read math, physics and programming books? Reading them the same way as you'd read a novel doesn't seem right. I try to go chapter after chapter and make notes but I often get bored because I don't see the usage in my real life coding. Maybe I'm not working on problems that are challenging enough? Also after few chapters it of…

Here's Alain Connes, Fields medalist, on how a mathematician works and should read a book [0]: "To understand any subject, above all, a mathematician SHOULD NOT pick up a book and read it. It is the worst error! No, a mathematician needs to look in a book, and to read it backwards. Then, he sees the statement of a theorem. And, well, he goes for a walk. And, above all, he does not look at the book. He says, "How the…

That's a lot of walking.

Re: A Programmer's Introduction to Mathematics

#210

Post by mattkrause » Mon, Dec 03, 2018, 5:12 PM UTC

Gritt wrote: post #134

amelius wrote: post #91

Earlier quoted context omitted.

> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.

I'm reading Calculus, Multivariable from William L. Briggs (amazon link: shorturl.at/ltGVY) ; it has the answers at the back of the book ; I'm quiet happy about it for someone who always sucked in maths. If anybody has books to share, i'm especialy interested in linear algebra and signal processing

I like Gilbert Strang’s Introduction to Linear Algebra (there are videos too: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...). The book has answers for some, but not all, of the problems.

I think Strang does a good job balancing intuition and rigor, without too much mindless grinding. Other books I’ve used either leap right into “Let F be a field....” or have you learn a bunch of matrix manipulations but don’t really explain why these are interesting or useful.