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

A Programmer's Introduction to Mathematics

jeremykun.com

Post reply on HN
Print view View original

61–70 of 223 posts

Re: A Programmer's Introduction to Mathematics

#61

Post by adrianmonk »

andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

Regarding the first point, if you are the type of person who just wants it to get to the equations with a minimum of talk, you're probably not the intended audience of this book.

The culture of mathematics (including its lingo) has always been a big barrier for me. Thus far, I've only skimmed it, but that part looks promising to me.

It seems reasonable to guess that if someone has learned a good bit about programming but managed to avoid learning about math, reasons like culture, terminology, accessibility, and motivation might be a big part of why. So including that sort of material in this book makes sense to me.

Re: A Programmer's Introduction to Mathematics

#62

Post by mlevental »

andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

wtf is wrong with hn.

>[sorry if I am being blunt, but it's how I feel]

you should learn to keep your feelings to yourself when the only function they serve is to denigrate others and derive cruel satisfaction for yourself.

>Here is a rule of thumb that in my experience applies well to almost everything in mathematics

this is aspirational pretension - everyone claims to appreciate formal purity /after/ they've learned something but when you're /learning/ none of that matters because you're just trying to develop intuition. to be one of those people that understands after their own stumblings/ruminations and then begrudge the next person the same is despicable. shame on you and i hope you're never in a position where someone depends on you to teach them absolutely anything.

>Imprecise definitions. This defeats the purpose of learning mathematics. Like Leslie Lamport says, rigour in mathematics is not a hurdle or a chore one must endure,

but that's just like your opinion man (or leslie lamport's). there are shelves and shelves of books for people like you - go read bourbaki or rudin or mochizuki or whomever you'd like. this book is not for /you/ - it's stated purpose is to excite and entice people that don't have formal mathematical training to learn mathematics and those sorts of people decidedly don't enjoy austere definitions and succinct theorems and terse proofs.

hence the only purpose your comment serves is to hurt the author's feelings, an author whom i might add has done infinitely more for the math community than you have with your pedantry and vitriol by maintaining a blog https://jeremykun.com/ with literally reams of interesting mathematical content that is simultaneously exciting /and/ rigorous. and furthermore iirc jeremy was originally a math ed phd student so i trust his opinion of the right way to teach math infinitely more than i do yours mr random internet physics guy.

next time think twice before posting this kind of lowbrow mean shit.

Re: A Programmer's Introduction to Mathematics

#63

Post by Brakenshire »

andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

I personally think this is exactly wrong. Most people struggle with Maths because they don’t have the implicit understanding that books like you’re talking about rely on. It’s like telling a novice programmer to read the documentation. I’m not sure how successful this book is but it seems a worthy attempt.

Re: A Programmer's Introduction to Mathematics

#64

Post by andrepd »

jbasrai wrote: post #54
andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

I enjoyed reading this opinion, do you have any recommendations for math textbooks that reach the standards you've described?

Not exactly math, but physics, since that was my background. Perhaps my favourite textbooks are Landau and Lifschitz[1]. They pretty much exemplify what I mean. They are concise, lucid, entirely self-contained. All the relevant information is there and not one bit more. The material is reduced to its key ideas, therefore making their exposition as clear as it can possibly be. Many people I've spoken to, however, don't like it precisely for being "too terse", so there you have it as well: ymmv.

Another book that fits this is Cohen-Tannoudji's Quantum Mechanics[2]. The first two chapters explain quantum mechanics from absolute scratch. It starts as all physics does: with an experiment. Then everything else follows from looking carefully at the consequences of that observation, and the concepts are truly explained for what they are, because they are presented in the simplest way possible. "Idea" is more understandable than "Idea+Cruft". This is remarkable to me: much fuss is made about how quantum mechanics is strange and confusing and difficult to grasp, and it is indeed so. In that first chapter, however, I've found the most illuminating explanation of quantum mechanics I've ever read.

[1] https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

[2] https://en.wikipedia.org/wiki/Claude_Cohen-Tannoudji#Selecte...

EDIT: I just opened Landau's Mechanics Vol I, and here's what his colleague had to say about his writing and teaching style: "[These are] all the features of his characteristic scientific style: clarity and lucidity of physical statement of problems, the shortest and most elegant path towards their solution, no superfluities.". Indeed.

Re: A Programmer's Introduction to Mathematics

#67

Post by westoncb »

andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

There is a common category of misguided book review that the parent comment falls under: the reviewer has some particular things they are looking for from a book and fails to see that there are more uses for it than their own; so they generalize, reading the book's failures to meet their personal criteria as a failure intrinsic in the book's content, and mistakenly lambaste the work.

> 19 pages of droning before you start with something concrete.

One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. I can offer another perspective that what the author wrote on polynomials within the first 19 pages there is in fact pretty unique and interesting.

> Imprecise definitions. This defeats the purpose of learning mathematics.

The commenter is again taking a minority viewpoint and baselessly extending it. There is a special kind of paranoia that often manifests in discussions of mathematical pedagogy that any departure from perfect rigor will weaken the minds of students. This is a blatantly shallow and one-sided view of things: the fact that rigor has value does not imply that the most effective method of teaching—which is a matter of both mathematics and human psychology—is to offer nothing but the most rigorous presentation possible.

This particular book is explicitly targeted at helping to transition programmers into mathematics. Given that goal, do you really think the pedagogically superior approach would be to offer a more rigorous definition of polynomial than:

"A single variable polynomial with real coefficients is a function f that takes a real number as input, produces a real number as output, and has the form: f(x) = a0 + a1x + a2x^2 + ... + anx^n"

—in the introductory chapter of the book?

I would urge potential readers to take the parent comment with a grain of salt. And also, if you're among this book's target audience and trying to teach yourself mathematics, be aware of such personalities preaching this particular dogma of mathematical instruction: it's fairly common on the internet. But it basically represents the same corner of the mathematics world as that of the programming world where folks insist on using nothing but VI/Emacs on Linux with C++ and/or Haskell, and are all too ready to belittle any alternatives perceived as softer/weaker. These aren't necessarily the most impressive programmers—they just project the most intimidating auras. Don't let their counterparts in mathematics scare you off.

Re: A Programmer's Introduction to Mathematics

#68

Post by andrepd »

Brakenshire wrote: post #63
andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

I personally think this is exactly wrong. Most people struggle with Maths because they don’t have the implicit understanding that books like you’re talking about rely on. It’s like telling a novice programmer to read the documentation. I’m not sure how successful this book is but it seems a worthy attempt.

That's not at all the point I was trying to make. Indeed, if you check my other comment, both the books I give as an example have precisely the feature of being self-contained. Landau's Mechanics starts with the basic concept of a particle. Cohen-Tannoudji's Quantum Mechanics starts with the simplest possible description of the double-slit experiment. Again, they assume no prior knowledge about what they are trying to teach (wouldn't be much of a textbook about the subject if it did require previous knowledge about the subject, now would it? :))

Re: A Programmer's Introduction to Mathematics

#69

Post by alan_wade »

I really wish this book would include probability and statistic sections. My guess is that a lot of people, like me, will want to read it because they're getting started with ML and need help getting used to the math, and probability/stats is an important part of it that's missing.

Any chance you could add it in the future?

Re: A Programmer's Introduction to Mathematics

#70

Post by hyeomans »

mlevental wrote: post #62
andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

wtf is wrong with hn. >[sorry if I am being blunt, but it's how I feel] you should learn to keep your feelings to yourself when the only function they serve is to denigrate others and derive cruel satisfaction for yourself. >Here is a rule of thumb that in my experience applies well to almost everything in mathematics this is aspirational pretension - everyone claims to appreciate formal purity /after/ they've learne…

I'm grateful for OP opinion and your opinion. I agree with you except in "next time think twice...", I think that opinion trigger your response which was great!

Enjoy your weekend, both of you!

Post reply on HN