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

71–80 of 223 posts

Re: A Programmer's Introduction to Mathematics

#71

Post by andrepd »

westoncb wrote: post #67
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…

>One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things.

You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me.

You are very wrong on the other point: none of what I said is borne out of a view that mathematics should be difficult and "hard" an impenetrable (rather than soft and approachable). Indeed I view this sort of overlong prose as impenetrable and confusing, and the succinct style of e.g. Landau textbooks much clearer (see my other comment).

>The commenter is again taking a minority viewpoint and baselessly extending it.

This is not a minority viewpoint. I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head.

It is also plainly true: mathematics is about rigour. It is not an obstacle, nor is it an end in itself, but it is a fundamental part of mathematical study and reasoning. If you aren't being rigorous, you're not doing mathematics, it's just a waste of time. I'll let Michael Spivak speak for me:

"In addition to developing the students’ intuition [...], it is important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions."

>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

Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart), and again, not in the least bit what I mean with my criticism.

Re: A Programmer's Introduction to Mathematics

#72

Post by diffeomorphism »

andrepd wrote: post #64
jbasrai wrote: post #54

Earlier quoted context omitted.

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…

Landau-Lifschitz as a reference is also very polarizing. There are people that really like the style (myself included), but I have also met many people that really dislike it, think it is too hard, too brief, too dry, too little description of intuition... . Similarly, the Feynman lectures are loved by some and disliked by others.

Re: A Programmer's Introduction to Mathematics

#73

Post by theoh »

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…

"wtf is wrong with hn"

One thing that's wrong with HN is that perceived "negativity" often gets condemned in exactly the way you have done here.

It seems as if a significant number of HN readers have never really participated in a spirited discussion with arguments made from multiple different perspectives. Maybe any kind of apparent conflict scares them, maybe they project their own aggression onto a comment that seems to go against the grain of the discussion. It will never change.

Re: A Programmer's Introduction to Mathematics

#74

Post by andrepd »

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…

>wtf is wrong with hn.

I believe you must have mistaken me for someone else. My name is andrepd. Is this "hn" a friend of yours?

>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.

It never ceases to amaze me how some people are so perceptive that they can confidently deduce the intentions and personality of a person half a world away by reading a short text online. Are you available for therapy sessions? I could use your valuable insights.

Also, I was under the impression that I was making constructive criticism. I made concrete points and showed examples of books that in my opinion did those things right (see my other comment). I regret the "very very poor" phrase at the start though. I've changed it to just "poor".

>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

Oh, I see you know more about how I felt learning stuff than I do myself! Lovely.

I can tell you that I found it was almost always reading the most succinct treatments that I truly understood the greatest insights. Although from your tone I suspect that none of this will make a difference about how you feel. I won't repeat myself. You can (re)read my other comments if you're interested (and if you find I didn't explain myself well I'd be happy to discuss it more), and also check the examples I've mentioned.

>shame on you and i hope you're never in a position where someone depends on you to teach them absolutely anything

>an author whom i might add has done infinitely more for the math community than you have with your pedantry and vitriol

>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.

I am doing a maths PhD and (woe is you) I teach undergraduate classes AND I've been tutoring students of physics, maths and computer science for over 4 years now, online and in person. I can say with no false modesty that I've been repeatedly complimented by students on my ability to teach and explain concepts.

What Nobel prizes have you got, since that seems to be so important to you?

Re: A Programmer's Introduction to Mathematics

#75

Post by westoncb »

andrepd wrote: post #71
westoncb wrote: post #67

Earlier quoted context omitted.

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…

>One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me. You are very wrong on the other point: none of what I said is borne out of a…

> I'd daresay is the majority opinion among mathematicians. It is also the opinion of prominent computer scientists: Dijkstra, Leslie Lamport, Donald Knuth, to name a few off the top of my head.

There are reasons partly historical and partly due to the subject matter of CS that mathematicians closer to it tend to place relatively higher value on formality.

> It is also plainly true: mathematics is about rigour.

This is taking taking it too far and you're placing yourself in the formalist camp, which is a minority viewpoint. You gave a nice quote from Spivak where he characterizes rigor, "...the natural medium in which to formulate and think about mathematical questions."

Labelling it a 'medium' is very informative. Computer programs likewise depend totally on the formality of the medium; it's in intrinsic part of how they are able to operate. Same with the magic of formality + inference in mathematics.

That said, the psychological questions of pedagogy involve much more than the intrinsic features of some subject. In learning to write completely formal computer programs, one benefits immensely from instruction which departs from total formality. I'm assuming this would be obvious to the readership here so I won't go into more detail.

> Completely nonsensical comparison (C++ and Haskell?? two languages who could not be further apart)

I was referring to the social standing of the languages (which is all that matters for the points I was making), not their intrinsic features.

Re: A Programmer's Introduction to Mathematics

#76

Post by andrepd »

adrianmonk wrote: post #61
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…

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

I don't want "no talk" and "just equations, I want the "minimum of talk possible" that communicates the ideas and nothing more. I find the more stuff you write the more there is to confuse people. The best way is to strip everything that is superfluous. You are left with the essential, in the clearest form there can be.

Re: A Programmer's Introduction to Mathematics

#77

Post by yantrams »

I am a huge fan of Jeremy's blog. Found his primers on a multitude of topics very useful - https://jeremykun.com/primers/

As a Math guy who got into the world of programming relatively recently, I am on the opposite side of the spectrum I suppose but I'm gonna order this nonetheless to support him.

Re: A Programmer's Introduction to Mathematics

#78

Post by j2kun »

alan_wade wrote: post #69

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?

Well, two chapters have singular value decomposition and neural networks as the applications. So it does have a lot of ML :)

But yes, I unfortunately had to cut a probability chapter. I think someone who reads this book would have a much easier time learning probability after, and a better foundation.

Re: A Programmer's Introduction to Mathematics

#79

Post by yantrams »

j2kun wrote: post #78
alan_wade wrote: post #69

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?

Well, two chapters have singular value decomposition and neural networks as the applications. So it does have a lot of ML :) But yes, I unfortunately had to cut a probability chapter. I think someone who reads this book would have a much easier time learning probability after, and a better foundation.

Have just ordered the e-book. Didn't expect to find a chapter on Hyperbolic tessellations. Nice!

Re: A Programmer's Introduction to Mathematics

#80

Post by krick »

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…

As far as I can tell, you are what's wrong with HN. His post is a well-justified opinion, with reasoning provided, whether you chose to agree or disagree with that. Somebody may (or may not) take it into consideration. Yours are simply "how dare you!"-post, adding absolutely no value to the discussion. Also, learn capitals, it's hard to read you like that.
Post reply on HN