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

51–60 of 223 posts

Re: A Programmer's Introduction to Mathematics

#51

Post by chii »

Koshkin wrote: post #32
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking.

Also, if you can't prove a solution correct, then you haven't solved it!

Re: A Programmer's Introduction to Mathematics

#52

Post by dustycat »

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 am curious how many people the author has taught mathematics to.

It doesn't seem a good idea to jump into writing a textbook teaching mathematics unless one has experience of teaching mathematics.

But the author makes the very point about early failures of programming, due to lack of experience, so perhaps he can supply information about what his pedagogical experience consists of.

Teaching other people is a craft, similar to programming or mathematics, with its own necessities.

Re: A Programmer's Introduction to Mathematics

#53

Post by ptd »

chii wrote: post #51
Koshkin wrote: post #32

Earlier quoted context omitted.

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking. Also, if you can't prove a solution correct, then you haven't solved it!

Is this a feature or a bug? If it takes you two weeks to apply creative solutions and it take me one week to apply a “rote” solution, what is the benefit?

Re: A Programmer's Introduction to Mathematics

#54

Post by jbasrai »

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?

Re: A Programmer's Introduction to Mathematics

#55

Post by jacobolus »

dustycat wrote: post #52
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 am curious how many people the author has taught mathematics to. It doesn't seem a good idea to jump into writing a textbook teaching mathematics unless one has experience of teaching mathematics. But the author makes the very point about early failures of programming, due to lack of experience, so perhaps he can supply information about what his pedagogical experience consists of. Teaching other people is a craft,…

Apparently he was a TA as a math PhD student at UIC. Now is a programmer working at Google. He wrote a bunch of posts on his website over the years, https://jeremykun.com/main-content/

Re: A Programmer's Introduction to Mathematics

#56

Post by thatcat »

k__ wrote: post #45
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

I read once, the key to mastery is perceptual exposure and deliberate practice. Don't know how the first part would work with Math.

Observing someones approaches at solutions and proofs would be perceptual exposure to mathematical analysis.

Re: A Programmer's Introduction to Mathematics

#57

Post by marktangotango »

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…

Attempting to shoe-horn programming "lingo" into mathematics.

This statement is particularly amusing and highlights to me the fact that mathematics are a natural language, and not a programming language. Sussman had a really great presentation on this point; anyone who’d argue this please watch!

https://www.infoq.com/presentations/Expression-of-Ideas

Re: A Programmer's Introduction to Mathematics

#58

Post by marktangotango »

Koshkin wrote: post #32
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

I also champion this method; I used solutions manuals as guides until I could internalize and reproduce the logic on my own. I was a particularly dense student though.

Re: A Programmer's Introduction to Mathematics

#59

Post by threwythrw »

chii wrote: post #51
Koshkin wrote: post #32

Earlier quoted context omitted.

Agree. Actually, studying a good solution even if you have one of your own is one of the best ways to learn mathematical tricks of the trade, so to speak - just as it's a great way to learn coding: one learns from the master (as one should) and not just "from the book."

being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking. Also, if you can't prove a solution correct, then you haven't solved it!

>Also, if you can’t prove a solution correct, then you haven’t solved it!

This is the type of thinking I’m talking about. A beginner can think they “proved a solution correct” but have a subtle or even blantant error that isn’t obvious to them.

Also, if reader wants to just skip to the solutions then that’s their fault. But don’t let such people rob the student that put serious effort into their work from seeing the solution.

Re: A Programmer's Introduction to Mathematics

#60

Post by throwawaymath »

marktangotango wrote: post #57
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…

Attempting to shoe-horn programming "lingo" into mathematics. This statement is particularly amusing and highlights to me the fact that mathematics are a natural language, and not a programming language. Sussman had a really great presentation on this point; anyone who’d argue this please watch! https://www.infoq.com/presentations/Expression-of-Ideas

Do you mind summarizing Sussman's presentation? I can't view it on the link you provided without making an account. I can't tell from your comment whether you agree or disagree with the parent's point.
Post reply on HN