How to Solve It (1945) • Hacker News Board

Re: How to Solve It (1945)

#101

Post by sverona » Wed, Aug 23, 2023, 6:32 PM UTC

i_am_a_peasant wrote: post #83

vkazanov wrote: post #80

Earlier quoted context omitted.

I have both the book discussed here, and How to prove it, and back in the day the Proof book was a revelation, unlike Polya's one, which was interesting but that's about it How to prove it just made proofs click, and I wish I understood the material earlier, by high school the latest. I am convinced that all the half intuitive half ("kind of like") mechanical ("just remember this") explanations we get in school and u…

There are other books in the literature that mainly focus on how to go about proving things rather than proving specific things. Some titles that come up are: Mathematical Proofs: A transition to Advanced Mathematics by Chartrand, Polimeni and Zhang. Book of Proof: Richard Hammack Jay Cumming’s Proofs I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in…

> I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know.

Every discrete math book I've ever seen has a strong proof component; it's supposed to be an undergraduate's introduction to rigor. The classes taught out of those books may not actually be that rigorous, depending on whether the students are going to be expected to rigorously prove things later, or if it's just Leetcode combinatorics.

But for a guess, maybe Kenneth Rosen?

Re: How to Solve It (1945)

#102

Post by i_am_a_peasant » Wed, Aug 23, 2023, 6:53 PM UTC

sverona wrote: post #101

i_am_a_peasant wrote: post #83

Earlier quoted context omitted.

There are other books in the literature that mainly focus on how to go about proving things rather than proving specific things. Some titles that come up are: Mathematical Proofs: A transition to Advanced Mathematics by Chartrand, Polimeni and Zhang. Book of Proof: Richard Hammack Jay Cumming’s Proofs I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in…

> I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know. Every discrete math book I've ever seen has a strong proof component; it's supposed to be an undergraduate's introduction to rigor. The classes taught out of those books may not actually be that rigorous, depending on whether the…

Ah yes, I think this was it, I see a note that I have the 7th edition and I wanted to get a hold of the 8th.

Re: How to Solve It (1945)

#103

Post by agencies » Wed, Aug 23, 2023, 7:01 PM UTC

OldGuyInTheClub wrote: post #28

boppo1 wrote: post #25

This summary really undersells the book IMO. It's one of the more interesting books I've read in that it is not structured linearly. He introduces a few ideas which have very particular language he defines in the remainder of the book which is essentially a dictionary. If you don't come from a math-y background and you are trying to get into serious mathematics, this definitely helps to 'lift the veil' on how you mig…

"How To Solve It" does not account for actual ability. It was recommended in high school to those of us interested in math contests. My big lesson was that if you need this book, you're going to be roadkill in math contests. If you have the chops to be a successful mathlete, you don't need this book. And so it came to pass. There are some people who have the ability to see a problem well enough to analyze it and make…

You say that if someone has the chops to be a real mathlete they won't need Polya's _How To Solve It_

I'll say I went to college 25 years ago with people who had competed internationally in high school and who placed competitively on the Putnam, and they LOVED Polya's book.

I think whether you enjoy seeing strategies laid out well--—whether or not you've been able to figure some of it out yourself---depsnds more on your personality than on how good you are at solving creative math problems.

Re: How to Solve It (1945)

#104

Post by im_lince » Thu, Aug 24, 2023, 11:03 AM UTC

In our team we recommend this book to new joiners. The principles and methods shared by polya is valid for solving the not only the mathematical problems also engineering problems in effective way.