Earlier quoted context omitted.
Definitely. Whatever one may think of "How to Solve It," Polya was a renowned mathematician. The book is like the Richard Hamming lectures that often come up on HN: Great thoughts from a great mind but not easily applied by the average or even above average Joe.
Richard hamming lectures? I'd google, but I wouldn't know if I'd found the ones you meant.
How to Solve It (1945)
51–60 of 104 posts
Re: How to Solve It (1945)
#52Earlier quoted context omitted.
"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…
beyond the book, what contributions did he make? it would seem like the techniques should have helped him solve problems but Wikipedia does not show anything else
Every so often there's a comment on here that's simultaneously so ignorant and so arrogant that it crosses from offensive to hilarious. Congrats, this one is up there with the likes of "it could just be rsync".
Re: How to Solve It (1945)
#53Rich Hickey (creator of Clojure) references Polya several times in his classic talk "Hammock Driven Development". Here's a transcript:
https://github.com/matthiasn/talk-transcripts/blob/master/Hi...
I've long been impressed by Hickey's problem solving skills, so I took much of this talk to heart, and even bought a copy of HTSI. Can't say it really helped me any more than Rich's talk (as a programmer) but I'm thinking I'll give it another look.
Re: How to Solve It (1945)
#54How well does this book work for solving problems in Walter Rudin's "Principles of Mathematical Analysis?"
Baby Rudin, despite the somewhat patronizing name, is a second analysis text. There are many things that should have explanations that he expects you to already know. Swallow your pride and start with Abbott. You'll thank me later.
Now here's what I really think: I don't know your situation, but the odds are better than even that you should forget about it entirely. Doubly so if you're out of school. The bizarre math pride held by college kids (I did Math 55! I took a class with Stephen Wolfram's kid! I did all the exercises in Hartshorne! I proved X at age Y!) is real fucking stupid, coming from someone who badly wanted it. Your academic career or lack thereof will be determined about 90% by the people around you. It may piss you off, but you'll find it to be the same bitter truth I did.
Re: How to Solve It (1945)
#55Ah yes, just four steps: 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Look back. --- Compare with the Fenyman Algorithm: 1. Write down the problem. 2. Think real hard. 3. Write down the solution. https://wiki.c2.com/?FeynmanAlgorithm (The discussion on FeynmanAlgorithm links back to Polya's book since not everyone is Feynman.)
Reminds me of the official Microsoft guidance for big projects like migrating Exchange to the cloud, merging an Active Directory, or whatever. They’re all verbatim the same, except for the product name. 1. Gather requirements. 2. Devise plan. 3. Run a proof of concept 4. Run production migration …etc. It’s about as helpful as someone telling you to “do your job”.
Classic:
How to draw an owl:
1. carefully darw a circle as the head of the owl
2. draw the rest of the owlRe: How to Solve It (1945)
#56This 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…
If you don't come from a math-y background and are trying to "get into serious mathematics", the only way to do this is to get a PhD. I realize this might come across as gatekeeping, but the reality is that each subfield of math (or any scientific discipline) has its own set of tactics for approaching problems, which have been developed over the years by the people actually in the trenches. These problem solving stra…
There are a few books which admirably explain the assumptions etc.
- A Programmers Introduction to Mathematics (amazing for building intuition, explaining how to read mathematics papers, understanding beauty of proofs etc.)
- Elements of Mathematics for Economics and Finance (a quick jog through typical the high school and college math a non-mathematician would study)
- Papula's Mathematik für Ingenieure und Naturwissenschaftler (rigorous (for practitioners) and comprehensive. Starts from nothing, with sets, then teaches you fractions, then quadratic equations until you're doing vector analysis and Laplace transformations)
- Foundations and Fundamental Concepts of Mathematics by Howard Eves (wide overview of the man developments in mathematics, up to its publication)
Re: How to Solve It (1945)
#57How well does this book work for solving problems in Walter Rudin's "Principles of Mathematical Analysis?"
Baby Rudin, despite the somewhat patronizing name, is a second analysis text. There are many things that should have explanations that he expects you to already know. Swallow your pride and start with Abbott. You'll thank me later. Now here's what I really think: I don't know your situation, but the odds are better than even that you should forget about it entirely. Doubly so if you're out of school. The bizarre math…
My question was more rhetorical and for _synchronicity's_ sake than anything; I wanted to see what sort of replies would pop out.
As a recreational student, I've already committed to this text, difficulty be damned. I am no stranger to intellectual masochism. Nor do I care one iota for an "academic career," only for an understanding of results that were taken for granted in my prior CS mathematics undergraduate education at UWaterloo, which involved a few years of formal proof.
Would that I could have finished said undergraduate program, but tuition is expensive, and being rendered homeless partway through a CS program certainly complicates the financing, especially absent the monetary privileges afforded to one of a more affluent upbringing.
I appreciate the elitist and somewhat exclusionary language, though, despite admitted lack of knowledge regarding my situation.
Re: How to Solve It (1945)
#58Earlier quoted context omitted.
beyond the book, what contributions did he make? it would seem like the techniques should have helped him solve problems but Wikipedia does not show anything else
Every so often there's a comment on here that's simultaneously so ignorant and so arrogant that it crosses from offensive to hilarious. Congrats, this one is up there with the likes of "it could just be rsync".
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Re: How to Solve It (1945)
#59Earlier quoted context omitted.
Every so often there's a comment on here that's simultaneously so ignorant and so arrogant that it crosses from offensive to hilarious. Congrats, this one is up there with the likes of "it could just be rsync".
[flagged]
the guy clearly says
>but Wikipedia does not show anything else
go look at the wikipedia page for george polya and tell me what state of mind you need to be in to conclude that he didn't accomplish anything outside of publishing that book.
also btw
>born in 1887
he lived very long and had a very long career so you're still not close
>Died September 7, 1985 (aged 97)
Re: How to Solve It (1945)
#60Earlier quoted context omitted.
Baby Rudin, despite the somewhat patronizing name, is a second analysis text. There are many things that should have explanations that he expects you to already know. Swallow your pride and start with Abbott. You'll thank me later. Now here's what I really think: I don't know your situation, but the odds are better than even that you should forget about it entirely. Doubly so if you're out of school. The bizarre math…
My question was more rhetorical and for _synchronicity's_ sake than anything; I wanted to see what sort of replies would pop out. As a recreational student, I've already committed to this text, difficulty be damned. I am no stranger to intellectual masochism. Nor do I care one iota for an "academic career," only for an understanding of results that were taken for granted in my prior CS mathematics undergraduate educa…
You're right, I'm sorry. I took my frustrations out on you. Funny, I was also homeless in the middle of undergrad. I don't know what real analysis has to do with CS, except as a pre-pre-prerequisite to boring old ML math, but it's not my place. Good luck.