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Ask HN: Math books like SICP?

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Re: Ask HN: Math books like SICP?

#81

Post by radmuzom »

karamazov wrote: post #66

I'm a big fan of SICP. I'd describe it as "hard-core": requiring hard work, but extremely rewarding for the people who take the time and effort to go through it. I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology): 1. Principles of Mathematical Analysis by Rudin ( http://www.amazon.com/Principles-Mathematical-Analysis-Inter... ) 2. Al…

Great list. Another addition to the list would be

4. Topics in Algebra by I.N.Herstein.

It has a slightly better (and tougher) set of problems than what you would find in the book by Artin.

Re: Ask HN: Math books like SICP?

#82

Post by pervycreeper »

auvrw wrote: post #74
hf wrote: post #46

Earlier quoted context omitted.

Absolutely astounding: I have been looking for this book ever since I pored over it in the Wolfson Reading Room in Manchester Central Library 5 years ago. I didn't take down the authors' names, though, referring to it as "that yellow mathematics book" then and ever since. I credit that book with much if not all my mathematical insight. Thank you. (Just seeing that cover leaves me all tear-eyed, reminiscing over that…

> "that yellow mathematics book" replace "that" with "those" ( http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics ). the dover books are also a good series, and pretty much anything by Artin is good. i also looked at the Halmos book a couple of people have mentioned. perhaps one thing to be aware of, though, is that you're not always going to learn things in the linear way they're layed out on the page. moreo…

But that's not a Springer book, it appears to be published by Dover, and the covers look totally different. The GTM series is also highly variable in quality.

Re: Ask HN: Math books like SICP?

#85

Post by caraboga »

jjoonathan wrote: post #16
nextos wrote: post #12

Earlier quoted context omitted.

Thanks. Axler's LADR is indeed fantastic, I have already worked through 1/2 of it. I'm really happy to see my opinion seconded. It's really short and precise. Some people seem to prefer Halmos' Finite Dimensional Vector Spaces, but I found the presentation less didactic. Perhaps it's also more of an upper division text, and I'm not there yet. I was looking for a real analysis companion, perhaps baby Rudin. I was also…

I third the recommendation on Axler's LADR. I'd actually like to hear about alternatives to Rudin. My undergrad analysis class used it, but it's lack of diagrams was particularly bothersome. I'd spend an hour digesting a rat's nest of a paragraph only to discover that the underlying concept was simple enough that even a rough sketch ought to be able to get the gist of it across in seconds.

Wade's an easier book that has more undergraduate aids. http://www.amazon.com/Introduction-Analysis-Edition-William-...

I also like Strang for Linear Algebra for undergrads. Beyond that it's Hoffman and Kunze.

Re: Ask HN: Math books like SICP?

#86

Post by tel »

nextos wrote: post #69
tel wrote: post #51

Earlier quoted context omitted.

I was going to recommend this one. Conceptual Mathematics is wonderful in that it provides a narrative of intuition instead of just the proofs. It's kind of like seeing How It Is Made for algebra.

Do Conceptual Mathematics and Sets for Mathematics cover the same ground?

I've only read Conceptual Mathematics; sorry for the confusion.

CM covers Category Theory as a general tool for probing and exploring algebraic concepts beginning as simply as endomorphism and extending all the way out to how it can be the foundations of a generalization of set theory via Toposes... all in a cheery and explorative fashion which really illuminates why the ideas work instead of merely stating them.

I'm not sure what the required background might be, but it's probably pretty minimal.

Re: Ask HN: Math books like SICP?

#87

Post by j2kun »

dkural wrote: post #75
j2kun wrote: post #8

Sheldon Axler's "Linear Algebra Done Right" has my highest recommendation if you want expertise in linear algebra. As a followup, Paolo Aluffi's "Algebra: Chapter Zero" is the best synthesizing text for abstract algebra for a beginning graduate student. The thing that makes it so amazing is the writing style: it introduces and demystifies category theory, and then discusses groups, rings, modules, linear algebra, fie…

Axler's book is a bit troublesome in inventing new terminology unnecessarily. There are also a number of minor errors, and while the abstract structure is fleshed out, it's not often well "motivated". I like the focus on theoretical instead of a matrix-first approach, I just think it's not well done.

Like what specifically?

Re: Ask HN: Math books like SICP?

#88

Post by auvrw »

pervycreeper wrote: post #82
auvrw wrote: post #74

Earlier quoted context omitted.

> "that yellow mathematics book" replace "that" with "those" ( http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics ). the dover books are also a good series, and pretty much anything by Artin is good. i also looked at the Halmos book a couple of people have mentioned. perhaps one thing to be aware of, though, is that you're not always going to learn things in the linear way they're layed out on the page. moreo…

But that's not a Springer book, it appears to be published by Dover, and the covers look totally different. The GTM series is also highly variable in quality.

perhaps the GTM series has some bad titles; i haven't read them all. but it has some good titles, and from the description original poster's background, it's probably as far as the person wants to stretch right now. sure, the cambridge advanced math series might be more "quality," but those also tend to be both very focused (in terms of specificity of the topic) and very dense (in terms of delivering a lot of results with almost zero fluff).

Re: Ask HN: Math books like SICP?

#89

Post by decasteve »

nextos wrote: post #69
tel wrote: post #51

Earlier quoted context omitted.

I was going to recommend this one. Conceptual Mathematics is wonderful in that it provides a narrative of intuition instead of just the proofs. It's kind of like seeing How It Is Made for algebra.

Do Conceptual Mathematics and Sets for Mathematics cover the same ground?

A lot of the same ground but Sets for Mathematics is more concise and probably goes into more depth by the end. If you've previously done rings, groups, vector spaces, topological spaces, the concepts tie nicely together in Sets for Mathematics.

Conceptual Mathematics puts a lot more time up front motivating the material with examples and tries to build your intuition before getting into the details. If all you've done previously was linear algebra and some discrete math, this book is probably better.

Re: Ask HN: Math books like SICP?

#90

Post by swordswinger12 »

karamazov wrote: post #66

I'm a big fan of SICP. I'd describe it as "hard-core": requiring hard work, but extremely rewarding for the people who take the time and effort to go through it. I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology): 1. Principles of Mathematical Analysis by Rudin ( http://www.amazon.com/Principles-Mathematical-Analysis-Inter... ) 2. Al…

Personally I have heard nothing but bad things about Artin. Most people I know recommend Dummit and Foote instead; its increase in difficulty is supposedly offset by superior presentation of the material.
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