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Ask HN: Math books like SICP?

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Ask HN: Math books like SICP?

#1

Post by nextos »

I'd like to start learning undergrad math at a rigorous level.

As a CS grad I already covered certain topics like abstract algebra at a respectable level. But I'm lacking consistent and broad knowledge throughout all areas.

I'm looking for math books covering undergrad topics like SICP, which Peter Norvig described as "[...] a way of synthesizing what you already know, and building a rich framework onto which you can add new learning over a career" [1].

[1] http://www.amazon.com/review/R403HR4VL71K8

Re: Ask HN: Math books like SICP?

#4

Post by jvreeland »

It's not nearly as easy to work through as SICP is but Principles of Mathematical Analysis by Walter Rudin (sometimes referred to as little Rudin) is a great place to start if you're interested in analysis. It's a hard book, but it's pretty much the standard for undergrad analysis.

Re: Ask HN: Math books like SICP?

#5

Post by kliao »

jvreeland wrote: post #4

It's not nearly as easy to work through as SICP is but Principles of Mathematical Analysis by Walter Rudin (sometimes referred to as little Rudin) is a great place to start if you're interested in analysis. It's a hard book, but it's pretty much the standard for undergrad analysis.

Echo the above. Pairing little Rudin with a more user-friendly book like Understanding Analysis by Abbott is a great way to learn the material if you get stuck.

Re: Ask HN: Math books like SICP?

#6

Post by cabacon »

gms wrote: post #2

It's difficult to find what you are looking for, since maths is a much older field. However, Spivak's 'Calculus' is pretty close: http://www.amazon.com/gp/aw/d/0914098918 .

I clicked on this topic in order to make this suggestion. To expand on it a little bit, I was a math major and read Spivak's 'Calculus' after I had already taken real analysis. I found it delightful - it really approaches the topics from first principles and unlike many calculus textbooks actually goes through the effort of presenting proofs of the theorems. Highly recommended.

As some recreational reading, less suiting the original request, I very much enjoyed David Foster Wallace's 'Everything and More: A Compact History of Infinity' (http://www.amazon.com/Everything-More-Compact-History-Infini...). DFW is not for everyone, but I enjoyed it a lot. Maybe just check it out of the library first to see if it's for you.

Re: Ask HN: Math books like SICP?

#8

Post by j2kun »

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, fields, r-modules, and advanced topics (toward the end) with the unifying theme of how they work and relate as categories. It is very much a book that focuses on the why over the what and how. And there are many many many juicy exercises.

I would recommend against Spivak's Calculus on manifolds. It's too dense and too focused on advanced topics (unless you're an ivy league undergrad, you don't learn cohomology). That being said I don't have an analysis reference that fits your request.

As a CS person I can continue with book recommendations related to computing-related topics in math (computational algebraic geometry comes to mind). Let me know if you're interested.

Re: Ask HN: Math books like SICP?

#9

Post by zodiac »

Math is a much, much broader field than the part of Computer Science than SICP covers, so it's really hard to search for "consistent and broad knowledge throughout all areas". Do you really need to learn analytic number theory? category theory? axiomatic set theory? tensor calculus?

My suggestion would be to narrow it down to a specific field you're interested in like abstract algebra and ask for suggestions about that field. Even narrowed down the field might be too big - a basic introduction to abstract algebra would probably contain the same amount of information as SICP.

CS people tend to find discrete math and linear algebra most useful in their work, but maybe you want to learn something just for the sake of it and not for work.

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