Reddit reviews The Art of Computer Programming, Vols. 1-3

sipser (I have the first edition which you can get on the cheap, it's very good.)

AIMA

Dragon

Naturally, TAOCP.

Many will also recommend SICP, though I'm not quite sure that's what you're angling at here, it's probably worth browsing online to see.

I'm assuming he/she will have to read them first and get back to you, but set gets some great reviews on amazon

I'm slogging through Donald Knuth's The Art of Computer Programming and starting to suspect that my smidgen of post-high school math won't quite cut it. I'm a bit of an autodidact, but I'm not an idiot, so -- what books does reddit suggest for a thorough grounding in number/set/group theory, calculus, problem-solving strategies, proofs and proof-checking, before actually tackling TAoCP?

You know what, TAoCP books are pretty good at introducing the mathematical notation from a programming point of view and they do touch on a few subjects you mentioned above. Otherwise maybe a good introductory discrete mathematics book, they usually introduce all the notation and concepts you need to know without any prior knowledge.

Also it is probably better to pick a subject and then learn the notation that goes with that subject as the notation itself can vary from branch to branch. I don't think there is a universal mathematical notation that is standard throughout the world. There is a lot of commonality but it is the small variations that can cause confusion.

The goto theory book by Sipser.
Excellent for C programming.
Programming in general.
My favourite.
You can probably find all of these at a library.

Anything by Simon Singh is worth reading. In addition to what others have recommended, these books are good:

[The man who loved only numbers](http://www.amazon.com/MAN-WHO-LOVED-ONLY-NUMBERS/dp/0786884061/ref=sr_1_1?ie=UTF8&s=books&qid=1254333710&sr=8-1
)

Flatland

Prisoner's Dilemma

A mathematician reads the newspaper

A mathematician plays the stock market

Innumeracy: mathematical illiteracy and its consequences

Also, while not exactly about Maths:

Surely you are joking, Mr Feynman

What do you care what other people think?

The Art of Computer Programming

Might be biased, but I'm a big fan of Jeff Erickson's Algorithm Notes, which I think are better than a lot of textbooks.

If you really want a book, CLR Algorithms and The Art of Computer Programming both get recommended a lot, with good reason.

If you're interested in computational theory, the New Turing Omnibus and Spiser's Theory of Computation are two good choices.

Finally, I'd check out Hacker's Delight. It's a lot more on the electrical/computer engineering side of things, which might interest you, and it's very detailed while still being quite excellent.

How about this lovely knick-knack

Some books on my wishlist (not sure if you're okay with math):

TAOCP

Operating System Principles

Computer and the Brain

Path to the Quantum Computer

Thanks for the encouraging words, they definitely help. :)

I started in a language of old called BASIC, which if anything only really taught me about code flow. The first language I began to really do anything with though was C, and today I work mostly in C++ and some other compiled languages like Java for desktop applications.

Anything that isn't a desktop application I'll generally rely on an interpreted language such as Perl. They're great for gluing software and services together, or if you just don't want the hassle of porting compiled code where the target machine can feasibly run an interpreter.

Java's a good place to start, in my opinion. You'll have direct exposure to having to using datatypes properly (such as character strings and integers) as well as have an earlier understanding of object-oriented programming, since basically everything in Java is a class/object instance. It's also C-style in syntax, which a lot of languages tend to share in common. So when you go to learn other languages like C++, D, and lots of others I'm forgetting, it'll be easier to just kind of pick them up and go.

Also I've mentioned it elsewhere in the AMA, but it's worth repeating. Pay extra attention to the hows and whys of what's happening when you're learning programming. It's really tempting to learning all the features of a language or attempting to get into more advanced topics of programming, but having an idea of why you're doing things the way they are will be key to your success. So you should put equal emphasis on not just learning Java as a language, but as a tool to express programming concepts. The Art of Computer Programming has essentially been the go-to literature since I can remember for that.

I love Ruby Koans.
If we're going back to other references for general programming and algorithmic knowledge I would also recommend:

• Don Knuth's "Art of Computer Programming"
  
• Abelson, Sussman and Sussman's "The Structure and Interpretation of Computer Programs" (free)
  
• Reading lots of code. Reading other people's code and learning from it is one of the most valuable reference materials around. :)
  
  Edit: "general" was the wrong word to use. Thanks worst!

As far as I know to understand how a computer works it's also important to understand the algorithms running on that.

I'd suggest you to read something light like this (http://www.cse.ohio-state.edu/~gurari/theory-bk/theory-bk.html) and after that read things like Knuth (http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=pd_sim_b_2/191-9538329-5615213) (http://www.amazon.com/Art-Computer-Programming-Volumes-Boxed/dp/0201485419).

MIT's introduction to CS is also a nice begin (http://academicearth.org/courses/introduction-to-computer-science-and-programming)

All I know is anyone in the computer science, computer engineering, networking, etc. should attempt to get their hands on the Art of Computer Programming.

Link to books

Knuth's Art of Computer Programming

edit: I suppose a ";-)" smiley would have made the sardonicism a bit more obvious.

The Art of Computer Programming by Donald Knuth

Donald Knuth:

http://www.amazon.com/Art-Computer-Programming-Volumes-Boxed/dp/0201485419/