Mary L Boas "Mathematical Methods in the Physical Sciences" [1] has absolutely been my favorite and most-used maths text in the 9 years since graduating uni. It's like a reference manual of just about all the non-CS (i.e. continuous/non-discrete) mathematical techniques required in my career. Highly accessible. It's a little too terse in places but I prefer this style of presentation over the insane long-form verbiage in other books I've since discarded which can make even simple topics seem overwhelming: the "Boas" book gets right to the point.
Edit: Calling it a mini-TAOCP of most of the maths needed for physics/EE work might be a bit of a stretch, but I've yet to see another maths text that does better as a highly readable, self-contained and compact reference.
Edit2: I moved house once and thought I'd lost my copy from university. I eventually found it, and yes, I have two copies... It's that important to me for brushing off the things I've forgotten :)
It is a fantastic book. It isn't (only) a reference book though. For me it was the best way of learning the maths used in my physics degree.
The book has many worked examples, and the extensive end-of-section questions have the answers in the back of the book (for every 2nd question). This means you can learn by "reading then doing", and see if you have got the answers right - something many textbooks lack.
When I try to learn from other technical books, I often find myself thinking "I wish they'd written this in the same style as Boas".
I see a lot of complaints in amazon reviews about the lack of answers making self-study difficult.
It got me wondering...suppose there were a website for autodidacts in math and similar topics? Something where people could post and discuss their answers to exercises. It'd solve the whole problem.
You can use math.stackexchange.com for this today. It's frowned upon to just ask an exercise from a book w/o even trying to solve it, but if you show that you made an effort but got stumped, or if you show your solution and ask if it's correct, people will gladly help you out.
I think academics would get pretty annoyed :) Most of my professors just use the exercises from the textbook for homework, usually on the assumption that you can't find the answers online.
I'm sure they would, but I'm more concerned about people in my shoes. University tuition has gotten so expensive these days that I think we need solid alternatives...and that they can use some of that fancy tuition money to write their own exercises, if they don't trust students to do their own work.
Or they could just trust the students. At my university the honor code such a big deal that they let students take closed-book tests at home.
Not a problem - Boas has the answers for every 2nd question - for tutorials, we would be asked to do the ones without answers.
Maybe DennisP's idea could do the same thing - only post answers to the odd-numbered questions. Of course, DennisP's scheme would only work for books that actually have decent end-of-section questions, unless people made up extra questions as well ...
Concrete Mathematics by Graham,Knuth, Patashnik is (explicitly, even) a mini-TAOCP for much* of the mathematical underpinnings of computer science.
* I say much rather than most or all since it's focused on asymptotics, recurrences, number theory. Modern theoretical Computer Science draws on a much wider variety of mathematical methods.
Concrete Mathematics is outstanding, and I'm happy to think I'm getting an overview of TAOCP by (very slowly) working my way through Concrete Mathematics.
Edit: Calling it a mini-TAOCP of most of the maths needed for physics/EE work might be a bit of a stretch, but I've yet to see another maths text that does better as a highly readable, self-contained and compact reference.
Edit2: I moved house once and thought I'd lost my copy from university. I eventually found it, and yes, I have two copies... It's that important to me for brushing off the things I've forgotten :)
[1] http://www.amazon.com/Mathematical-Methods-Physical-Sciences...