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Resources
		Eric Weisstein's Mathworld	A comprehensive encyclopedia of mathematics which is improving and expanding all the time. This website was shut down for a year because of legal action by the CRC Press. Eric Weisstein approached CRC to publish a book containing a snapshot of the website, and they duped him into signing a contract that gave them exclusive rights to the entire website. Subsequently, they obtained an injunction forcing him to shut it down. The website is now online again, but Wolfram Research (Weisstein's employers, who host the site) have to pay CRC Press if sales of the book fall below projected targets. Additionally, CRC press have the right to publish copies of the website at any point in the future, even though they have no involvement in its development. A boycott of CRC by the mathematical community makes this unlikely to happen, though.
		Ask Dr. Math	A maths question and answer service. You can search the archives for previous questions that have been answered, or ask your own question.
		Online publications of Julius Orion Smith	Julius Orion Smith is at the Center for Computer Research in Music and Acoustics at Stanford. He's written several books on signal processing.
		BJMath.com	A website about the mathematics of gambling, including a number of downloadable books and papers.
Recommended books
			Logic - A Very Short Introduction by Graham Priest This is a great introduction to logic – well worth reading before you look at anything else on the subject. It doesn’t go into a lot of technical detail, making it easier to understand than most books on logic. However, it tackles head-on many philosophical difficulties that even quite advanced books tend to brush under the carpet.
			100% Mathematical Proof by Rowan Garnier & John Taylor This is a brilliant book on mathematical logic and proof. Most books on logic are very specialized, and focus on detailed formal proofs of arcane theorems that are far removed from the kind of semi-formal proofs that mathematicians actually write. This book gives a very clear explanation of the relationship between formal logic and the proofs found in normal mathematics. Tragically, this wonderful book didn't sell well, and it is now out of print. Its rarity makes it difficult (and expensive) to find secondhand – I've seen it for prices between £25 and £100. I contacted one of the authors, John Taylor, and he said that he gets around one enquiry a year about the book, but not enough to interest a publisher. So, if you want to see this book in print again, get in touch with him.
			The Foundations of Mathematics by Ian Stewart & David Tall This book starts off with the maths you did at school, and gradually introduces the more formal approach used by professional mathematicians. First, it describes the basic concepts of sets, relations, and functions. Then it describes the formal construction of the natural numbers, integers, rational numbers, real numbers, complex numbers and quarternians. It ends with a chapter on infinite numbers. The last few chapters are challenging, but there's no other book that gives such an accessible introduction to the foundations of mathematics.
			Mathematics of the Discrete Fourier Transform (DFT) by Julius Orion Smith This explains the DFT pretty much from first principles, including an incredibly clear explanation of complex numbers and Euler's formula, eiθ = cosθ + isinθ. If you want to really understand the DFT, as well as know how to use it, this is the book to read. I found it much easier to understand and more useful than books on the continuous Fourier transform (e.g. Bracewell): firstly, you don't need much calculus to derive the DFT; secondly, if you ever Fourier-transform anything on a computer, you'll be doing the DFT, so that's what you need to know about anyway. You can read the book online here.