# Mathematical analysis - text book recommendation sought

A rather subjective question, I admit, but I'm looking for a recommendation for a textbook to help me improve my understanding of mathematical analysis.

I come from a computing background, with a University level degree. My high-school mathematics was all focused on mechanics/physics rather than pure maths and statistics. I've followed formal undergraduate courses on signal processing, and informal postgraduate lecture series subsequently - for personal interest, not credit. I feel confident that I have the skills to digest any well-written undergraduate or masters-level text.

I recognise that I am (relatively) weak with respect to analysis when I read the Wikipedia pages for subjects such as:

I am interested to bolster my understanding of the principles of mathematical analysis and to go on from this to improve my understanding of distributions and how they relate to both analytic and non-analytic functions. While I recognise the value of proofs, and I'm not looking for a reference book from which to crib formulae, my principal interest is in the practical application of theory rather than its elegant abstract justification. For this reason, I'm drawn more to presentations with intuitive over formal justifications for theorems.

Suggestions?

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At the very least you should start with Rudin's Principles of Mathematical Analysis. It is abstract, it is formal, but with many things mathematical, the devil is in the details. "Intuition" can easily lead you astray if you are not prepared to back it up with solid understanding. (Intuition is also usually developed after doing a lot of homework problems ;p.)

Then, since you are interested in developing "pure" intuition, I would suggest reading through Counterexamples in Analysis by Gelbaum and Olmsted. Analysis is largely naively intuitive... except where it is not. And if you want to come to an understanding of mathematical analysis by acquiring intuition, it is better to be forewarned about where your intuitions may go wrong.

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Many thanks for the suggestions - both look as if they're appropriate... now I've some Xmas reading. BTW: I hadn't intended to show an absolute aversion to rigour (I don't consider myself a complete lightweight) just that, on this subject, for now, I prefer to read pragmatic expositions to pedantic ones. –  aSteve Dec 2 '11 at 15:15