An Introduction to Mathematical Reasoning

Run, don't walk, and get "An Introduction to Mathematical Reasoning"by Peter Eccles. That will open your eyes to mathematics, as done by mathematicians. After that, anything by Serge Lang. He is a first-rate mathematician and a fine educator. A master of mathematical exposition, a rare talent. I started with two books: "Principles of Mathematical Analysis" by Walter Rudin, and "Abstract Algebra" by Israel Herstein. Keyword is "started". Nearly every paragraph of either book sent me to a goose-chase of research and reading up on supporting materials. Safe to say that by the time I was nearly done with either, I have acquired about 50 other math books and had about zero social life ;-) Good news is that good math books are cheap, compared to anything computing. You can find classics for $1-$5 in most yard sales and 2nd hand bookstores. The trick is to buy thin math books; the giant, multi-color text books they use in schools are highly confusing, at least to me. It's 200 pages of math stretched to 1200, with a similar jump in price.…

I second the Eccles recommendation. It's a really great introduction to formal mathematics.

Fantastic reply, thank you. An Introduction to Mathematical Reasoning loks good, just going to read some reviews on Amazon first. Would 'How To Solve It' be aimed at someone like myself?

"An Introduction to Mathematical Reasoning" by Peter J Eccels. Teaches the vocabulary of mathematics, just the basics you need to think like a mathematician, not a mathematics user like most science texts. "How To Solve It" George Polya. Heurists and problem solving skills, by a great mathematician. Do a google search, specially in the sci.math newsgroup. Again, read books by mathematicians for mathematicians; they're often far more enjoyable and actually far more straightforward (I was often confused by the examples in my school work; I didn't care for "vehicle moving at speed X" or "object falling at from height Y". We all have a different internal visual mind and I tended to think in abstract patterns, usually colors, lines or nested bodies, without real physical objects distracting me.)