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It is a bit of strange that I haven't be trained on such a topic. It wouldn't influence my daily work but I would like to study some materials on my own.

So, dear fellows, you got any classic ref in your mind? I expect the material can cover logics commonly used in math proofs on a daily base.

Thank you in advance.

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As a start, you might consider the tutorial that comes with my DC Proof software. Download it at dcproof.com –  Dan Christensen Oct 7 '12 at 4:03
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up vote 6 down vote accepted

The deductive reasoning "commonly used in math proofs on a daily base" is regimented by classical first-order logic. So that's where to start.

If you asked me to suggest just one book for beginners at logic with some mathematical background, then I think I would nowadays recommend the particularly accessible and well-written Ian Chiswell and Wilfrid Hodges, Mathematical Logic (OUP 2007) as the best starting point.

But different people with different backgrounds will like different books. As an introductory guide to just some of what is on offer, you'll find an annotated Teach Yourself Logic reading list/study guide at http://www.logicmatters.net/tyl

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