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There are a number of freely available online resources for proofs & mathematical reasoning. Besides the already mentioned "Book of Proof", try:

https://sites.google.com/site/mathematicalreasoning3ed/

http://www.math.vt.edu/people/day/ProofsBook/

http://giam.southernct.edu/GIAM/

For anybody looking for freely available maths related texts online, three great resources are:

http://aimath.org/textbooks/approved-textbooks/

http://web.archive.org/web/20170126161813/http://people.math...

http://www.openculture.com/free-math-textbooks




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