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Textbook

Bob Dumas and John McCarthy, Transition to Higher Mathematics: Structure and Proof (2nd edition).
Please note that the 2nd edition is a free download in pdf format, available from McCarthy's webpage at http://www.math.wustl.edu/~mccarthy/SandP2.pdf .
Please download the book and keep it on your device. You should seriously consider acquiring a hard copy, either by printing it yourself or by taking it to Copy Cow.

Websites

Wikipedia is, perhaps surprisingly, not a bad source for background material on basic definitions and results in many areas of mathematics.