References for Math 220 Fall 2012:
Proof in Mathematics, Philosophy, and Law

These are classics — probably available in your local library. They are very different from each other.
George Polya, How to Solve It, Princeton University Press (paperback)
George Polya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics   and   Volume 2: Patterns of Plausible Inference, Princeton University Press (paperback)
Richard Courant & Herbert Robbins, What Is Mathematics?, Oxford University Press (paperback)
Hilbert's Foundations of Geometry, a classic revisiting Euclid with a critical eye to clarifying the foundations.
Douglas R. Hofstadter, Godel, Escher, Bach: An Eternal Golden Braid, Basic Books, 1999, ISBN-10: 0465026567

The following text gives some examples of proofs in mathematics:
D'Angelo & West, Mathematical Thinking: Problem-Solving and Proofs, second edition, Prentice-Hall

Tribe, "Trial by Mathematics: Precision and Ritual in the Legal Process" From Harvard Law Review, Vol. 84, April 1971
Kerr, "Why Courts Should Not Quantify Probable Cause", GWU Law School Public Law Research Paper No. 543, 2010.

Whither Mathematics? by B Davies - 2005 1350. NOTICES OF THE AMS. VOLUME 52, NUMBER 11.

Highly complex proofs and implications of such proofs. BY MICHAEL ASCHBACHER.

Skolem and pessimism about proof in mathematics. BY PAUL J. COHEN

Judith V. Grabiner, "Why did Lagrange 'Prove' theParallel Postulate?"

Chandler Davis The Role of the Untrue in Mathematics