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I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the "Ham Sandwich Theorem". I feel a good source for the types of things I'd like them to read is this post. I would have each (group) student do a write up on a particular subject. Does anyone know of any books that give a list of results that are understandable for a calculus student?

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Proofs from the book. Martin Aigner, Gunter M. Zeigler. This is not exactly what you are asking for, but this is an amazing collection of proofs which everyone must see. – Norbert Jan 30 '12 at 20:24
up vote 9 down vote accepted

Journey through Genius: The Great Theorems of Mathematics, William Dunham. Definitely within the grasp of calculus students (maybe too easy?), and contains discussion of twelve classic theorems. The theorems come from throughout the history of mathematics (from the quadrature of the lune and Archimedes' calculation of circular area to Cantor's proof of the uncountability of the reals), so it also provides a nice perspective on some of the most famous mathematicians. I loved this book when I first read it in high school.

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Thougher going than Dunham's books (very higly recommended!) is Aigner-Ziegler's "Proofs from THE BOOK". Consider also Pólya's classic "How to solve it", it shows not finished results, but how to go from the problem to a clean solution.

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The Mathematical Universe: An Alphabetical Journey Through the great Proofs, Problems, and Personalities, by William Dunham.

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$Q.E.D.$ is a cute, compact, little book of proofs easily found at Barnes and Noble.

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