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I'll be teaching college algebra this summer. Last summer when I taught the same course, I finished lectures early (thanks mainly to LaTeX's Beamer package). I want to fill these gaps this time around.

To show students that advanced mathematics can be fun, and to mainly keep them engaged and focused during the summer course, I'd love to spend 10-20 in the middle of most lectures doing some riddles and paradoxes (e.g., the "Monty Hall Problem"), demonstrating a few things from, say, topology (e.g., by using Möbius strips), discussing nonintuitive theorems found in advanced mathematics (e.g., the Banach-Tarski Theorem, $\operatorname{card } \mathbb{N} = \operatorname{card } \mathbb{Z} = \operatorname{card } \mathbb{Q}$, etc.), and so on.

Obviously, I don't expect the students to actually learn this extra stuff. I just want to insert fun things in some of my lectures.

QUESTIONS:

  • What are some interesting topics, riddles, and paradoxes to discuss?
  • What are some fun math activities/experiments to demonstrate?
  • What are some books that I should consider looking through to find other ideas?
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The first time I saw this video, I enjoyed it. It also serves as a good illustration. –  Clayton Mar 24 '13 at 4:47
    
Yes, that's a very sweet video. I remember the first time I watched it too. I'll definitely consider it. Thanks for the suggestion, Clayton. –  Sara Mar 24 '13 at 4:56
    
Also, this page of riddles is a bit of a gem if you ask me, with varying difficulties. –  Clayton Mar 24 '13 at 5:01
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2 Answers

My all-time favorite collection of mathematical puzzles are two books by Peter Winkler: http://www.amazon.com/dp/1568813368 http://www.amazon.com/dp/1568812019

This is also good: http://www.amazon.com/dp/0486281523

Volumes 1-4 of this book are full of fun games (although the theory might be a little much for summer schoolers): http://www.amazon.com/dp/1568811306

And here's a cute video explaining the nature of exponential growth, lol: http://youtu.be/Q4gTV4r0zRs

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Concerning the paradoxes, I recommend the birthday problem. For most people it is truly an amazing result, and the phenonemon even has applications in cryptography (the birthday attack).

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