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Mathcamp Lectures

General Lecture     Short Course

General Lecture: The Hardest Math I've Ever Really Used

Abstract. What's the hardest math I've ever used in real life? Me, myself, directly - not by using a cellphone or a GPS device that somebody else designed. And in "real life" - not while studying or teaching mathematics?

I use addition and subtraction daily, adding up bills or calculating change. I use percentages often, though mostly it is just "add 15 percents". I seldom use multiplication and division: when I buy in bulk, or when I need to know how many tiles I need to replace my kitchen floor. I've used powers twice in my life, doing calculations related to mortgages. I've used a tiny bit of 2x2 linear algebra for a tiny bit of non-math-related computer graphics I've played with. And for a long time, that was all. In my talk I will tell you how recently a math topic discovered only in the 1800s made a brief and modest appearance in my non-mathematical life. There are many books devoted to that topic and a lot of active research. Yet for all I know, nobody ever needed the actual gory formulas for such a simple reason before.

Handout. hardest.html, hardest.pdf, hardest.png (source files: hardest.zip).

Short Course: Solving the Rubik Cube Using Group Theory

Abstract. The 3x3x3 Rubik cube has 43,252,003,274,489,856,000 reachable configurations; this is more than a human or a computer can crunch through in his or her lifetime. So how do we know this number is right? And how do we program a computer to solve the Rubik cube without going through all these configurations? By abstract thought alone and a powerful tool called "group theory", we will answer these question and many similar ones involving other "permutation group" puzzles, in a completely systematic manner.