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Primes, Divisibility, and Modular Arithmetic

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Number theory is all about adding and multiplying integers: pretty simple stuff, good for elementary school or for PhD mathematicians. Dr. Arnold Ross says of number theory, that the purpose is “to think deeply of simple things.” So let’s do that together.

This session includes multiple problem sets beginning with prime numbers, continuing to divisibility and its rules, and concluding with Modulo (Modular Arithmetic).

Coins in Twoland

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In Twoland, the only money is coins with value 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and so on. How many ways can change be given, following Twoland’s strict rules? In this whimsical session, participants will practice precision and organizational skills.

This session is also suitable for student math circles and the classroom.

The 1-to-100 problem

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This exercise can be used for middle school students and older. The original problem seems almost impossibly difficult, but there are obviously many ways to approach it by considering simpler problems. As they investigate it, students are actually drilling their multiplication and addition facts. In addition, depending on how detailed a study you want to make, the students will be forced to do a lot of simple algebra to obtain the results they need. They may also learn something about commutativity, associativity, and symmetric functions.