Ages: 13-18

How do you know for sure that the commutative property works? In other words, can you prove that ab=ba? And can we really trust the Pythagorean Theorem? And how many prime numbers are there anyway? Is it okay to take things on faith in mathematics? We will do formal proofs collaboratively to begin to understand the underlying foundations of mathematics. Humans have an inherent desire to seek structure. Proofs can satisfy this architectural instinct. It can be very powerful for a teenager to successfully prove something – to know that something is absolutely true, no matter what, no ifs ands or buts. This course requires a basic ability to use variables

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