# ETH Math Youth Academy

The ETH Math Youth Academy is a project for students who want to engage in creative thinking and to delve deeper into exciting mathematics. The regular weekly classes are in the form of mini-courses on various extracurricular topics.

## From clock arithmetic to Diophantine equations |
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(Information Days, ETH Zurich, 04.09.2019) Introduction to modular arithmetic with applications to Diophantine equations. An example of Fermat's method of infinite descent is included in the end. Kaloyan Slavov (ETH Zurich, R. Pandharipande's Group) |
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## Catalan numbers |
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(Information Days, ETH Zurich, 05.09.2018) Introduction to Catalan numbers approached from different and yet equivalent perspectives. Kaloyan Slavov /ETH Zurich, R. Pandharipande's Group) |
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## Cantor's diagonal argument and uncountability of the reals |
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(Information Days, ETH Zurich, 07.09.2017) This lecture starts with the integers, goes through the rational and the algebraic numbers, and concludes with a proof that the set of transendental numbers in the interval [0,1] is uncountable by Cantor's diagonal argument. Kaloyan Slavov (ETH Zurich, R. Pandharipande's Group) |
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## Mathematical games and a nonconstructive existence proof |
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(Kantonsschule Baden, 07.04.2016) This lecture discusses three mathematical games, explains the notion of a winning strategy, and gives an example of a nonconstructive existence proof. Kaloyan Slavov (ETH Zurich, R. Pandharipande's Group) |
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## Patterns in plane drawings: Euler's formula for planar graphs |
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(Information Days, ETH Zurich, 06.09.2017) Introduction to planar graphs and Euler's formula. The lecture concludes with a proof that the sphere and the torus are topologically different. Kaloyan Slavov (ETH Zurich, R. Pandharipande's Group) |
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## Pick's formula: proof and applications |
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(Hull's school 25.06.2019) After giving a proof of Pick's formula, we discuss various - sometimes surprising - applications. Kaloyan Slavov (ETH Zurich, R. Pandharipande's Group) |
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## The second root of the quadratic equation Kaloyan Slavov |
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(Information Days, ETH Zurich, 05.09.2019) We use Fermat's method of descent to study a Diophantine equation which has an infinite - and interesting - set of solutions. (ETH Zurich, R. Pandharipande's Group) |