ETH Math Youth Academy

Objectives

The ETH Math Youth Academy is an ambitious long-term project especially designed for Gymnasium students (age 13 or above) who like mathematics and want to delve deeper into its exciting world. The regular weekly sessions take place at ETH Zentrum and treat various topics that go beyond the regular Gymnasium curriculum.

Even though Switzerland is best in Europe in terms of the general quality of mathematical education in school and the level of the students is homogeneously very high, opportunities for the enthusiastic students to reach a level beyond the standard mathematical curriculum do not abound, at least in comparison to other countries (in Eastern Europe or the US, for instance). Our goal is to close this gap by providing students with such opportunities.

Topics outside the regular curriculum

The focus is on creative, out-of-the-box thinking and on rigorous proofs. The treated topics are not part of the regular Gymnasium or university curriculum and are not relevant for exams in school. Instead, the classes can lead to participation in mathematical Olympiads and can inspire various projects. Students will gain momentum for further university pursuits in technical disciplines. Just as a student who likes music can play in an orchestra outside of school, a student who likes mathematics is welcome to attend our programme.

Prerequisits

Participation is free of charge. There are absolutely no specific prerequisites besides being comfortable with the standard school material and having the interest and motivation to come to ETH Zurich for two hours of extra mathematics a week. The classes are fun, friendly, and intellectually stimulating. The language of instruction is English.

Organization of classes

The classes are organized in the form of mini-courses on various topics, each one starting completely from scratch and reaching interesting and challenging problems. In this way, students can attend as often as their schedules allow.

There are also separate intermediate and advanced classes. It is therefore possible for a student to attend the programme over the course of several years.

Current situation

About 40 enthusiastic students currently attend the programme, without formal credit or grades, but just for personal enrichment and academic satisfaction. Most of them are from Zurich, but some commute from Wetzikon, Zug, Luzerne, or even Solothurn or Romanshorn in order to attend the classes. We are pleased that the engineers and scientists of the next generation have such a zeal for challenging mathematics already during years in school.

This Downloadarticle (PDF, 709 KB)vertical_align_bottom in the Bulletin of the VSMP, Issue 131, has been addressed specifically to mathematics teachers and includes a full detailed class sample, giving readers a concrete idea of how a class at the ETH Math Youth Academy looks like.

The project was featured at ETH News: Creative proofs with pigeons and boxes.

The following Downloadone-page article (PDF, 55 KB)vertical_align_bottom has been written for the European Mathematical Society Newsletter and is addressed to the entire mathematical community in Europe.

This external pageinterview (Russian)call_made was published in the Russian-language Swiss newspaper Nasha Gazeta and is also available as an unofficial Downloadtranslation to English (PDF, 82 KB)vertical_align_bottom.

Parallel to the weekly classes, we have launched an initiative for giving public talks at various Gymnasiums in Switzerland, emphasizing the aesthetic side of mathematics. We would love to communicate some of the most beautiful pieces of mathematics and to present them in an elementary and accessible way. These talks are designed for a broad general student audience. We are looking forward to further invitations.

Visited Schools

27.10.2015: Literargymnasium Rämibühl, Zurich

• Mathematical Induction: 
  external pagevideocall_made
  

07.04.2016: Kantonsschule Baden

• Mathematical Games:
  external pagevideocall_made, Downloadslides (PDF, 350 KB)vertical_align_bottom
  

31.09.2016: Realgymnasium Rämibühl, Zurich

• Mathematical Colorings

09.02.2017: Kantonsschule Enge, Zurich

• Algebra, Geomtery and Pythagorean Triples:
  external pagevideocall_made, Downloadslides (PDF, 381 KB)vertical_align_bottom
• Mathematical Colorings: 
  external pagevideocall_made, Downloadslides (PDF, 291 KB)vertical_align_bottom
• The Extreme Element Principle:
  external pagevideocall_made, Downloadslides (PDF, 459 KB)vertical_align_bottom

06.09.2017: Information days, ETH Zurich

• Patterns in plane drawings: Euler's formula:
  video

07.09.2017: Information days, ETH Zurich

• From integers to reals: a walk in the world of numbers:
  video

02.02.2018: Kollegium Spiritus Sanctus, Brig

• Have a second perspective. Double counting:
  external pagevideocall_made

08.05.2018: Kantonsschule Solothurn

• Pick's formula

05.09.2018: Information days, ETH Zurich

• The answer is ... 1,2,5,14,42,...
  video

25.06.2019 Hull's school

• Pick's formula
  external pagevideocall_made

04.09.2019: Information days, ETH Zurich

• From clock arithmetic to Diophantine equations
  video

05.09.2019: Information days, ETH Zurich

• The second root of the quadratic equation
  video
  

Talk: Diffie-Hellman key exchange

Is it possible for two parties to establish a common secret, if they are only allowed to interact through an insecure channel? The talk is fully accessible to advanced high school students, who are familiar with elementary number theory (specifically with modular arithmetic). external pageVideocall_made

YouTube channel

Some of the talks are also available on our external pageYouTube channelcall_made.