2020 YAU INTERNATIONAL MATHCAMP

Number Theory

Lecturer:	Prof. Jiu Kang Yu (于如岡), The Chinese University of Hong Kong
E-mail:	jkyu@ims.cuhk.edu.hk

 

Course Description

In this course, we will have some fun with the problems of constructions using ruler and compass. There are of course the three famous problems from the greek heritage. In addition, we will consider the following problems that fascinated some very famous mathematicians in their teen years:

• C.F. Gauss asked: what regular n-gons are constructible. He found out, among other things, that the regular 17-gons is constructible.
• E. Galois asked: how to understand the solutions of a polynomial equation? can the solution be expressed in terms of square roots, cubic roots, etc?
• S.-T. Yau asked: given an angle, a side length and the length of an angle bisector, can one recover the triangle? can this be done using ruler/compass construction?

Although such problems seem all about geometry, the key to these problems is really algebraic and number theoretic in nature, leading to tools that are fundamental to modern research in number theory. We will take the mathcampers on this remarkable journey. The only required background is an eagerness to explore, just like the teenager mathematicians who started this journey.

 

Course Web Page

Number Theory: https://moodle.keep.edu.hk/course/view.php?id=1058