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Elementaire Getaltheorie
| Credits |
8 credit points |
| Instructors |
Beukers, F. (Universiteit Utrecht) |
| E-mail |
F.Beukers@math.uu.nl |
| Aim |
To build a basic knowledge of Elementary Number Theory
and see it functioning in applications. |
| Description |
Number Theory can be best described as the science of integer numbers 1,2,3,... Some of the oldest and most famous problems in mathematics belong to Number Theory. One of them, Fermat's Last problem, has made newspaper headlines because it was solved in 1994 by Andrew Wiles after 350 years of failed attempts. Another one, Riemann's hypothesis, comes with a one million dollar prize for anyone who solves it. In this course we will not go into the full details of these problems, but we will discuss enough of it for the students to appreciate them.
The main goal of this course is to introduce the basic techniques in number theory and see them at work in several applications. Among these applications are cryptography, continued fractions, diophantine equations (among them Fermat's equation), the distribution of the primes (including Riemann's hypothesis) and possibly irrationality and transcendence. This course also provides a background for prospective high school teachers who like to develop extra-curricular activities. |
| Organization |
Each session will consist of a lecture followed by exercise
classes and computer sessions. |
| Literature |
The basic material for this course is contained in the Course notes Elementary Number Theory, to be sold before the course starts. |
| Prerequisites |
Knowledge of elementary group theory is required, knowledgeof some ring theory is recommended. |
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