Number Theory

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted to number theory with focus on continued fractions and fundamentals of algebraic number theory.

Requirements:

Knowledge of analysis and algebra (both linear and abstract) in the extent of bachelor's curriculum of mathematical modeling at FNSPE.

Syllabus of lectures:

1. Algebraic number fields, field isomorphisms

2. Diophantic equations, Pell's equation

3. Rational approximations, continued fractions

4. Algebraic and transcendental numbers

5. Rings of integers in algebraic number fields and divisibility

6. Applications for diophantic equations and in geometry

7. Number representation in non-integer bases, finite and periodic expansions

Syllabus of tutorials:

Study Objective:

Knowledge: overview of fundamental tools of elementary and algebraic numer theory

Skills: application of methods for solution of concrete problems

Study materials:

Obligatory:

[1] Z. Masáková, E. Pelantová, Teorie čísel, Skriptum ČVUT 2010.

Optional:

[2] E. B. Burger, R. Tubbs, Making transcendence transparent, Springer-Verlag 2004.

[3] M. Křížek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers, Springer-Verlag 2001.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: