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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

Number Theory

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Code Completion Credits Range Language
01TC ZK 4 2+0 Czech
Lecturer:
Zuzana Masáková (guarantor)
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The subject is devoted to elementary number theory and to fundamentals of transcendental and algebraic 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:
Time-table for winter semester 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-09-18
For updated information see http://bilakniha.cvut.cz/en/predmet12073105.html