Number Theory

Course guarantor:

Zuzana Masáková

Lecturer:

Zuzana Masáková, Edita Pelantová

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

1. Algebraic and transcendental numbers

2. Algebraic number fields, field isomorphisms

3. Rational approximations, continued fractions

4. Diophantic equations, Pell's equation

5. Rings of integers in algebraic number fields and divisibility

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

Requirements:

Basic knowledge of linear and general commutative algebra: matrices, groups, rings, fields.

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Obligatory:

[1] Takahasshi Ono, An Introduction to Algebraic Number Theory, Springer-Verlag New York Inc.; 2013

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 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (elective course)
• Matematické inženýrství (elective course)
• Matematická informatika (compulsory course in the program)