Number Theory
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
01TEC | ZK | 5 | 4P+0C | Czech |
- 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)