PřF:M6520 Number theory - Course Information
M6520 Number theory
Faculty of ScienceAutumn 2024
The course is not taught in Autumn 2024
- Extent and Intensity
- 2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching - Teacher(s)
- Mgr. Michal Bulant, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- Basics of divisibility.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 7 fields of study the course is directly associated with, display
- Course objectives
- At the end of this course, students should be able to:
understand the basics of elementary number theory, especially basic facts about primes
use congruences
solve linear congruences and their systems and selected types of congruences of higher order
apply various methods for solving diophantine equations - Learning outcomes
- At the end of this course, students should be able to:
understand the basics of elementary number theory
use properly congruences
solve linear congruences and their systems and selected types of congruences of higher order
apply various methods for solving diophantine equations - Syllabus
- Elementary number theory (prime numbers, congruences, Fermat theorem, Euler theorem).
- Congruences in one variable (linear congruences, algebraic congruences, primitive root). Quadratic congruences, Legendre symbol, quadratic reciprocity law.
- Diophantine equations (linear diophantine equations, elementary methods for solving of some special-type diophantine equations).
- Literature
- recommended literature
- HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Metody řešení matematických úloh. Vydání druhé přepracovan. V Brně: Masarykova univerzita, 1996, 278 stran. ISBN 8021012021. info
- SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. Brno: Masarykova univerzita, 2013, 773 pp. ISBN 978-80-210-6307-5. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
- not specified
- IRELAND, Kenneth F. and Michael I. ROSEN. A classical introduction to modern number theory. 2nd ed. New York: Springer, 1990, xiv, 389. ISBN 038797329X. info
- Bookmarks
- https://is.muni.cz/ln/tag/PříF:M6520!
- Teaching methods
- Lectures: theoretical explanation with practical examples Exercises: solving problems for understanding of basic concepts and theorems, contains also some basic applications (e.g. public-key cryptography)
- Assessment methods
- Mid-term exam (1/3 points), final written (2/3) and oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~bulik/vyuka/Algebra-2/
- Enrolment Statistics (Autumn 2024, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2024/M6520