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PřF:MUC33 Number theory - Course Information

## MUC33 Number theory

**Faculty of Science**

autumn 2021

**Extent and Intensity**- 2/2/0. 5 credit(s). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- Mgr. Michal Bulant, Ph.D. (lecturer)

Mgr. Pavel Francírek, Ph.D. (assistant) **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 **Timetable**- Wed 16:00–17:50 M6,01011
- Timetable of Seminar Groups:

*M. Bulant* **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**- HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA.
*Metody řešení matematických úloh.*2., přeprac. vyd. Brno: Masarykova univerzita, 2001. 278 s. 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. doi:10.5817/CZ.MUNI.O210-6308-2013.*Základní učebnice matematiky pro vysokoškolské studium*info

*recommended literature*- 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

*not specified*- HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA.
**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) Homeworks and their reflection
**Assessment methods**- Mid-term exam (1/3 points), final written and oral exam. Small portion of points will be assigned by means of homeworks.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- Study Materials

The course is taught annually. **Teacher's information**- http://www.math.muni.cz/~bulik/vyuka/Algebra-2/

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2021/MUC33