## 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
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:
MUC33/01: Fri 10:00–11:50 M4,01024, 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
recommended 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
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
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