M6520 Number theory

Faculty of Science
Autumn 2020
Extent and Intensity
2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
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
Timetable
Mon 10:00–11:50 prace doma
  • Timetable of Seminar Groups:
M6520/01: Fri 12:00–13:50 M6,01011, M. Bulant
M6520/02: Fri 10:00–11:50 M6,01011, 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
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
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~bulik/vyuka/Algebra-2/
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.
  • Enrolment Statistics (recent)
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