M8195 Number theory seminar

Faculty of Science
Spring 2012
Extent and Intensity
0/2. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Mgr. Michal Bulant, Ph.D. (seminar tutor)
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 of Seminar Groups
M8195/01: Tue 14:00–15:50 M5,01013, M. Bulant, R. Kučera
Prerequisites (in Czech)
M3150 Algebra II
Je vhodné absolvování předmětu Algebra II.
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 6 fields of study the course is directly associated with, display
Course objectives
This is the second semester of a two-semester course to study rings R of algebraic integers. The last semester was devoted to the book Algebraic Number Theory and Fermat's Last Theorem written by I.Stewart and D. Tall. We have shown that the nonzero ideals of R uniquely factorizes into the product of prime ideals and we have introduced the ideal class group of R. Minkowski convex body theorem was used to prove that the class group is finite and to prove Dirichlet theorem describing the structure of the group of units of R. Usefulness of these notions was illustrated by Kummer’s proof of the first case of Fermat Last Theorem for a regular prime exponent.
This semester we are going to use the book Number Theory written by Z.I.Borevič and R.I. Šafarevič. We shall study Bernoulli numbers and the analytical class number formula.
During this course, prof. L.Skula is going to describe his result on cubic polynomials in 2 or 3 lectures.
Syllabus
  • Bernoulli numbers
  • Infiniteness of irregular primes
  • Factorization of cubic polynomials
  • Dedekind zeta-function
  • Analytical class number formula
Literature
  • BOREVIČ, Z. I. and I.R. ŠAFAREVIČ. Number Theory. New York, London: Academic Press, 1966, 431 pp. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M8195!
Teaching methods
Lectures and homeworks.
Assessment methods
Credit will be given in the case of the active work in seminars - the study of the mentioned book during the term, regular solutions of homeworks.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught each semester.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2010 - only for the accreditation, Spring 2005, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Spring 2013, Autumn 2013, Spring 2014, Autumn 2014, Spring 2015, Autumn 2015, Spring 2016, Autumn 2016, Spring 2017, autumn 2017, spring 2018, Autumn 2018, Spring 2019, Autumn 2019, Spring 2020, Autumn 2020, Spring 2021, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Spring 2012, recent)
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