M8195 Number theory seminar

Faculty of Science
Spring 2009
Extent and Intensity
0/2. 2 credit(s) (fasci plus compl plus > 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
Timetable of Seminar Groups
M8195/01: Tue 14:00–15:50 M5,01013, M. Bulant, R. Kučera
Prerequisites (in Czech)
M3150 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
In this semester we shall continue to study the book of D.A.Cox which we started in the previous semester.
At the end of this course, students should be able to: understand basic notions of algebraic number theory and relations among them.
Syllabus
  • 1. Fermat, Euler and quadratic reciprocity;
  • 2. Lagrange, Legendre a quadratic forms;
  • 3. Gauss, composition anda genera;
  • 4. Cubic and biquadratic reciprocity;
  • 5. The Hilbert class field and p=x^2+n.y^2 for infinitely many n.
Literature
  • COX, David A. Primes of the form x² + ny² : Fermat, class field theory, and complex multiplication. New York, N.Y.: John Wiley & Sons, 1989, xi, 351. ISBN 0471190799. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M8195!
Assessment methods
Credit will be given in the case of the active work in seminars - the study of the Cox's book during the term, regular solutions of homeworks, work with the software package PARI.
Language of instruction
Czech
Further Comments
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, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Spring 2012, 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 2009, recent)
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