M8195 Number theory seminar

Faculty of Science
Autumn 2024
Extent and Intensity
0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
Mgr. Pavel Francírek, Ph.D. (lecturer)
prof. RNDr. Radan Kučera, DSc. (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
Thu 10:00–11:50 M6,01011
Prerequisites
The knowledge of algebra and rudiments of Galois theory in the range of M3150 Algebra II are necessary. Understanding the basics of algebraic number theory would be useful (for example in the range of the two previous semesters of this seminar).
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
This semester will be devoted to Abelian fields (i.e., finite Galois extensions of the field of rational numbers with Abelian Galois group). We shall study the group of units of the ring of algebraic integers of an Abelian field, concentrating on its subgroup of circular units.
Learning outcomes
At the end of this course, students should be able to:
define basic notions of the studied theory;
explain learned theoretical results;
apply learned methods to concrete exercises.
Syllabus
  • Circular (or cyclotomic) units of Abelian fields (several groups obtained by different definitions: Ramachandra, Sinnott, Washington).
Literature
  • IRELAND, Kenneth. A classical introduction to modern number theory. 2nd ed. New York: Springer-Verlag, 1990, xiv, 389 s. ISBN 0-387-97329-X. info
  • 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!
Teaching methods
In this semester, we will meet in person. Home preparation will play an important role.
Assessment methods
Credit will be given in the case of active work in seminars: the study of the mentioned book during the term, regular delivering of solved homeworks. To get the credit, students must deliver at least 50% 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, 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, Spring 2025.
  • Enrolment Statistics (Autumn 2024, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2024/M8195