PřF:M8195 Number theory seminar - Course Information
M8195 Number theory seminar
Faculty of ScienceAutumn 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).
- Teacher(s)
- Mgr. Pavel Francírek, 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
- 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
- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Mathematics (programme PřF, B-MA)
- 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
- The course is taught each semester.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2024/M8195