#
PřF:M8195 Number theory seminar - Course Information

## M8195 Number theory seminar

**Faculty of Science**

Spring 2021

**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)**- 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 **Prerequisites**-
**M3150**Algebra II

To understand the topic, some basic knowledge of algebra, algebraic number theory, and complex analysis is necessary. **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 study the third and fourth chapter of the 2nd edition of the book "Primes of the form x^2+ny^2" written by Cox.
**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**- Elliptic functions and complex multiplication;
- Modular functions and ring class fields;
- Modular functions and singular j-invariants;
- The class equation;
- Elliptic curves;
- Shimura reciprocity.

**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

- COX, David A.
**Bookmarks**- https://is.muni.cz/ln/tag/PříF:M8195!
**Teaching methods**- Lectures, homeworks.
**Assessment methods**- Credit will be given in case of active work in seminars - the study of the mentioned book during the term, regular solving of homework.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course is taught each semester.

The course is taught: every week. **Teacher's information**- The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/spring2021/M8195