PřF:M8195 Number theory seminar - Course Information
M8195 Number theory seminar
Faculty of ScienceSpring 2020
- 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 - Timetable
- Thu 10:00–11:50 M6,01011
- Prerequisites
- M3150 Algebra II
To understand the topic, some basic knowledge of algebra 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 modular forms, our main source will be the first chapter of the book "The 1-2-3 of Modular Forms". This chapter, written by Don Zagier, contains not only the introduction to the theory of modular forms but also some applications.
- 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
- Basic definitions;
- Eisenstein series and the discriminant function;
- Theta series;
- Hecke eigenforms and L-series.
- Literature
- https://www.jmilne.org/math/CourseNotes/MF.pdf
- KILFORD, L. J. P. Modular forms : a classical and computational introduction. Hackensack, NJ: Imperial College Press, 2008, xii, 224. ISBN 9781848162136. info
- BRUINIER, Jan Hendrik. The 1-2-3 of modular forms : lectures at a summer school in Nordfjordeid, Norway, August 2004. 1st ed. New York: Springer, 2007, x, 266. ISBN 9783540741176. info
- 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)
- Study Materials
The course is taught each semester. - 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 (Spring 2020, recent)
- Permalink: https://is.muni.cz/course/sci/spring2020/M8195