PřF:M8195 Number theory seminar - Course Information
M8195 Number theory seminar
Faculty of ScienceAutumn 2016
- Extent and Intensity
- 0/2. 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
- Mon 19. 9. to Sun 18. 12. Thu 10:00–11:50 M6,01011
- Prerequisites
- The knowledge of Galois theory and basic informations concerning elliptic curves in the range of M8190 Algorithms of Number Theory will be useful. However, even the students who did not attend the lecture M8190 can acquire the mentioned knowledge of elliptic curves on their own easily.
- 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
- Understanding the basic theory of elliptic curves.
- Syllabus
- Weierstrass Equation
- The Group Law
- Other Equations for Elliptic Curves
- Other Coordinate
- The j-invariant
- Elliptic Curves in Characteristic 2
- Endomorphisms
- Singular Curves
- Elliptic Curves mod n
- Torsion Points
- Division Polynomials
- The Weil Pairing
- The Tate-Lichtenbaum Pairing
- Elliptic Curves over Finite Fields
- The Frobenius
- Determining the Group Order
- Supersingular Curves
- Literature
- WASHINGTON, Lawrence C. Elliptic curves : number theory and cryptography. Boca Raton: Chapmann & Hall/CRC, 2003, xi, 428. ISBN 1584883650. info
- Bookmarks
- https://is.muni.cz/ln/tag/PříF:M8195!
- Teaching methods
- Lectures, home reading, homeworks.
- 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.
- Enrolment Statistics (Autumn 2016, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2016/M8195