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)
Mgr. Pavel Francírek, Ph.D. (assistant)
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 1. 3. to Fri 14. 5. Thu 10:00–11:50 online_M6
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
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
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.
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, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2021/M8195