M8195 Number theory seminar

Faculty of Science
Spring 2025
Extent and Intensity
0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
Mgr. Pavel Francírek, Ph.D. (lecturer)
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
The knowledge of algebra and rudiments of Galois theory in the range of M3150 Algebra II are 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
Understanding the basics of algebraic number theory.
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
  • During the last semester we were studying rudiments of algebraic number theory. After recalling and improving this knowledge, the seminar will be devoted to the study of abelian number fields.
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
In this semester, we will meet in person. Home preparation will play an important role.
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.
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, Spring 2021, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2025/M8195