M8195 Number theory seminar

Faculty of Science
Spring 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)
Mgr. Michal Bulant, Ph.D. (seminar tutor)
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 (in Czech)
M3150 Algebra II
Je vhodné absolvování předmětu Algebra II.
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 book of J. Buchmann and U. Vollmer "Binary quadratic forms, an algorithmic approach". Comparing to the book of Cox we read in 2013-14 there are important differences: this book covers also indefinite forms in full details, describes complexity issues of the algorithms, searching for algorithms as effective as possible.
At the end of this course, students should be able to: understand the algorithms for computations in the form class group of a given discriminant.
Syllabus
  • 1. Binary quadratic forms and their equivalence;
  • 2. Forms, bases, points, and lattices;
  • 3. Reduction of positive definite forms;
  • 4. Reduction of indefinite forms;
  • 5. Multiplicative lattices;
  • 6. Quadratic number fields;
  • 7. Class groups;
  • 8. Cryptographic applications.
Literature
    required literature
  • BUCHMANN, Johannes A. and Ulrich VOLLMER. Binary quadratic forms : an algorithmic approach. Berlin: Springer, 2007, xiv, 318. ISBN 9783540463672. 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
Study Materials
The course is taught each semester.
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, 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, Spring 2025.
  • Enrolment Statistics (Spring 2016, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2016/M8195