- LLL algorithm,
- Algebraic number fields, rings of integers, units, class groups,
- Behaviour of decomposition of prime numbers,
- Algorithmic computation of these values.
Module MAT-40-13-M-7
Algorithmic Number Theory (M, 9.0 LP)
Module Identification
Module Number | Module Name | CP (Effort) |
---|---|---|
MAT-40-13-M-7 | Algorithmic Number Theory | 9.0 CP (270 h) |
Basedata
CP, Effort | 9.0 CP = 270 h |
---|---|
Position of the semester | 1 Sem. irreg. |
Level | [7] Master (Advanced) |
Language | [EN] English |
Module Manager | |
Lecturers | |
Area of study | [MAT-AGCA] Algebra, Geometry and Computer Algebra |
Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |
Livecycle-State | [NORM] Active |
Courses
Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | SL | SL is required for exa. | PL | CP | Sem. | |
---|---|---|---|---|---|---|---|---|---|---|
4V+2U | MAT-40-13-K-7 | Algorithmic Number Theory
| P | 84 h | 186 h | - | - | PL1 | 9.0 | irreg. |
- About [MAT-40-13-K-7]: Title: "Algorithmic Number Theory"; Presence-Time: 84 h; Self-Study: 186 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 84130 ("Algorithmic Number Theory")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
Competencies / intended learning achievements
Upon successful completion of this module, the students have studied and understand the basic propositions on the structure of algebraic number fields and the algorithms for the explicit computation of invariants of algebraic number fields. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements. They are able to analyze the algorithms and to apply them to solve concrete problems.
By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.
Literature
- H. Cohen: A Course in Computational Algebraic Number Theory,
- M. Pohst, H. Zassenhaus: Algorithmic Algebraic Number Theory,
- M. Pohst: Computational Algebraic Number Theory,
- D. Marcus: Number Fields.
Requirements for attendance (informal)
Basic properties of Dedekind rings from the course [MAT-40-11-K-4] are used. Knowledge of the module [MAT-40-29-M-4] is desirable and helpful.
Modules:
Courses
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
Requirements for attendance (formal)
None
References to Module / Module Number [MAT-40-13-M-7]
Module-Pool | Name | |
---|---|---|
[MAT-43-MPOOL-7] | Specialisation Algebra and Number Theory (M.Sc.) | |
[MAT-RM-MPOOL-7] | Pure Mathematics (Advanced Modules M.Sc.) |