Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-40-13-K-7

Algorithmic Number Theory (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP
4 V Lecture 56 h 124 h
2 U Exercise class (in small groups) 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • LLL algorithm,
  • Algebraic number fields, rings of integers, units, class groups,
  • Behaviour of decomposition of prime numbers,
  • Algorithmic computation of these values.

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.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

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

Requirements for attendance (formal)

None

References to Course [MAT-40-13-K-7]

Module Name Context
[MAT-40-13-M-7] Algorithmic Number Theory P: Obligatory 4V+2U, 9.0 LP