## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-40-13-M-7

## 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 1 Sem. irreg. [7] Master (Advanced) [EN] English Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [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

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

## 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.

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.)