Module 24-B-EZT Elementary Number Theory

Faculty

Person responsible for module

Regular cycle (beginning)

Every summer semester

Credit points and duration

10 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Die Studierenden besitzen ein Basiswissen der klassischen Zahlentheorie. Sie können die grundlegende Theorie analysieren und im mathematischen Kontext einordnen und Querverbindungen zur Algebra, Analysis, Geometrie und Kombinatorik aufzeigen. Sie sind fähig, in dem Gebiet mathematische Beweise eigenständig zu führen.

Den Kompetenzerwerb in den Techniken der elementaren Zahlentheorie, die Fähigkeit zur Anwendung der Methoden, die Präsentations- und Kommunikationsfähigkeit sowie Ausdauer als mathematische Grundkompetenz weisen die Studierenden in den Übungen nach. Das Verständnis der Zusammenhänge und Begriffe sowie die Sicherheit in der Anwendung der Methoden auch in neuen Problemstellungen wird in der Abschlussprüfung nachgewiesen.

Content of teaching

Die Veranstaltung behandelt Theorie und Methoden der elementaren Zahlentheorie
Lehrinhalte sind:
Primzahlen
Teilbarkeit
Euklidische Algorithmus
Kongruenzen und der chinesische Restsatz
Kleiner Satz von Fermat
Anwendungen in der Kryptographie
Quadratisches Reziprozitätsgesetz
Diophantische Gleichungen

Recommended previous knowledge

Kenntnisse der Analysis und Linearen Algebra

Necessary requirements

Explanation regarding the elements of the module

Module structure: 1 SL, 1 bPr 1

Courses

Elementare Zahlentheorie
Type lecture
Regular cycle SoSe
Workload5 60 h (60 + 0)
LP 2 [Pr]
Übungen zu Elementarer Zahlentheorie
Type exercise
Regular cycle SoSe
Workload5 90 h (30 + 60)
LP 3 [SL]

Study requirements

Allocated examiner Workload LP2
Teaching staff of the course Übungen zu Elementarer Zahlentheorie (exercise)

Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises.

see above see above

Examinations

e-portfolio with final oral examination o. e-portfolio with final written examination o. portfolio with final oral examination o. portfolio with final written examination
Allocated examiner Teaching staff of the course Elementare Zahlentheorie (lecture)
Weighting 1
Workload 150h
LP2 5

The (e-)portfolio is passed if
- a sufficient number of correctly solved exercises, which are completed as part of the study requirements , are demonstrated, usually by at least 50% of the points achievable in the semester for solving the exercises, and
- a final exam in the form of a final written exam (usually 90 min) or a final oral exam (usually 30 min) is passed. The final exam relates to the content of the lecture and the tutorial and is used for assessment.

A remote electronic written examination is not permitted as a final exam.

The module is used in these degree programmes:

Degree programme Version Recom­mended start 3 Duration Manda­tory option 4
Informatics for the Natural Sciences / Bachelor of Science [FsB vom 01.04.2025] Bachelor with One Core Subject (Academic) 2. o. 4. one semester Compul­sory optional subject
Informatics for the Natural Sciences / Master of Science [FsB vom 01.04.2025] 2. o. 4. one semester Compul­sory optional subject

Automatic check for completeness

The system can perform an automatic check for completeness for this module.


Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
Study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
This academic achievement can be reported and recognised.