What are number theoretic concepts

Module description

Module: Elementary Number Theory

Lectures:

titleTypeSWSPeriod
Elementary number theorylecture4Summer and winter semester
Elementary number theoryGroup exercise2Summer and winter semester

Responsible for the module:

Prof. Ulf Kühn

Admission requirements:

No

Recommended previous knowledge:

Linear Algebra

Module objectives / desired learning outcomes:

Professional competence

Knowledge
  • Students can describe basic concepts of elementary number theory such as congruences, square remainders, the ring of whole numbers and Diophantine problems and explain them using examples.
  • Students are able to discuss logical relationships between these concepts and to explain them using examples.
  • They know strategies of evidence and can reproduce them.
Skills
  • Students can model tasks from elementary number theory with the help of the concepts they have learned and solve them with the methods they have learned.
  • Students are able to independently develop further logical connections between the concepts they have learned and can verify them.
  • Students can develop a suitable approach to a given problem, pursue it and critically evaluate the results.

Personal competencies

Social skills
  • Students are able to work together in teams and master mathematics as a common language.
  • In particular, you can communicate new concepts in a way that is appropriate to the target group and use examples to check and deepen the understanding of fellow students.
independence
  • Students can independently check their understanding of complex concepts, bring open questions to the point and, if necessary, get specific help.
  • Students have developed enough stamina to work on difficult problems in a targeted manner over longer periods of time.

Credit points module:

9 LP

Academic achievement:

Oral exam

Workload in hours:

Self-study: 186, face-to-face study: 84


Course: Elementary Number Theory

Language:

German English

Period:

Summer and winter semester

Content:

  • Calculating with congruences (Chinese remainder theorem, small Fermatian theorem, application to asymmetric encryption)
  • Quadratic remainders (Legendre symbol, quadratic reciprocity law)
  • Properties of the ring of whole numbers (unit theorem, arithmetic with ideals, ideal classes)
  • Application to Diophantine Problems

Literature:

  • A. Beutelspacher, M.-A. Zschiegner: Discrete Mathematics for Beginners. Vieweg
  • F. Ischebeck: Invitation to number theory. BI
  • J. Kramer: Numbers for beginners. Vieweg
  • K. Reiss, G. Schmieder: Basic knowledge of number theory. Jumper