What are number theoretic concepts
Module: Elementary Number Theory
|Elementary number theory||lecture||4||Summer and winter semester|
|Elementary number theory||Group exercise||2||Summer and winter semester|
Responsible for the module:
Prof. Ulf Kühn
Recommended previous knowledge:
Module objectives / desired learning outcomes:
- 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.
- 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.
- 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.
- 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:
Workload in hours:
Self-study: 186, face-to-face study: 84
Course: Elementary Number Theory
Summer and winter semester
- 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
- 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
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