This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.

# Number Theory (dt. Zahlentheorie)

 Level, degree of commitment Advanced module, depends on importing study program Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Subject, Origin Mathematics, B.Sc. Mathematics Duration,frequency One semester, Regularly alternating with other advanced modules Person in charge of the module's outline Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske

## Contents

• Fundamental theorem of arithmetic,
• elementary theory of primes,
• Examples of public-key cryptographic methods,
• Diophantine equations,
• Modular arithmetic, power residues, reciprocity laws.

## Qualification Goals

The students shall

• learn the basics of classical number theory,
• recognize the links to methods from algebra and analysis,
• practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction and formulating proofs),
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

## Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.

• Remmert, Ullrich: Elemetare Zahlentheorie, Birkhäuser.
• Everest, Ward: An Introduction to Number Theory, GTM, Springer (hier insbesondere Kapitel 1-3)
• Stein: Elementary Number Theory: Primes, Congruences, and Secrets (a computational approach), UTM, Springer.