Elementary Number Theory (2V+1U, 4.5 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||4.5 CP||93 h|
|1||U||Exercise class (in small groups)||14 h|
|(2V+1U)||4.5 CP||42 h||93 h|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. in SuSe|
|Level|| Bachelor (Core)|
|Area of study||[MAT-GRU] Mathematics (B.Sc. year 1 and 2)|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83170 ("Exercise Class Elementary Number Theory")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
- Unique prime decomposition in ℤ, linear diophantine equations,
- Euler's phi function, structure of the primary residual class group (ℤ/nℤ)*,
- Gaussian reciprocity law,
- quadratic number fields, decomposition behaviour of prime numbers, sums of squares.
Competencies / intended learning achievements
The students know the basic concepts, statements and methods of number theory. In particular, an advanced ability of abstraction was promoted.
- R. Remmert, P. Ullrich: Elementare Zahlentheorie,
- R. Schulze-Pillot: Einführung in die Algebra und Zahlentheorie,
- T. Apostol: Introduction to Analytic Number Theory.
Further literature will be announced in the lecture(s); exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)None
References to Course [MAT-12-21-K-3]
|[MAT-12-20L_ERW-M-3]||Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation||WP: Obligation to choose||2V+1U, 4.5 LP|
|[MAT-12-20L-M-3]||Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation||WP: Obligation to choose||2V+1U, 4.5 LP|
|[MAT-10-KPOOL-3]||Pure Mathematics (B.Sc. Mathematics)|