Introduction to Algebra (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 WiSe|
|Level|| Bachelor (Core)|
+ further Lecturers of the department Mathematics
|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): 83110 ("Exercise Class Introduction to Algebra")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
- principal ideal domains, unique factorization domains (UFD),
- groups, operations, Sylow theorems,
- stem and splitting fields,
- fundamental theorem of Galois theory,
- solvability of equations, constructions with compass and ruler.
Competencies / intended learning achievements
The students understand (using the example of field theory) how the interaction of different areas of algebra leads to new insights (in particular, to answers to classical questions of antiquity). This deepened the fundamental knowledge that different areas of mathematics often have to cooperate for being able to solve concrete problems.
- F. Lorenz: Einführung in die Algebra,
- B.L. van der Waerden: Algebra,
- G. Wüstholz: Algebra.
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)
- [MAT-10-11B-K-2] Fundamentals of Mathematics I: Linear Algebra (2V+2U, 6.0 LP)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
Requirements for attendance (formal)
References to Course [MAT-12-22-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)|
|[MAT-18-KPOOL-3]||Geometry (B.Ed. Mathematics)|