Course MAT-02-11-K-1
Mathematics for Computer Science Students: Algebraic Structures (4V+2U, 8.0 LP)
Course Type
| SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
|---|---|---|---|---|---|
| - | K | Lecture with exercise classes (V/U) | 8.0 CP | 156 h | |
| 4 | V | Lecture | 56 h | ||
| 2 | U | Exercise class (in small groups) | 28 h | ||
| (4V+2U) | 8.0 CP | 84 h | 156 h | ||
Basedata
| SWS | 4V+2U |
|---|---|
| CP, Effort | 8.0 CP = 240 h |
| Position of the semester | 1 Sem. in WiSe/SuSe |
| Level | [1] Bachelor (General) |
| Language | [DE] German |
| Lecturers |
+ further Lecturers of the department Mathematics
|
| Area of study | [MAT-Service] Mathematics for other Departments |
| Livecycle-State | [NORM] Active |
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
- propositions, sets, methods of proof, mappings, semi-orderings and equivalence relations,
- integers, division with remainder, greatest common divisor and Euclidean algorithm, fundamental theorem of arithmetic, Chinese remainder theorem over ℤ,
- groups, orbit equation, symmetry groups, normal subgroup and quotient group, applications (e.g. counting isomorphism classes of graphs),
- rings, polynomial rings, unity group of ℤ/nℤ, applications (e.g. public key cryptography, Pollard factorization, Diffie-Hellman key exchange), ideals and quotient rings, integral domains and fields, finite fields, Euclidean rings, Chinese remainder theorem, applications (e.g. modular computing, interpolation),
- vector spaces, Gaussian algorithm, bases and dimension, vector space homomorphisms, solving linear systems of equations, representing matrix of a homomorphism, algorithms for kernel and image,
- isomorphisms, base change, application (e.g. wavelet transformation), classification of homomorphisms, homomorphism theorem, applications (e.g. linear codes), determinants, eigenvectors, applications (e.g. page-rank algorithm).
Literature
- G. Fischer: Lineare Algebra,
- S. Bosch: Lineare Algebra,
- K. Jänich: Linear Algebra,
- J. Böhm: Grundlagen der Algebra und Zahlentheorie,
- B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen,
- V. Shoup: A Computational Introduction to Number Theory and Algebra.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
none
Requirements for attendance (formal)
None
References to Course [MAT-02-11-K-1]
| Module | Name | Context | |
|---|---|---|---|
| [INF-82-51-M-2] | Formal Foundations of Computer Science | P: Obligatory | 4V+2U, 8.0 LP |
| [MAT-02-11-M-1] | Mathematics for Computer Science Students: Algebraic Structures | P: Obligatory | 4V+2U, 8.0 LP |