Mathematics for Computer Science Students: Algebraic Structures (4V+2U, 8.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||8.0 CP||156 h|
|2||U||Exercise class (in small groups)||28 h|
|(4V+2U)||8.0 CP||84 h||156 h|
|CP, Effort||8.0 CP = 240 h|
|Position of the semester||1 Sem. in WiSe/SuSe|
|Level|| Bachelor (General)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-Service] Mathematics for other Departments|
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.
- 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).
- 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 for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)