Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

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