Universität Wien
Warning! The directory is not yet complete and will be amended until the beginning of the term.

250381 VO Combinatorics (2006S)

Combinatorics

8.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Erstmals am Mittwoch, 1.3.2006

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 01.03. 09:00 - 11:00 Seminarraum
  • Monday 06.03. 09:00 - 11:00 Seminarraum
  • Wednesday 08.03. 09:00 - 11:00 Seminarraum
  • Wednesday 15.03. 09:00 - 11:00 Seminarraum
  • Monday 20.03. 09:00 - 11:00 Seminarraum
  • Wednesday 22.03. 09:00 - 11:00 Seminarraum
  • Monday 27.03. 09:00 - 11:00 Seminarraum
  • Wednesday 29.03. 09:00 - 11:00 Seminarraum
  • Monday 03.04. 09:00 - 11:00 Seminarraum
  • Wednesday 05.04. 09:00 - 11:00 Seminarraum
  • Monday 24.04. 09:00 - 11:00 Seminarraum
  • Wednesday 26.04. 09:00 - 11:00 Seminarraum
  • Wednesday 03.05. 09:00 - 11:00 Seminarraum
  • Monday 08.05. 09:00 - 11:00 Seminarraum
  • Wednesday 10.05. 09:00 - 11:00 Seminarraum
  • Monday 15.05. 09:00 - 11:00 Seminarraum
  • Wednesday 17.05. 09:00 - 11:00 Seminarraum
  • Monday 22.05. 09:00 - 11:00 Seminarraum
  • Wednesday 24.05. 09:00 - 11:00 Seminarraum
  • Monday 29.05. 09:00 - 11:00 Seminarraum
  • Wednesday 31.05. 09:00 - 11:00 Seminarraum
  • Wednesday 07.06. 09:00 - 11:00 Seminarraum
  • Monday 12.06. 09:00 - 11:00 Seminarraum
  • Wednesday 14.06. 09:00 - 11:00 Seminarraum
  • Monday 19.06. 09:00 - 11:00 Seminarraum
  • Wednesday 21.06. 09:00 - 11:00 Seminarraum
  • Monday 26.06. 09:00 - 11:00 Seminarraum
  • Wednesday 28.06. 09:00 - 11:00 Seminarraum

Information

Aims, contents and method of the course

Combinatorics, in its simplest form, deals with the enumeration of elements of a finite set. The most frequent basic combinatorial objects are permutations, rearrangements, lattice paths, trees and graphs. The appeal of combinatorics comes from the fact that there is no uniform approach for the treatment of the different problems, but many different methods, each of which providing a conceptual approach to a particular type of problem, respectively shedding light on these problems from different angles. The fact that there are no limitations on imagination in combinatorics has given a boost to this area in the past. In particular, the interrelations to other areas, such as theory of finite groups, representation theory, commutative algebra, algebraic geometry, computer science, and statistical physics, became more and more important. This course will build on the material of the course "Diskrete Mathematik". Some topics from there will be treated here in a more profound manner, and there will be new topics, to be precise:
1. Combinatorial structures and their generating functions
2. Pölya theory and the enumeration of objects with symmetries
3. Combinatorial theory of partielly ordered sets
4. Integer partitions and combinatorial theory for linear diophantine equations (including magic squares)

Assessment and permitted materials

Minimum requirements and assessment criteria

Combinatorics, in its simplest form, deals with the enumeration of elements of a finite set. The most frequent basic combinatorial objects are permutations, rearrangements, lattice paths, trees and graphs. The appeal of combinatorics comes from the fact that there is no uniform approach for the treatment of the different problems, but many different methods, each of which providing a conceptual approach to a particular type of problem, respectively shedding light on these problems from different angles. The fact that there are no limitations on imagination in combinatorics has given a boost to this area in the past. In particular, the interrelations to other areas, such as theory of finite groups, representation theory, commutative algebra, algebraic geometry, computer science, and statistical physics, became more and more important. This course will build on the material of the course "Diskrete Mathematik". Some topics from there will be treated here in a more profound manner, and there will be new topics, to be precise:
1. Combinatorial structures and their generating functions
2. Pölya theory and the enumeration of objects with symmetries
3. Combinatorial theory of partielly ordered sets
4. Integer partitions and combinatorial theory for linear diophantine equations (including magic squares)

Examination topics

Reading list

Empfehlenswerte Bücher sind:
P. J. Cameron, "Combinatorics", Cambridge University Press, 1994.
R. P. Stanley, "Enumerative Combinatorics", Vol. 1, Wadsworth & Brooks/Cole, 1986.
D. Stanton und D. White, "Constructive Combinatorics", Springer-Verlag, 1986.

Association in the course directory

Last modified: Mo 07.09.2020 15:40