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

250050 VO Combinatorics (2012S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 05.03. 09:00 - 11:00 Seminarraum
  • Thursday 08.03. 09:00 - 11:00 Seminarraum
  • Thursday 15.03. 09:00 - 11:00 Seminarraum
  • Monday 19.03. 09:00 - 11:00 Seminarraum
  • Thursday 22.03. 09:00 - 11:00 Seminarraum
  • Monday 26.03. 09:00 - 11:00 Seminarraum
  • Thursday 29.03. 09:00 - 11:00 Seminarraum
  • Monday 16.04. 09:00 - 11:00 Seminarraum
  • Thursday 19.04. 09:00 - 11:00 Seminarraum
  • Monday 23.04. 09:00 - 11:00 Seminarraum
  • Thursday 26.04. 09:00 - 11:00 Seminarraum
  • Monday 30.04. 09:00 - 11:00 Seminarraum
  • Thursday 03.05. 09:00 - 11:00 Seminarraum
  • Monday 07.05. 09:00 - 11:00 Seminarraum
  • Thursday 10.05. 09:00 - 11:00 Seminarraum
  • Monday 14.05. 09:00 - 11:00 Seminarraum
  • Monday 21.05. 09:00 - 11:00 Seminarraum
  • Thursday 24.05. 09:00 - 11:00 Seminarraum
  • Thursday 31.05. 09:00 - 11:00 Seminarraum
  • Monday 04.06. 09:00 - 11:00 Seminarraum
  • Monday 11.06. 09:00 - 11:00 Seminarraum
  • Thursday 14.06. 09:00 - 11:00 Seminarraum
  • Monday 18.06. 09:00 - 11:00 Seminarraum
  • Thursday 21.06. 09:00 - 11:00 Seminarraum
  • Monday 25.06. 09:00 - 11:00 Seminarraum
  • Thursday 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 partially ordered sets
4. Methods for asymptotic enumeration

Assessment and permitted materials

Examination at the end of the semester

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 partially ordered sets
4. Methods for asymptotic enumeration

Examination topics

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 partially ordered sets
4. Methods for asymptotic enumeration

Reading list

Empfehlenswerte Bücher sind:
P. Flajolet, R. Sedgewick, "Analytic Combinatorics", Cambridge University Press, 2009.
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

MALK

Last modified: Mo 07.09.2020 15:40