Michael Schlosser

Combinatorics

(Lecture course and introductory seminar in the winter semester 2024)

E-mail:

Tel.: (+43-1) 4277-50455

Office hours: by appointment, OMP1, Room 11.124 (or, in exceptional cases, online)

This  Lecture Course [LVA-Nr. 250002, 4 hours, 6.0 ECTS credits] runs from October 2, 2024 until January 30, 2025. Classes meet Wednesdays from 09:45 until 11:15 and Thursdays from 16:45 until 18:15 in Seminar Room 8 (SR 8), OMP1, second floor.

Contents: This lecture course will be given in a classical way (with blackboard talks). The general aim is to focus deeply on basic topics in Combinatorics which were not (or so far insufficiently) treated in the lecture course "Discrete Mathematics". In particular, the following topics are to be covered:

1. Generating functions and Lagrange's inversion formula
2. Species: Enumeration of combinatorial objects
3. Partially ordered sets
4. Asymptotic enumeration

Literature: Lecture Notes Combinatorics (in English) by Markus Fulmek, 2018.

The course Combinatorics assumes prior knowledge in Discrete Mathematics, as provided, for instance, in the lecture notes Diskrete Mathematik (in German) by Markus Fulmek and Christian Krattenthaler, 2017.

Examination topics: All the covered topics are a priori relevant for the oral exam. Individual appointments for the exam can be made until the end of October, 2025.

The lecture course is accompanied by an  Introductory Seminar (Proseminar) [LVA-Nr. 250003, 2 hours, 3.0 ECTS credits]. It runs from October 4, 2024 until January 31, 2025, Classes meet Fridays from 08:00 to 09:30 in the Lecture Room 2 (HS 2), OMP1, ground level.

The homework exercises are available here online (in PDF format):  Exercises 1-58

Participants for the lecuture course and the introductory seminar are asked to officially register for theses courses on USPACE.
For the introductory seminar, registration is open from Sunday 01.09.2024 00:00 to Monday 23.09.2024 23:59; deregistration possible until Thursday 31.10.2024 23:59.

Attendance on all days is obligatory for earning credit in the Introductory Seminar!
No exercises are to be prepared for October 4, but sample problems will be presented and discussed which include some applications of Lagrange inversion.
For all the introductory seminar appointments after October 4, students will be expected to prepare homework exercises.
The following homework problems are due on October 11: Exercises A.1-A.4. Later assignments include Exercises A.5-A.9, in addition to those from the regular sheets of Exercises 1-58.