Michael Schlosser

Combinatorics

(Lecture course and introductory seminar in the summer semester 2020)

E-mail:

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

Office hours: by appointment, OMP1, Room 11.124


This  Lecture Course [LVA-Nr. 250059, 4 hours, 6.0 ECTS credits] runs from March 2, 2020 until June 30, 2020. Until March 10, 2020 classes met Mondays from 11:30 until 13:00 in the Seminar Room 8, OMP1, 2nd floor, and Tuesday from 11:30 until 13:00 in the Seminar Room 12, OMP1, 2nd floor.

Due to current rules adopted by the university as a consequence of the epidemic Covid-19 outbreak, there are no classes with physical presence from March 16 to June 30, 2020. (Until March 10, the material of the lecture notes until page 15 (excluding Subsection 2.3.1) were covered in class.) Home learning applies from March 16 on. Students are asked to read and study further the lecture notes by themselves! Until Easter, students were asked to complete reading (and to study) Chapter 2 (Species). For the time after the Easter break, from Monday, April 20, on, as home learning generally prevails, students are asked to continue with Chapter 3 (Partially Ordered Sets) on page 43, and later on, in due course, with Chapter 4 (Asymptotic Enumeration) on page 73. As a rule, roughly four pages in the lecture notes are to be covered per day of regular class (i.e. eight pages per week), which will allow us to formally cover the entire lecture notes. (However, to lighten the students' burden in these exceptional times, only pages 1-84 of the lecture notes will be relevant for the exam!)

Contents: This lecture course started in a classical way (with blackboard talks), however, from March 16 on, students have been asked to do home learning. 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.

Examination topics: Only pages 1-84 of the lecture notes are relevant for the oral exam. Individual appointments for the exam can be made until the end of March, 2021.


The  Introductory Seminar (Proseminar) [LVA-Nr. 250060, 2 hours, 3.0 ECTS credits] is governed by Markus Fulmek and runs from March 5, 2020 until June 25, 2020 (and, if home learning would not apply, would regularly meet Thursdays from 11:30 until 13:00 in the Seminar Room 10, OMP1, 2nd floor).

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

Participants for the introductory seminar were asked to register in person on March 5, when the class first meets. Attendance on all days, including March 5, is obligatory (unless the university is closed)!
No exercises were to be prepared for March 5, but sample problems (on Lagrange inversion) were discussed.

For the appointment on March 19, students were expected to prepare the homework exercises 1-6. The later homework is assigned by Markus Fulmek.


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