TU Wien:Discrete Mathematics VO (Gittenberger)

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Daten[edit]

Lecturers Bernhard Gittenberger; Michael Wallner
ECTS 4
Alias Discrete Mathematics (en)
Department Diskrete Mathematik und Geometrie
When winter semester
Last iteration 2021WS
Language English
Mattermost discrete-mathematicsRegisterMattermost-Infos
Links tiss:104271, Homepage
Zuordnungen
Master Logic and Computation Pflichtmodul Discrete Mathematics
Master Technische Informatik Pflichtmodul Discrete Mathematics


Inhalt[edit]

The first part of the lecture is about Graph theory and goes from simpler (Kruskal, Dijstra, ...) to more advanced topics (Max-Flow).

The second part is about combinatorics using basic counting principles and generating functions.

WS 2020/2021:

  1. Graph Theory: Trees, Forests, Matroids, Algorithms, Graph classes, Bipartite Graphs, Graph colorings
  2. Higher Combinatorics: Counting Principles, Generating functions, combinatorial constructions, Combinatorics on posets
  3. Number Theory: Divisibility and Factorization, Residue Classes, Euler-Fermat theorem, RSA
  4. Polynomials over Finite Fields: Rings, Fields, Finite Fields, Applications

Ablauf[edit]

Lecture twice a week, weekly excercise (extra course)

Benötigte/Empfehlenswerte Vorkenntnisse[edit]

Algebra & Discrete Mathematik from Bachelor

Vortrag[edit]

WS 2020/2021: Lecture by Prof. Drmota. He put videos on TUWEL and also offered question hours via Zoom. Lecture goes along with the Discrete Mathematics UE (by Stufler) very well. Answers to questions by mail or in the question hour were very friendly & helpful.

Übungen[edit]

WS 2020/2021: Separate UE by Prof Stufler

Prüfung, Benotung[edit]

WS 2020/2021: Written + oral part. Written was on February 5th. Notification that we should register for the oral exam on February 15. Oral Exams were then on February 19, 22, 23 and March 1st and 2nd. Drmota tells you the points for the written part and final grade during the oral exam.

Drmota gives nice hints during the exam.

Dauer der Zeugnisausstellung[edit]

noch offen

Zeitaufwand[edit]

WS 2020/2021: 16 lecture videos of more or less 2 hours length.

Unterlagen[edit]

Not sure if this is because of a curriculum change, but it looks like Diskrete_Mathematik_für_Informatik_VO_(Drmota) https://vowi.fsinf.at/wiki/TU_Wien:Diskrete_Mathematik_f%C3%BCr_Informatik_VO_(Drmota) has some old exams.

Prof. Drmota recommended by mail the book "Analytic Combinatorics" http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html for the topic Generating Functions and mentioned that for number theory and fields there are really many books available.

I found Contemporary Abstract Algebra by Joseph A. Gallian a good addition: https://people.clas.ufl.edu/cmcyr/files/Abstract-Algebra-Text_Gallian-e8.pdf

OpenMathbooks has some explanations about Generating Functions: http://discrete.openmathbooks.org/dmoi2/section-27.html

Analysis of Algorithms about Generating Functions has a nice summary: https://aofa.cs.princeton.edu/30gf/

Tipps[edit]

Generating functions was the hardest topic for me, and it seemed like many students felt the same.

Verbesserungsvorschläge / Kritik[edit]

noch offen