TU Wien:Discrete Mathematics VO (Gittenberger)

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Daten[Bearbeiten | Quelltext bearbeiten]

Vortragende Bernhard Gittenberger
Abteilung Diskrete Mathematik und Geometrie
Letzte Abhaltung 2023WS
Sprache English
Mattermost discrete-mathematicsRegisterMattermost-Infos
Links tiss:104271 , Homepage
Master Logic and Computation Pflichtmodul Discrete Mathematics
Master Technische Informatik Pflichtmodul Discrete Mathematics

Inhalt[Bearbeiten | Quelltext bearbeiten]

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[Bearbeiten | Quelltext bearbeiten]

Lecture twice a week, weekly excercise (extra course)

Benötigte/Empfehlenswerte Vorkenntnisse[Bearbeiten | Quelltext bearbeiten]

Algebra & Discrete Mathematik from Bachelor

Vortrag[Bearbeiten | Quelltext bearbeiten]

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[Bearbeiten | Quelltext bearbeiten]

WS 2020/2021: Separate UE by Prof Stufler

Prüfung, Benotung[Bearbeiten | Quelltext bearbeiten]

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[Bearbeiten | Quelltext bearbeiten]

noch offen

Zeitaufwand[Bearbeiten | Quelltext bearbeiten]

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

Unterlagen[Bearbeiten | Quelltext bearbeiten]

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: https://discrete.openmathbooks.org/dmoi3/sec_addtops-genfun.html

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

Tipps[Bearbeiten | Quelltext bearbeiten]

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

Highlights / Lob[Bearbeiten | Quelltext bearbeiten]

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Verbesserungsvorschläge / Kritik[Bearbeiten | Quelltext bearbeiten]

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