# TU Wien:Discrete Mathematics VO (Gittenberger)

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## Daten

Vortragende Bernhard Gittenberger 4,0 2023W English discrete-mathematics • Register • Mattermost-Infos tiss:104271

## Inhalt

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

Lecture twice a week, weekly excercise (extra course)

## Benötigte/Empfehlenswerte Vorkenntnisse

Algebra & Discrete Mathematik from Bachelor

## Vortrag

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

WS 2020/2021: Separate UE by Prof Stufler

## Prüfung, Benotung

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.

WS 2023/24: Modalities are still the same. Look at exercises and definitions for written exam. Look at definitions for oral exam.

WS 2024/24 oral exam: The atmosphere of the oral exam was rather relaxed. I got questions about the topics combinatorial structures, shift registers and primitive polynomials. For the first two topics, I talked about the definitions, why these concepts are useful, and some of the main results we had in the lecture. It is definitely not required to know the proofs of complex theorems in detail - there is also certainly not enough time in the oral exam to present them. For the third topic, I could not quite recall the definition of a primitive polynomial. After some hints, I could reconstruct it correctly, and it did not negatively affect my grade.

noch offen

## Zeitaufwand

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

WS 2023/24: I have been in every lecture, took the exam in april (so if you do it earlier you might not have to repeat so much as i did). It took me 131h20m (~30h for the oral exam) only for learning to achive a 1... omg way too much :/

## Unterlagen

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

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

Very important in my opinion! (old exams) TU Wien:Diskrete Mathematik für Informatik VO (Gittenberger)

## Tipps

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

WS 23/24: Generating functions are easy in my optinion. A bit wired but okay. Finite fields are way harder to undrestand. To pass to written exam I focused on the exercies and old exams (also look at old vowi page). Looking at old exams was a waste of time, nevertheless I would still recommend to look at them since sometimes there are similiar examples. For the oral exam I tried to learn all defintions and theorems, which had been enough. Try to understand the connections in each chapter (so Finte fields and codes, matroids and MST program, etc.)

noch offen

noch offen

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