Discrete and algebraic structures
LV-Nr. MAT.402UF (Lecture), MAT.403UF (Exercises)
M. Kang, P. Sprüssel
Institute of Discrete Mathematics
Winter term 2021/22

Course dates and venue

The lecture is held from 4 October 2021 to 13 December 2021, Mondays from 8:00AM to 10:00AM and Tuesdays from 8:00AM to 9:45AM.
The exercises take place Thursdays from 3:30PM to 5:00PM.
Due to the lecture not taking place on various holidays, the exercises will also take breaks during some weeks. Please consult the schedule in TUGonline for a full list of dates.

The venue is chosen depending on the respective Corona traffic light status:

Contents of the course

The course consists of two parts.

Part I: Algebraic Structures
Chapter 1: Multilinear Algebra
Chapter 2: Rings and modules
Part II: Combinatorics and Graph Theory
Chapter 3: Combinatorics
Chapter 4: Graph Theory
Chapter 5: Stochastic Aspects

Grades for the lecture

The lecture will be graded by a written exam. There will be one exam in winter term 2021/22, three exams in summer term 2022, and two exams in the winter term 2022/23. Participants can register for any of these exams; registration in TUGonline will be open starting three weeks before the respective exam. The exams will either take place in a lecture hall or via video conference, according to traffic light status with the same rules as described above.

Winter term 2021/22: Mon, 17 January 2022, 8:00-10:00
Summer term 2022: Fri, 11 March 2022, 16:00-18:00
Fri, 29 April 2022, 16:00-18:00
Fri, 10 June 2022, 16:00-18:00
Winter term 2022/23: TBA
TBA

You can bring a sheet of paper (size DIN A4) with any handwritten notes (both sides of the sheet may be used for the notes). Any other resources are prohibited at the exam.

The exam will take 90 minutes and comprise four problems, two from each part of the course. Each problem will be worth 5 points, thus a maximum of 20 points can be reached in the exam. Grades are given according to the points P as follows. (For students not familiar with the Austrian grade system: 5 is failing, all other grades are passing.)


P < 10   nicht genügend (5),
10 P < 12.5   genügend (4),
12.5 P < 15   befriedigend (3),
15 P < 17.5   gut (2),
17.5 P 20   sehr gut (1).

Grades for the exercises

The exercises will be graded based both on the participation in the exercise sessions and points gained in a written exam at the end of the course. The exam will take 90 minutes; there will be a makeup exam end of february/beginning of march for those who missed the original exam or did not gain enough points to pass. For those who take part in the makeup exam, the points from that exam will replace the points from the original exam. The exams will either take place in a lecture hall or via video conference, according to traffic light status with the same rules as described above

Exams for the exercises

Regular exam: Thu, 13 January, 15:30-17:00
Makeup exam: TBA

You can bring a sheet of paper (size DIN A4) with any handwritten notes (both sides of the sheet may be used for the notes). Any other resources are prohibited at the exam.

The exam will take 90 minutes and comprise four problems, two from each part of the course. Each problem will be worth 5 points, thus a maximum of 20 points can be gained in the exam.

Exercise sessions

The exercise sheets will be available at the bottom of this page about a week before the respective exercise session. You can then use an online system (link below) to mark which exercises you solved. The deadline for marking is precisely one hour before the start of the session. After the deadline, no changes can be made. The choice who shall present their solution of which exercise in class is made by a random generator. If you mark an exercise, you need to be present at the respective exercise session.

Points will also be awarded for presenting solutions of exercises. Everyone needs to present at least one solution in order to pass.

You should present solutions in a way that enables the other participants to follow your arguments. If it becomes apparent that someone did not do an exercise they marked in the system (it is fine if the exercise has been done, but mistakes have been made), this can be penalised by scaling all points from the exercises by 0.5. The same holds if someone marks exercises and does not turn up to the exercise session.

Points for solving exercises

Up to 15 points can be gained by marking exercises. For each sheet, the points awarded for marking the exercises on this sheet will be

2.5 • (marked exercises) / (exercises on this sheet).

Out of the eight exercise sessions, the best six will be counted for the total points.

If you miss a session, you will not be awarded any points for that session. Points lost by missing more than two sessions cannot be compensated.

Points for presenting solutions

Depending on the quality of the solution and the presentation, between 0 and 5 points will be awarded. For each participant, only the best performance among their presentations will count. Thus, no more than 5 points can be gained by presenting solutions.

Attention: Keep in mind that in case of an online class, you present your solution via a video conference. The optimal way would be if you have the possibility to write the solution during the presentation (e.g. using a tablet or a camera filming you writing on paper). If such methods are not available to you, prepare your written solution as a file (e.g. scan or photograph the handwritten solution) that you can then share during the exercise session while verbally explaining the solution.

Online system for marking exercises

Before you log in for the first time, enter your student ID number; the system will then automatically send a password to your student email address. The system will update the list of participants daily. If you just registered for the course, it might take a day until the system recognises you.

Online classes

As stated above, exercise classes might take place via video conference if the traffic light status requires us to do so. For presenting solutions during such exercis classes, you will have to be able to attend a Webex meeting with a device that has a working microphone. A webcam or a tablet (in order to write on the screen) would be a plus, but are not strictly necessary.

Grades

The total number of points is the sum P of the points M gained by marking solved exercises in the online system (M≤15), the points S for presenting solutions (S≤5), and the points E from the exam (E≤20). Depending on P, the grade will be



P < 20   nicht genügend (5),
20 P < 25   genügend (4),
25 P < 30   befriedigend (3),
30 P < 35   gut (2),
35 P 40   sehr gut (1).

Exercise sheets

All exercise sheets will be linked here.

Exercise sheet 1 for 14 October 2021
Exercise sheet 2 for 21 October 2021
Exercise sheet 3 for 4 November 2021
Exercise sheet 4 for 11 November 2021
Exercise sheet 5 for 25 November 2021
Exercise sheet 6 for 2 December 2021
Exercise sheet 7 for 9 December 2021
Exercise sheet 8 for 16 December 2021

Last changed 28 January 2022