Discrete Mathematics

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Summary

After successful completion of the course, students are able to carry out graph theoretical proofs, to describe important graph theoretical concepts and algorithms, to understand advanced methods in combinatorics, number theory and algebra as well as to explain application of the theory of finite fields.

Time and place

Tue 11:15 - 13:00 in EI 8
Fr 09:15 - 11:00 in EI 5

Please keep in mind all lecture free days and public holidays.
The first lecture takes place on October 1st. We will discuss the modalities of this course on this day.
During the first week of the lecture no exercise sessions will take place.

Literature

D. Jungnickel: Graphs, Networks and Algorithms
M. Aigner: Combinatorial Theory
R. Diestel: Graph Theory
W. Tutte: Introduction to the Theory of Matroids
P. Laud: Algorithms 1 Hamiltonian cycles (link)
L. Comtet: Advanced Combinatorics
M. Bona: Introduction to Enumerative Combinatorics
M. Aigner: A Course in Enumeration
P. Flajolet and R. Sedgewick: Analytic Combinatorics
B. van der Waerden: Algebra (Vol.1)
T. Hungerford: Algebra
R. Lidl and H. Niederreiter: Finite Fields
F. McWilliams and N. Sloane: The Theory of Error-Correcting Codes

Exam

The exam is divided into a written and an oral part, but administratively it is one exam and so there is only one grade for the whole exam.
The first opportunity for the written exam is at the end of the winter term. Then, three exam dates per semester will be offered.
For admission to the oral part, the score in the written exam has to be at least 50% of the maximally possible score.
The oral part is taken preferrably at one of the dates offered on the list provided during the written examination, which lie usually within one month after the written exam (most of the time slots are about one week after the written exam).
If not taken within six months after the written exam, you resign from it and will get the final grade "Failed".
In case of failing, the exam (and thus both parts) has to be repeated.

Exercise Sessions

Please register in TISS for one of the exercise groups. After the registration period you will receive access to TUWEL.
Attendance of exercise sessions is mandatory.

Homework Assignments

Please register in TISS for one of the exercise groups. After the registration period you will receive access to TUWEL.
Homework assignments will be published on TUWEL. Your solutions need to be uploaded and indicated there before the corresponding deadline. During the exercise sessions you will be asked to present your solutions at the blackboard.

Modalities

• Prepare the homework given on the exercise sheets before the respective deadline.
• For each problem you have solved and you think you can present the solution on the blackboard, tick the appropriate box in TUWEL before the respective deadline.
• Attendance to the exercise sessions is mandatory.
• After the course, you must have solved 60% of all problems.
• The final grade depends on the percentage of problems you solved and on your presentations on the blackboard.
  This means precisely: If P is the precentage of problems you have solved and B is the average score of your blackboard presentations (where 100 is the maximum; thus 0≤B≤100 and 0≤P≤100), then your grade is determined as follows:
  • The overall percentage is calculated with the formula
    • A=B+0.5*P−50.
  • If P<60 the final grade is failed, else the value of A determines your grade:
    • 60≤A<70 is sufficient,
    • 70≤A<80 is satisfactory,
    • 80≤A<90 is good,
    • 90≤A≤100 is very good.