Listed below are the administrative details regarding the course.
There will be two lectures every week, as detailed below.
Lectures: Tuesdays from 14:30 to 16:00 in Takustrasse 9, SR 46 and Wednesdays from 12:30 to 14:00 in Arnimallee 6, SR 7/8.
You are also encouraged to attend one of the following exercise classes.
(We won't stop you from attending both if you really want to.)
Exercises: Tuesdays from 16:15 to 18:00 in Takustrasse 9, SR 6 and Thursdays from 10:30 to 12:00 in Arnimallee 6, SR 31.
Arnimallee 3, Room 211a
Arnimallee 3, Room 206
Office hours are by appointment, so please e-mail as needed.
Exams and Requirements
The final grade for this course will be from a written exam. The first exam will be held on Wednesday, February 20th, from 1 pm to 4 pm
The second exam will be held on April 2nd, from 1 pm to 4 pm.
The full set of requirements and formalities for the course can be found here.
Master's students at the Freie Universität Berlin may take this course either as
"Diskrete Mathematik II" or as an Ergänzungsmodul.
Phase I students from the Berlin Mathematical School may take this course as the basic course "Discrete Optimization" in teaching area 4.
We shall explore the use of algorithms in combinatorics. The main topics will be:
- Efficient discrete algorithms
- Sorting algorithms
- Shortest routes in graphs
- Maximum and stable matchings
- Brief introduction to complexity classes
- Algorithmic proofs of combinatorial theorems
- Network flows, connectivity and applications
- Linear programming and duality
- Integer programming and approximation
- Randomised algorithms
- Matchings in general graphs
- Algorithmic Local Lemma
The following texts are recommended for this course.
- D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó, Positional Games
- L. Lovász, J. Pelikán and K. Vesztergombi, Discrete Mathematics
- J. Matoušek and Bernd Gärtner, Understanding and Using Linear Programming
- D. West, Introduction to Graph Theory
The interested reader might also enjoy the following.
- V. Chvátal, Linear Programming
- A. Schrijver, Theory of Linear and Integer Programming
- A. Schrijver, Combinatorial Optimization
This course is a second course in the Discrete Mathematics module, and we assume our students are familiar with the basic concepts of graph theory and combinatorics covered in the Discrete Mathematics I course (see here for the relevant material).
We will also make use of undergraduate linear algebra, calculus and probability.
There will be a homework assignment you should solve in pairs.
Submit your solutions by the end of the Tuesday lecture, either in class itself, or to the tutor box of Anurag Bishnoi.
|Week 0||Sheet 0||Never||To be discussed on 16/10|
As we make our way through the semester, we will provide below a brief review of the topics covered each week.
|1||Sorting algorithms: (Binary) insertion sort, Mergesort; Analysis: running time, matching lower bound|
|2||Spanning trees: Depth-first and breadth-first search, Kruskal's algorithm for minimum-weight spanning trees||LPV 9.1