Discrete modelling

There are no prerequisites.

Generation of discrete mathematical structures (subsets, permutations).
Linear programming and the simplex method with the help of a computer.
Dynamical programming (longest increasing subsequence, maximum sum contiguous subsequence, optimal multiplication of matrices, etc.).
Graph algorithms with the help of a computer (shortest paths, minimum spanning tree, Hungarian method, etc.)
Simple modelling with spreadsheets. Computer modelling tools.

1. G. Appa, L. Pitsoulis, H. P. Williams, eds.: Handbook on modelling for discrete optimization, New York : Springer, cop. 2006.
2. D. L. Kreher, D. R. Stinson: Combinatorial algorithms : generation, enumeration, and search, Boca Raton : CRC, cop. 1999.

Students learn basic tools and methods for modelling with discrete mathematical structures. They also learn the necessary computer tools.

Knowledge and understanding: Understanding of the basic concepts of mathematical modelling, especially with discrete structures. Using computer tools for modelling.
Application: Forecasting the behaviour of the model. Choice of the appropriate tools for the desired goal.
Reflection: Combining mathematics and computer skills from different areas when solving problems.
Transferable skills: Stating real-life problems in a formal mathematical form, study of the models.
Solving problems with the help of a computer.

lectures, exercises, computer labs, homeworks, consultations

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Matjaž Konvalinka:
KONVALINKA, Matjaž, PAK, Igor. Geometry and complexity of O'Hara's algorithm. Advances in applied mathematics, ISSN 0196-8858, 2009, vol. 42, iss. 2, str. 157-175. [COBISS-SI-ID 15545945]
KONVALINKA, Matjaž, PAK, Igor. Triangulations of Cayley and Tutte polytopes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 245, str. 1-33. [COBISS-SI-ID 16706905]
DOLŽAN, David, KONVALINKA, Matjaž, OBLAK, Polona. Diameters of connected components of commuting graphs. The electronic journal of linear algebra, ISSN 1081-3810, 2013, vol. 26, str. 433-445. [COBISS-SI-ID 16707161]