Discrete modelling

2020/2021

Programme:

Practical Mathematics

Year:

3 year

Semester:

first or second

Kind:

optional

Group:

ECTS:

Language:

slovenian

Course director:

Prof. Dr. Matjaž Konvalinka, Prof. Dr. Marko Petkovšek

Hours per week – 1. or 2. semester:

Lectures

Seminar

Tutorial

Lab

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.

D. L. Kreher, D. R. Stinson: Combinatorial Algorithms: Generation, Enumeration, and Search, CRC, Boca Raton, 1999.
G. Appa, L. Pitsoulis, H. P. Williams (uredniki): Handbook on Modelling for Discrete Optimization, Springer, 2006.
priročniki za uporabljena računalniška orodja / manuals for the computer tools used

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]
Marko Petkovšek:
PETKOVŠEK, Marko. Counting Young tableaux when rows are cosets. Ars combinatoria, ISSN 0381-7032, 1994, let. 37, str. 87-95. [COBISS-SI-ID 8048473]
PETKOVŠEK, Marko, WILF, Herbert S., ZEILBERGER, Doron. A=B. Wellesley (Massachusetts): A. K. Peters, cop. 1996. VII, 212 str. ISBN 1-56881-063-6. [COBISS-SI-ID 4085337]
PETKOVŠEK, Marko. Letter graphs and well-quasi-order by induced subgraphs. Discrete Mathematics, ISSN 0012-365X. [Print ed.], 2002, vol. 244, no. 1-3, str. 375-388. [COBISS-SI-ID 11414873]