The development of e-learning applications solving problems from graph theory

Abstract

KOLMAN PAVEL, ZACH PETR, HOLOUBEK JOSEF:The development of e-learning applications solving problems from graph theory. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 2013, LXI, No. 7, pp. 2311-2316 Authors are in long term developing e-learning supports for some parts of Operation Research course. The original purpose was to prepare e-learning supports for students of FBE Mendelu, mainly for part-time form students, who have subscribed Economic mathematical methods course (EMM). Considering decreasing number of lessons on part-time form of study (16 hours in a semester, in comparison to 56 hours in full-time form of study), was for part-time form students even more diffi cult to fulfi ll exam requirements. As a help for students there was stage by stage prepared several of programs, they allow self-contained practicing of some linear programming methods. Programs did allow to users step-by-step verify their solution, i.e. whether their calculation are in accordance with algorithm described in lectures. Advantage for the students consists in fact, that each mistake (numerical or algorithmic) they were able to uncover, what contributes to increase of self-study eff ectiveness and from that resulting higher study motivation. Resulting from existing experience, authors decided to request for a new FRVŠ grant for academic year 2012, focused on e-learning support of selected graph theory problems. Within this project there was developed a tool allowing to make and according to the user needs interactively modify created graphs. On this graph it is possible individually, step by step (in compliance with on lectures presented algorithm) to practice solving of selected graph theory and network analysis problems (e.g. minimal spanning tree, shortest path in a graph, testing for cycles in a graph, critical path method etc.). Project is realized as modular and was realized in Delphi developing tool. Described algorithms are saved in dynamic linked libraries. There for it is very easy to add here new (newly programmed) algorithms. Project results (i.e. project experience obtained from e-learning supports) will be available for all FBE Mendelu members interested in this problematic. graph theory, optimization, operations research, Delphi Growing content of EMM course and decreasing time allowance, mainly in part-time form of study, led to request to off er students supporting study materials. This materials should students allow and ease their individual home preparation and raise their study motivation. Increased usage of information technologies off ers new ways in accessing study matherials to students. Several e-learning courses and educational so ware (e.g. Pokorný, Stávková, 2007) are implemented to improve study effi ciency. Foltýnek (2006) and Tomanová (2010) deal with methodology and effi ciency of e-learning matherials.Authors of this paper have in last few years prepared and released for students of FBE lot of programs, which allowed students to acquire linear programming methods ...

Characterizing Levels of Reasoning in Graph Theory

“…Discrete mathematics deals with the study of structures based on discrete sets (finite or numerable sets), such as integers, graphs, or codes (Biggs, 2003), which are fundamental in developing disciplines such as computer science, operations research, or combinatorial optimization (e.g., see Beineke & Wilson, 1997). In particular, graphs play a significant role in the mathematical training of undergraduate students in engineering, economics, and of course, in mathematics (González, Muñoz-Escolano, & Oller-Marcén, 2019;Kolman, Zach, & Holoubek, 2013;Milková, 2009;Vidermanová & Melušová, 2011). This is due to their usefulness as tools for modeling real-life problems, which gives them high applicability in different areas such as transportation networks, telecommunications, social networks, scheduling tasks, or big data (Derrible & Kennedy, 2011;Hart, 2008).…”