Discrete Math

Valentyna Pikalova, Kharkiv GeoGebra Institute, Dec 7, 2015

ABSTRACT 1 [color=#1551b5][b]GeoGebra-Integrated Professional Development of Future Math Teachers within Discrete Mathematics Course[/b][/color] [i]Valentyna Pikalova, G.S. Scovoroda Kharkiv National Pedagogical University, Ukraine[/i] [b]Discrete Mathematics [/b]and adjacent disciplines are studied in all universities, where specialists in the field of programming, mathematics, as well as economic, technical and humanitarian areas are trained. Traditionally, discrete mathematics includes following topics such as set theory, mathematical logic, combinatorics, graph theory, etc. GeoGebra provides a wide range of instruments, which allow teacher to expand the range of tasks, increase their complexity, foster research component, create dynamic demonstration to explore mathematical objects with multiple representation. The complex of interactive dynamic demonstrations designed in GeoGebra to support discrete mathematics course for future teachers (pre-service) of mathematics is considered. Complex focuses on four types of demonstrations: teaching and learning basic concepts, stages of theorem proving, implementation of well-known algorithms from graph theory, the real-life problem-solving. This complex was created within the framework of future math teachers training. The course assignment involves student project on creating dynamic demonstration. ABSTRACT 2 [color=#1551b5][b]The computer simulation of SDN routing algorithm [/b][/color] [i]Liliia Bodnar, South Ukrainian National Pedagogical University named after K D Ushinsky Kateryna Shulakova, Odessa National Academy of Telecommunications named after A.S. Popov[/i] In this article, the authors review how the management and transmission of SDN elements can open new horizons for innovation. SDN is an architectural concept and a marketing term that combines a plurality of closed solutions building and network management. Existing simulation methods were reviewed for such networks. The mathematical software of environment GeoGebra can be offered as a simulation system of SDN routing algorithm. In a demonstration of Dijkstra's algorithm for different network models can clearly see the benefits that can be achieved using this algorithm in SDN networks. This research is aimed at simplifying network configuration, and as a result of reducing the cost of network equipment when not changing the technical specifications of nodes.

Table of Contents

  1. Introduction
    1. Introduction
    2. GeoGebra Support of Stages of Future Math Teachers' Training
    3. GeoGebra Support. Sides
    4. Why Discrete Math Is Important?
  2. Set Theory
    1. Regions of a Venn Diagram with Two Sets
    2. Quiz with Venn Diagram
    3. Set Notation & Venn Diagrams
    4. Describing Venn Diagrams using Set Notation & Words
    5. Set Quiz
    6. Sets. Inequalities
    7. Sets. Inequalities. Demo
    8. Describe the following sets
    9. Quiz
  3. Graph Theory
    1. Adjacent Matrix
    2. Generate Graph
    3. Planar Graphs
    4. Nonplanar Graphs
    5. Euler Graph
    6. Hamilton Graph
    7. Petersen Graph
    8. Transformation of maps into graphs.
    9. Four colour theorem
    10. Real-life Problem. Store Chemicals in Warehouse
    11. Same Idea. Zoo Problem
    12. Real-life problem. Timetable
    13. Chromatic polynomials
    14. Theorem. Chromatic Polynomial
    15. Discrete Command
    16. The routing algorithm in traditional networks
  4. Combinatorics
    1. Polygonal Numbers. Triangular and Square
    2. General Modal for Polygonal Numbers

1.

Introduction

  • 1. Introduction
  • 2. GeoGebra Support of Stages of Future Math Teachers' Training
  • 3. GeoGebra Support. Sides
  • 4. Why Discrete Math Is Important?

1.1.

Introduction

[b]Pre-service Teachers[/b][br][br][b][color=#0c343d]Department of Computer Science [/color][/b][br]http://kafinfo.org.ua/[br][br]Faculty of Physics and Mathematics [br][b]G.S.Scovorodu Kharkiv National Pedagogical University[/b][br]UKRAINE[br][color=#0000ff][br][b]GeoGebra Institute of  Kharkiv[/b][/color][br][br][i]Author: [/i]Valentyna Pikalova[br]vpikalova@hotmail.com
– Valentyna Pikalova

1.2.

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1.3.

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1.4.

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2.

Set Theory

  • 1. Regions of a Venn Diagram with Two Sets
  • 2. Quiz with Venn Diagram
  • 3. Set Notation & Venn Diagrams
  • 4. Describing Venn Diagrams using Set Notation & Words
  • 5. Set Quiz
  • 6. Sets. Inequalities
  • 7. Sets. Inequalities. Demo
  • 8. Describe the following sets
  • 9. Quiz

2.1.

Regions of a Venn Diagram with Two Sets

Venn diagram with two sets - click to see the different parts in colour.
Modified version of file from Project Maths
– Valentyna Pikalova, GreenMaths

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Graph Theory

  • 1. Adjacent Matrix
  • 2. Generate Graph
  • 3. Planar Graphs
  • 4. Nonplanar Graphs
  • 5. Euler Graph
  • 6. Hamilton Graph
  • 7. Petersen Graph
  • 8. Transformation of maps into graphs.
  • 9. Four colour theorem
  • 10. Real-life Problem. Store Chemicals in Warehouse
  • 11. Same Idea. Zoo Problem
  • 12. Real-life problem. Timetable
  • 13. Chromatic polynomials
  • 14. Theorem. Chromatic Polynomial
  • 15. Discrete Command
  • 16. The routing algorithm in traditional networks

3.1.

Adjacent Matrix

– Valentyna Pikalova

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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4.

Combinatorics

  • 1. Polygonal Numbers. Triangular and Square
  • 2. General Modal for Polygonal Numbers

4.1.

Polygonal Numbers. Triangular and Square

[b]Polygonal number[/b] is a number represented as dots or pebbles arranged in the shape of a regular polygon.[br][br]Author: [b]prof. Liudmyla Gryzun[/b], G.S.Scovorodu Kharkiv National Pedagogical University
– Valentyna Pikalova

4.2.

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Information