This applet includes a comprehensive series of 24 lessons in graph theory, including complete graphs, graph coloring, Hamiltonian Circuits, Euler Circuits, spanning trees, and others.
Type of Material:
Tutorial & simulation
Classroom demo, student tutorials
JAVA 2 enabled browser, Peterson software
Identify Major Learning Goals:
Understand graph theory concepts including definitions of terms, properties and applications.
Target Student Population:
Undergraduate graph theory and discrete mathematics courses.
Prerequisite Knowledge or Skills:
None, provided the user follows the lessons in sequence, the lessons define all the terms and definitions.
The lessons are well sequenced and include all the expected topics in introductory graph theory. Instructions and definitions are clear and followed by examples for the user to follow, both in the applet and using the Peterson software. Lessons reinforce concepts defined in earlier lessons, increasing retention. The Peterson software allows the student to select one of dozens of standard graphs or to create their own. It analyzes the graph for all of the features that an elementary graph theory student would be interested in.
The author forwarded an exam copy of the Peterson software for completion of the review. It was excellent in its instruction, but limited to 16 vertices. Occasionally, a lesson requested use of a larger number of vertices than the program could accommodate, but using a smaller number was equally instructive. The complete version of Peterson software is available from the author for $15 and accommodates 64 vertices.
There are no real concerns regarding the applet or the Peterson software. The Peterson software is not available commercially and information on its purchase is not readily available. The reviewers contacted the author for an exam copy and found the order form on the menu under the heading About.
Potential Effectiveness as a Teaching Tool
This applet is excellent as a tutorial or as a resource for a course in graph theory. It could serve as the centerpiece of an online course or as a supplement for a traditional course in graph theory. Each lesson is designed to introduce the concept with definitions and examples. The user is instructed to create specific graphs and determine their properties. The user is then sent to the Peterson software to verify these properties with more complex graphs. A series of questions are provided in each lesson that complement the topic and connect the lesson to the previous ones. Answers are provided that are clear and concise. In some lessons,
applications are given that enable the user to apply the graph theory.
The lessons build on previous lessons and definitions. The lessons are extremely well sequenced and interrelated so that the concepts in earlier lessons are reinforced. The instructor must be cautioned not to arbitrarily assign a particular applet without verifying that all other terms used in that applet have been previously introduced.
Ease of Use for Both Students and Faculty
The navigation is excellent with forward and back buttons used to move from one lesson to another. It is equally easy to move from the lesson page to the answer page and back. The Quick Directions included on the main page provide instructions for each command in the Peterson software. Instructions needed for each lesson are also given within the text of that lesson.
Drawing the vertices and edges are easy and the user can easily modify a graph without starting over. The Peterson software has a menu interface and is also very easy to use.
For some computers, the vertices of the generated null graph and complete graph lie outside of the visible area and cannot be moved without using the menu item picture -> size -> smaller.
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