- Course 2, Unit 5
|In this unit, students studied important concepts and methods related to network optimization. The bolded words are vocabulary and concepts your student should be familiar with.|
|a.||Compare your concept map
from Task 3 [Looking Back lesson in student text] with those of other
students. Discuss similarities and differences.
Different students will make different connections among the ideas studied in this unit. Shown below is a map that shows major ideas.
|b.||Optimization or "finding
the best" is an important theme throughout this unit. Describe three
problem situations from the unit in which you "found the best." In
each case, explain how you used a graph model to solve the problem.
Students investigated many different problems in class. For example:
|c.||Describe one similarity between
minimal spanning trees and shortest paths. Describe one difference.
Minimal spanning trees and shortest paths are both the "shortest" in some sense, which could mean cheapest, or least in some way. But a minimal spanning tree is a shortest tree that includes all vertices as opposed to a shortest path that generally does not include all vertices.
|d.||Describe one similarity between
minimal spanning trees and the Traveling Salesperson Problem. Describe
In both minimal spanning tree problems and the Traveling Salesperson Problem, you are looking for something that is minimal and spanning (includes all vertices). In one case, you want a minimal spanning tree, and in the other, you want a minimal spanning circuit (starts and ends at the same vertex).
|e.||Describe one similarity between
the Traveling Salesperson Problem and shortest path problems. Describe
In both the Traveling Salesperson Problem and shortest path problems, you are looking for the "shortest," but in one case, it is a shortest circuit that includes all vertices, and in the other it is the shortest path (begins and ends at different vertices) that generally does not include all the vertices.
|f.||In this unit, you have explored
a variety of algorithms and methods for solving network optimization
problems, including best-edge algorithms and brute force methods.
For each of these two solution procedures, do the following.
If you would like to see specific problems from Course 2, Unit 5, a link is provided to Examples of Tasks from Course 2, Unit 5. If you are interested in following up on the Discrete Mathematics strand in general, then the Scope and Sequence will help you see where different concepts are introduced. On the Discrete Mathematics page, you can read an explanation of the main discrete mathematics concepts as they are developed in all four courses.