Topics in Contemporary Math (MAT 1171) <- Courses <- Sean Forman <- You Are Here
|
Second Exam Review. The second exam will be on Monday, October 29. Unless you are previously excused or are very ill, no make-ups will be given. You may use basic calculators for the exam. Topics you will be expected to know are as follows. You are also responsible for any other topics we covered in class.
Chapter 5
What is a graph?
Definitions of edges, vertices, loops, multiple edges, paths, circuits, connected graphs, disconnected graphs, bridges, and adjacency.
Euler circuits and paths.
You should be able to state and apply Euler's Theorems.
Fleury's algorithm
Eulerization and semi-eulerization of graphs.
Chapter 6
Hamilton circuits and paths.
Complete graphs.
The number of Hamilton Circuits for a complete graph with N vertices.
Weighted graphs.
What is a traveling salesman problem?
How do you solve TSP by Brute Force, Nearest Neighbor, Cheapest Link or Repititive Nearest Neighbor?
Which of these algorithms are efficient or inefficient and which are guaranteed to find the optimal solution and which are approximate algorithms?
What is a factorial?
Chapter 7
What is a tree and how do you know if you have one?
What is a spanning subgraph and can you list all potential ones?
What are the various properties of trees?
What is Kruskal's algorithm and can you apply it to a graph?
General
Generate a counterexample for a false statement.