Statistics DB Applications of Discrete Mathematics and Statistics in IT

Assignment Details

Assignment Description

The Discussion Board (DB) is part of the core of online learning. Classroom discussion in an online environment requires the active participation of students and the instructor to create robust interaction and dialogue. Every student is expected to create an original response to the open-ended DB question as well as engage in dialogue by responding to posts created by others throughout the week. At the end of each unit, DB participation will be assessed based on both level of engagement and the quality of the contribution to the discussion.

At a minimum, each student will be expected to post an original and thoughtful response to the DB question and contribute to the weekly dialogue by responding to at least two other posts from students. The first contribution must be posted before midnight (Central Time) on Wednesday of each week. Two additional responses are required after Wednesday of each week. Students are highly encouraged to engage on the Discussion Board early and often, as that is the primary way the university tracks class attendance and participation.

The purpose of the Discussion Board is to allow students to learn through sharing ideas and experiences as they relate to course content and the DB question. Because it is not possible to engage in two-way dialogue after a conversation has ended, no posts to the DB will be accepted after the end of each unit.

Assignment Details

Consider the following weighted graph:

In the table below, choose the bracket that contains the first letter of your last name. Then, choose 1 value for a and 1 value for b from the numbers listed for your bracket. (Put your chosen values for a and b in the heading for your first post for the week, so your classmates will know which values you have chosen for each and so they will not choose the same values as yours. Be sure to choose a combination of a and b that is different from your classmates who have already posted or have chosen their values.) The values chosen will be the weights in the paths labeled a and b in the weighted graph above.

Chosen Number for a = 16 Chosen number for b = 11

Last Name Begins With	a	b
A–K	10, 14, 16, 5	4, 6, 9, 11
L–Q	5, 11, 13, 8	2, 7, 12, 15
R–Z	3, 8, 10, 19	13, 15, 17, 18

· In the weighted graph above, find the shortest path from node A to node E using Dijkstra’s shortest path algorithm and using your chosen values for a and b.

· Explain your key steps in determining the shortest path, and give the node sequence that corresponds to that shortest path.

· Explain 2 examples where knowledge of a shortest path algorithm could be useful in an information technology career.

· Thinking of the graph above as undirected, does this graph have a Euler path? If so, give an example of such a path starting with a node you choose; if not, explain why not.

· Does this graph have a Euler circuit? If so, give an example; if not, explain why not.

· Does this graph have a Hamiltonian path? If so, give an example of such a path starting with a node you choose; if not, explain why not.

· If there is a Hamiltonian path, is there a Hamiltonian circuit? If so, give an example of such a circuit starting with a node you choose; if not, explain why not.

Respond to at least 2 classmates’ postings. If you think that there may be errors in your classmate’s post, feel free to help your classmate without providing the correct answer. Otherwise, analyze the post in comparison to yours, or add new information to the discussion.