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##### Math 221 Discrete Mathematics UOPX I need full Last 3 weeks of-(Answered)

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I have attached my Discrete Math syllabus for week 3 , week 4 and week 5 I need help on Class Participation, week 5 individual Assignments and week 4 and week 5 Student Connect express Solutions, ASAP Please take a look its very small work not much.?

Book Name: Discrete Mathematics and Its Applications ,Seventh Edition by Kenneth Rosen

?instructor name: stephen wiitala for University of Phoenix

Math 221 Discrete Mathematics UOPX

I need full Last 3 weeks of help all are listed

below

Make sure all of them are fresh work with

proper citation APA format, no used work

will be accepted thanks so much.

To be substantive, in addition to meeting the minimum content expectations, your posts

must include proper APA style citations at the point of use of information from a source. A

citation is a notation of the form (AuthorLastName, date, page). A page reference is

required if the information is a direct quote. Citations are required even if the information

is not directly quoted, but rather paraprased or summarized. You are also required to

provide references formatted in APA style.

Make sure while you write any of those answer please use it proper citations as you can see

above red lines from my instructor he is very restrict about citations, I request you to read

that and follow his instructions thanks so much.

Week3 Algorithmic Concepts

Class Discussions: 4 questions

Question 1:

Big O notation - a specific example

Suppose we are given the following program segment:

F(x) = 0

Input n

For x = 1 to x = n

F(x) = x(x+3)+2

Print x

Next x

1. Determine the number of steps the program will execute before entering the loop.

2. Determine the number of steps the program will execute each time it passes through the loop.

3. Determine the total number of steps that will be executed by the program if the value of n is 3,4,5,

n

4. This program segment is considered to be O(n). Explain why.

5. Suppose that another program segment is O(n?). Does this mean that the second segment will

always require more steps than this segment?

Question 2:

Explaining Induction

Many people when first ecountering induction find it very confusing, because it appears that one of

the steps in proving a statement by induction is to assume that the statement we are trying to prove

is true.

Suppose you are discussing this concept with a friend, and you friend tell you that induction does not

prove anything. How would you explain to this person why it is that induction actually does work. In

my follow up responses to you, I may ask you questions that your friend might as in response to your

explanation. Try to phrase those responses as though you were responding to somebody who was

very confused.

Question 3:

Recursion and Repetition

Here are two functions that both compute the same quantity. One is a recursively defined function

and the other is defined by repetition.

Function A(n)

Sum : = 0

For x := 1 to n do

Sum:= Sum + x

end do

A(n) := sum

end Function A(n)

Function B(n)

If n = 0 then B(n) : = 0

If n &gt; 0 then B(n) := n + B(n-1)

end Function B(n)

1.

2.

3.

4.

What do these two functions compute?

Which function is recursive and which function is repetive?

Which one do you find easiest to follow

What are the differences in the implementation of each function?

Individual Assignment will be posted once it available from instructor and it?s the lab student connect

I have to wait for him to get the information so please wait for that we might can work on this

assignment together via TeamViewer.

Week4 Graph Theory and Trees

Class Discussions:- 2 questions

Question 1:

An Application of Graph Theory in Network Design

Suppose that we have a communication network with 5 nodes, and each pair of nodes is connected

directly. This network can be represented by a graph with 5 vertices {A,B,C,D,E}, and 10 edges

Assume the the network has been hit with a disaster in such a a way that each link has a 50%

probability that the link is intact. Simulate that situation by flipping a coin 10 times, once for each

edge. If the coin is heads, the link has remaind intact. If the coin is tails, the link has been lost.

1. Draw the resulting graph

2. How many edges does the resulting graph have?

3. Is the graph that results connected? What does this mean for the ability to continue to

communicate through the network?

4. Do you think that if a 6th node were added to the network but we were limited to having only 10

edges if the situation would change? How would you arrange the edges make it as likely as possible

that the network would remain connected?

This is actually a discussion related to an interesting topic in graph theory known as random graphs.

This theory can explore the chances that various network configurations remain intact based on

various probabilities of failures of links in the network (we might change the probability of a failure

from 50% to some other value).

Question 2:

Trees and Computations

Trees occur in various venues in computer science: decision trees in algorithms, search trees, and

so on. One important kind of trees computer languages is the parse tree. It is used to break down

statements in a programming langue into a form that can be converted into machine code. The most

familiar of these kinds of trees are used to break down Arithmetic statements into trees.

For example, the computation 2*3 + 4, can be parsed into the following tree

+

/

\

*

/

2

4

\

3

On the other hand the computation 2 * (3 + 4) would have a different parse tree

*

/ \

2

+

/ \

3 4

1. What are the similarities differences between the two trees in terms of depth, roots, and breadth?

2. What do those differences between the trees tell us about the differences between the steps need

to do each computation.

3. Provide an arithmetic computation with at least three operations in it, and determine its parse

tree.

Individual Assignment will be posted once it available from instructor and it?s the lab student connect

I have to wait for him to get the information so please wait for that we might can work on this

assignment together via TeamViewer.

Please don?t forget to help me on this week Individual assignment

Week5 Applications of Discrete Mathematics

Class Discussions:- 4 questions

Question 1:

Solutions to Practice Problem 1

Practice Problem (1) on Counting Techniques

There are four practice problems available for you to discuss this week. They focus on content from

all four of the previous week of the course. Use these problems to test your readiness for the Final

Exam. Towards the end of the the week, I will post solutions to the problems. Your responses in this

discussion do count for participation credit

Suppose you are organizing a business meeting and are in charge of facilitating the introductions.

A. Suppose there are 5 people in the group

1.How would you arrange the group so each person can shake hands with every other person?

2. How many times will each person shake hands with someone else?

3. How many handshakes will occur?

B. Suppose there is an unknown number (n) people in the group

1.How would you arrange the group of n people so each person can shake hands with every other

person?

2. How many times will each person shake hands with someone else?

3. How many handshakes will occur? This answer should be expressed as a general counting

formula that depends on the value of n.

Question 2:

Solutions to Practice Problem 2

Practice Problem (2) on Logic

There are four practice problems available for you to discuss this week. They focus on content from

all four of the previous week of the course. Use these problems to test your readiness for the Final

Exam. Towards the end of the week, I will post solutions to the problems. Your responses in this

discussion do count for participation credit

Use a truth table or Venn diagram to show that the statement p v (q ^ r) is equivalent to (p v q) ^ (p v

r)

Show that this statement is not equivalent to (p v q) ^ r.

Be sure to explain your answer and don't just provide a truth table or Venn diagram. Why does your

table or diagram verify the result?

Question 3:-

Solutions to Practice Problem 3

Practice Problem (3) on Relations

There are four practice problems available for you to discuss this week. They focus on content from

all four of the previous week of the course. Use these problems to test your readiness for the Final

Exam. Towards the end of the week, I will post solutions to the problems. Your responses in this

discussion do count for participation credit

Define the following relation on the set of positive integers

xRy if x - y is an even integer

1. Show that R is an equivalence relation.

With an equivalence relation, the set on which the relation is defined is divided into subsets called

equivalence classes. These subsets consist of all elements that are equivalent to each other. The

equivalence class of 1, denoted by [1] consists of all elements that are equivalent to 1 under the

relation.

2. How many distinct equivalence classes are there in this example? Can you describe the sets?

Question 4:-

Solutions to Practice Problem 4

Practice Problem (4) on Tree Traversal Algorithms

There are four practice problems available for you to discuss this week. They focus on content from

all four of the previous week osf the course. Use these problems to test your readiness for the Final

Exam.. Your responses in this discussion do count for participation credit

The following algorithm describes a postorder tree traversal

Postorder(tree)

If left subtree exists then Postorder(left subtree)

If right subtree exists then Postorder(right subtree)

Print root

end

Can you apply that to the following tree

+

/

\

/

\

*

-

/ \

/

\

2 3

*

+

/ \

/ \

4 2 1 5

What is the result of the executing the algorithm? In the terminology of Week 3, what kind of

algorithm are we considering here?

Individual Assignment:-

Case Study Application Paper

Choose one of the following Case Studies:

Food Webs

Coding Theory

Network Flows

Write a 750- to 1,250-word paper in which you complete one of the following options:

Option 1: Food Webs Case Study

Explain the theory in your own words based on the case study and suggested readings.

Include the following in your explanation:

Competition

Food Webs

Boxicity

Trophic Status

Give an example of how this could be applied in other real-world applications.

Format your paper according to APA guidelines. All work must be properly cited and referenced. The

correct reference for this source is the following:

McGuigan, R. A.. (1991). Food Webs. Retrieved from McGuigan, R. A., MTH221 - Discrete

Math for Information Technology website

Submit your assignment to the Assignment Files tab.

Option 2: Coding Theory Case Study

Explain the theory in your own words based on the case study and suggested readings.

Include the following in your explanation:

Error Detecting Codes

Error Correcting Codes

Hamming Distance

Perfect Codes

Generator Matrices

Parity Check Matrices

Hamming Codes

Give an example of how this could be applied in other real-world applications.

Format your paper according to APA guidelines. All work must be properly cited and referenced. The

correct reference for this source is

Rosen, K. H.. (1991). Coding Theory . Retrieved from Rosen, K. H., MTH221 - Discrete

Math for Information Technology website.

Submit your assignment to the Assignment Files tab.

Option 3: Network Flows Case Study

Explain the solutions for examples 1, 2 and 3 from the text.

Explain the theory developed including capacitated s,t graphs and the lexicographic ordering rule

based on the case study and suggested readings.

Give an example of how this could be applied in other real-world applications.

Format your paper according to APA guidelines. All work must be properly cited and referenced.

The correct reference for this source is:

Hobbs, A. M. (1991). Network Flows. Retrieved from Rosen, K. H., MTH221 - Discrete Math for

Information Technology website.

Attached PDF file has all three documents for the week 5 case study application paper

Supporting documents?

Week -5 Food Webs

Week 5 Mt

Week -5 Mth

theory.pdf

h221_r3_coding_theory_case_study.pdf

221_r3_network_flows_case_study.pdf

There are 2 individual assignments on week 5, I only have one information so far and that is above listed

and waiting for the other one.

He is using this book Discrete Mathematics and Its Applications 7e

Kenneth H. ROSEN

Paper#9256343 | Written in 27-Jul-2016

Price : \$22