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 > 0 then B(n) := n + B(n1)
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
{AB,AC,AD,AE,BC,BD,BE,CD,CE, DE}.
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 1,250word 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 realworld 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 realworld 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 realworld 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 27Jul2016
Price : $22