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MTH/221 Discrete Mathematics 

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MTH/221 Week 1Everything listed for this week is included in purchase!!
Individual: Week 1 Connect Exercises (and Answers)!
SET #1  35 Questions 1. A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made? not contain the same digit twice? (b) How many strings of four decimal digits do not contain the same digit twice? Explanation to Question #2: The product rule must be used since there are 10 ways to choose the first digit, 9 ways to choose the second, and so on. If there are n_{1} ways to do the first task and for each of these ways of doing the first task, there are n_{2} ways to do the second task, then there are n_{1}n_{2} ways to do the procedure. Therefore you would calculate the answer as: 10 · 9 · 8 · 7 = 5040 ways. 3. b) Which rule must be used to find the number of strings of four decimal digits that end with an even digit? How many strings of four decimal digits end with an even digit? Explanation to Question #3: The product rule is used in this case, since there are 10 ways to choose each of the first three digits and 5 ways to choose the last. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n_{2} ways to do the second task, then there are n_{1}n_{2} ways to do the procedure. Therefore you would calculate the answer as: 10^{3}· 5 = 5000 ways.
SET #2  18 Questions 1. A particular brand of shirt comes in 13 colors, has a male version and a female version, and comes in 3 sizes for each sex. How many different types of this shirt are made? 2. How many strings of five decimal digits 3. How many strings of six uppercase English letters are there 4. In how many different orders can five runners finish a race if no ties are allowed? 5. How many bit strings of length 9 have ...
Discussion Questions Included Supporting Activity What is the difference between combinations and permutations? What are some practical applications of combinations? Permutations?
Supporting Activity Find the number of permutations of A,B,C,D,E,F taken three at a time (in other words find the number of "3letter words" using only the given six letters WITHOUT repetition).
Supporting Activity Suppose you are assigning 6 indistinguishable print jobs to 4 indistinguishable printers. In how many ways can the print jobs be distributed to the printers?
Supporting Activity Suppose UOPX has 3 different math courses, 4 different business courses, and 2 different sociology courses. Tell me the number of ways a student can choose one of EACH kind of course. Then tell me the number of ways a student can choose JUST one of the course.
Supporting Activity Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd?


MTH/221 Week 2Everything listed for this week is included in purchase!!
** NOTE: Connect Exercise questions may not be identical to what you have since they are change frequently. However, they are the same type of question, just different numbers involved. To assist, All Connect Exercise Questions include detailed explanations on how to arrive at the Correct answer (as shown above for #2 and #3 questions).
Individual: Week 2 Connect Exercises
SET #1  93 Questions
SET #2  12 Questions 1. Which of these are propositions? What is the truth value of those that are propositions? 2. Let p, q, and r be the propositions b) I come to class whenever there is going to be a quiz. c) A positive integer is a prime only if it has no divisors other than 1 and itself.
MTH/221 WEEK 2 Discussion Questions Supporting Activity There is an old joke, commonly attributed to Groucho Marx, which goes something like this: "I don't want to belong to any club that will accept people like me as a member." Does this statement fall under the purview of Russell's paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement.
Supporting Activity How do we distinguish relations from functions?
Supporting Activity What sort of relation is friendship, using the human or sociological meaning of the word? Is it necessarily reflexive, symmetric, antisymmetric, or transitive? Explain why it is or is not any of these. What other types of interpersonal relationships share one or more of these properties? Explain.
Supporting Activity Write the dual of the following Boolean equation: a+a'b = a+b?
Supporting Activity Reduce the following Boolean product to zero OR a fundamental product: xyx'z.


MTH/221 Week 3Everything listed for this week is included in purchase!!
** NOTE: Connect Exercise questions may not be identical to what you have since they are change frequently. However, they are the same type of question, just different numbers involved. To assist, All Connect Exercise Questions include detailed explanations on how to arrive at the Correct answer.
Individual: Week 3 Connect Exercises
SET #1  83 Questions 1. Identify the steps that are used to find the maximum element from the following finite sequence 1, 8, 12, 9, 11, 2, 14, 5, 10, 4. 2. Rearrange the following algorithm in the correct order to find the sum of all the integers in a list. 3. Rearrange the following algorithm that takes as input a list of n integers and products as output the largest difference obtained by subtracting an integer in the list from the one following it.
SET #2  28 Questions 1. List all the steps used by Algorithm 1 to find the maximum of the list 3, 9, 14, 7, 11, 4, 18, 3, 11, 2. 2. Determine which characteristics of an algorithm described in the text (after Algorithm 1) the following procedures have and which they lack. Select characteristics that the procedures have and leave characteristics unselected that the procedures lack. 3. Which of the following algorithms can be used to find the sum of all integers in a list?
MTH/221 WEEK 3 Class Discussion Questions Supporting Activity Describe a situation in your professional or personal life when recursion, or at least the principle of recursion, played a role in accomplishing a task, such as a large chore that could be decomposed into smaller chunks that were easier to handle separately, but still had the semblance of the overall task. Did you track the completion of this task in any way to ensure that no pieces were left undone, much like an algorithm keeps placeholders to trace a way back from a recursive trajectory? If so, how did you do it? If not, why did you not?
Supporting Activity Given this recursive algorithm for computing a factorial... procedure factorial(n: nonnegative integer) if n = 0 then return 1 else return n *factorial(n − 1) {output is n!} Show all the steps used to find 5!
Supporting Activity Describe an induction process. How does induction process differ from a process of simple repetition?
Supporting Activity List all the steps used to search for 9 in the sequence 1,3, 4, 5, 6, 8, 9, 11 using a binary search.


MTH/221 Week 4Everything listed for this week is included in purchase!!
** NOTE: Connect Exercise questions may not be identical to what you have since they are change frequently. However, they are the same type of question, just different numbers involved. To assist, All Connect Exercise Questions include detailed explanations on how to arrive at the Correct answer.
Individual: Week 4 Connect Exercises
SET #1  32 Questions 1. Identify the type of graph. 2. What is the number of vertices of the given graph? 3. Click and drag the vertices (in the right column) to their number of indegrees (in the left column).
SET #2  14 Questions 1. Determine whether the graph shown has directed or undirected edges, whether it has multiple edges, and whether it has one or more loops. Use your answers to determine the type of graph in Table 1.
2. The intersection graph of a collection of sets A1, A2, . . . , An is the graph that has a vertex for each of these sets and has an edge connecting the vertices representing two sets if these sets have a nonempty intersection. Select the intersection graph of these collections of sets. 3. Find the number of vertices, the number of edges, and the degree of each vertex in the given undirected graph. Identify all isolated and pendant vertices.
MTH/221 WEEK 4 Class Discussion Questions
Supporting Activity: Hamiltonian and Euler Graphs Note a Hamiltonian circuit visits each vertex only once but may repeat edges. A Eulerian graph traverses every edge once, but may repeat vertice.
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Supporting Activity: Path Analysis Class
Supporting Activity: Random Graphs Random graphs are a fascinating subject of applied and theoretical research. These can be generated with a fixed vertex set V and edges added to the edge set E based on some probability model, such as a coin flip. Speculate on how many connected components a random graph might have if the likelihood of an edge (v1,v2) being in the set E is 50%. Do you think the number of components would depend on the size of the vertex set V? Explain why or why not.
Supporting Activity: Trees and Language Processing Trees occur in various venues in computer science: decision trees in algorithms, search trees, and so on. In linguistics, one encounters trees as well, typically as parse trees, which are essentially sentence diagrams, such as those you might have had to do in primary school, breaking a naturallanguage sentence into its componentsclauses, subclauses, nouns, verbs, adverbs, adjectives, prepositions, and so on. What might be the significance of the depth and breadth of a parse tree relative to the sentence it represents? If you need to, look up parse tree and natural language processing on the Internet to see some examples.


MTH/221  Week 5Everything listed for this week is included in purchase!!
** NOTE: Connect Exercise questions may not be identical to what you have since they change frequently. However, they are the same type of question, just different numbers involved. To assist, All Connect Exercise Questions include detailed explanations on how to arrive at the Correct answer (as shown above for #2 and #3 questions).
Case Study Application Paper
Option 1: Food Webs Case Study
FINAL EXAM (2 Sets Included) 40 Questions 1. A particular brand of shirt comes in 8 colors, has a male version and a female version, and comes in 5 sizes for each sex. How many different types of this shirt are made? 2. A club has 22 members. a) How many ways are there to choose four members of the club to serve on an executive committee?3. In how many different ways can ten elements be selected in order from a set with four elements when repetition is allowed? 4. What is the probability that a fair die never comes up an odd number when it is rolled eight times? 5. Let p, q, and r be the propositions Supporting Activity After performing some research or based on your reading in the course, share with the class the most practical use of discrete mathematics (in your opinion). Please cite your source.
