MTH 221 ENTIRE COURSE
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MTH 221 Week 1 Individual Assignment Selected Textbook Exercises
Complete 10 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment.
Ch. 1 of Discrete and Combinatorial Mathematics
Supplementary Exercises 1, 2a
Ch. 2 of Discrete and Combinatorial Mathematics
Exercise 2.1, problem 2
Exercise 2.2, problem 2
Exercise 2.3, problem 4
Exercise 2.4, problem 1
Exercise 2.5, problem 1
Ch. 3 of Discrete and Combinatorial Mathematics
Exercise 3.1, problem 1
Exercise 3.2, problem 3a
Exercise 3.3, problem 1
MTH 221 Week 1 DQS
DQ 1
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?
DQ 2
There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect
DQ 3
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
DQ 4
after reading Chapter 1 in our ebook, what is the difference between combinations and permutations? What are some practical applications of combinations? Permutations?
MTH 221 Week 2 Individual Assignment Selected Textbook Exercises
Complete 10 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment.
Ch. 4 of Discrete and Combinatorial Mathematics
Exercise 4.1, problem 5a
Exercise 4.2, problem 18a
Ch. 4 of Discrete and Combinatorial Mathematics
Exercise 4.3, problem 4
Exercise 4.4, problem 1a
Ch. 5 of Discrete and Combinatorial Mathematics
Exercise 5.1, problem 4
Exercise 5.2, problem 4
Exercise 5.3, problem 1a
Exercise 5.4, problem 13a
Ch. 5 of Discrete and Combinatorial Mathematics
Exercise 5.7, problem 1a
Exercise 5.8, problem 5a
MTH 221 Week 2 Team Selected Textbook Exercises
Complete 3 questions below. Please review the rubric posted in week 1 for math problems. Have one team member submit to their assignment tab. Submit a certificate of originality for this assignment.
Ch. 4 of Discrete and Combinatorial Mathematics
Exercise 4.3, problems 12a, & 15
Ch. 5 of Discrete and Combinatorial Mathematics
Exercise 5.1, problem 8
MTH 221 Week 2 DQS
DQ 1
· 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?
DQ 2
· Describe a favorite recreational activity in terms of its iterative components, such as solving a crossword or Sudoku puzzle or playing a game of chess or backgammon. Also, mention any recursive elements that occur.
DQ 3
· Using a search engine of your choice, look up the term one-way function. This concept arises in cryptography. Explain this concept in your own words, using the terms learned in Ch. 5 regarding functions and their inverses.
DQ 4
· A common result in the analysis of sorting algorithms is that for n elements, the best average-case behavior of any sort algorithm—based solely on comparisons—is O(n log n). How might a sort algorithm beat this average-case behavior based on additional prior knowledge of the data elements? What sort of speed-up might you anticipate for such an algorithm? In other words, does it suddenly become O(n), O(n log n) or something similar?
MTH 221 Week 3 Individual Assignment Selected Textbook Exercises
Complete 10 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment.
Ch. 7
Exercise 7.1, problems 5a, 6
Exercise 7.2, problem 2
Exercise 7.3, problems 1, 6a
Ch. 7
Exercise 7.4, problems 1a, 2a
Ch. 8
Exercise 8.1, problems 4, 12
Exercise 8.2, problem 4
MTH 221 Week 3 Team Selected Textbook Exercises
Complete 3 questions below. Please review the rubric posted in week 1 for math problems. Have one team member submit to their assignment tab. Submit a certificate of originality for this assignment.
Ch. 7
Exercise 7.4, problems 12a, & 13
Ch. 8
Exercise 8.1, problem 20
MTH 221 Week 3 DQS
DQ 1
· 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 or why not. Can the friendship relation among a finite group of people induce a partial order, such as a set inclusion? Explain why or why not.
DQ 2
· Look up the term axiom of choice using the Internet. How does the axiom of choice—whichever form you prefer—overlay the definitions of equivalence relations and partitions you learned in Ch. 7?
DQ 3
· How is the principle of inclusion and exclusion related to the rules for manipulation and simplification of logic predicates you learned in Ch. 2?
DQ 4
· In Example 7.36, the author provides an example using PERT. MS Project is a software program for project management. How do you think the programmers of MS Project apply the learning in Chapter 7 to their algorithms?
MTH 221 Week 4 Individual Assignment Selected Textbook Exercises
Complete 10 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment.
Ch. 11 of Discrete and Combinatorial Mathematics
Exercise 11.1, problems 3, 11
Ch. 11 of Discrete and Combinatorial Mathematics
Exercise 11.2, problem 4
Exercise 11.3, problem 5a
Exercise 11.4, problem 3a
Exercise 11.5, problem 2
Ch. 12 of Discrete and Combinatorial Mathematics
Exercise 12.1, problem 2
Exercise 12.2, problem 6
Exercise 12.3, problem 2
Exercise 12.5, problem 1
MTH 221 Week 4 Team Selected Textbook Exercises
Complete 4 questions below. Please review the rubric posted in week 1 for math problems. Have one team member submit to their assignment tab. Submit a certificate of originality for this assignment.
Ch. 11 of Discrete and Combinatorial Mathematics
Exercise 11.1, problems 6, & 16a
Ch. 12 of Discrete and Combinatorial Mathematics
Exercise 12.1, problems, 7, & 11
MTH 221 Week 4 DQS
DQ 1
· 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.
DQ 2
· You are an electrical engineer designing a new integrated circuit involving potentially millions of components. How would you use graph theory to organize how many layers your chip must have to handle all of the interconnections, for example? Which properties of graphs come into play in such a circumstance?
DQ 3
· 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 natural-language sentence into its components—clauses, 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.
DQ 4
· In Section 12.4 we learn about the Merge Sort algorithm; it is more efficient that the Bubble sort we learned about in Chapter 10. Doing some research on the Internet can you find a sorting algorithm more efficient than the Merge Sort? If you find one please describe it and list your reference.
MTH 221 Week 5 Individual Assignment Selected Textbook Exercises
Complete 5 questions below. Please review the rubric posted in week 1 for math problems. Submit to your assignment tab. Submit a certificate of originality for this assignment.
Ch. 15 of Discrete and Combinatorial Mathematics
Exercise 15.1, problems 1a, 2a,4a, 9, & 12
MTH 221 Week 5 Learning Team Research Presentation
Submit the final Research Presentation.
Please review the rubric posted in week 1 for the team project
Have one team member submit to their assignment tab
Submit a certificate of originality for this assignment
MTH 221 Week 5 DQS
DQ 1
· How does Boolean algebra capture the essential properties of logic operations and set operations?
DQ 2
· How does the reduction of Boolean expressions to simpler forms resemble the traversal of a tree, from the Week Four material? What sort of Boolean expression would you end up with at the root of the tree?
`
DQ 3`The introduction of Chapter 15 in your book introduces you to two founders of Boolean algebra and its applications (Boole and Shannon). After performing some research, share with the class some practical applications of Boolean algebra. Please cite your source.
DQ 4
· In review of the material you have learned over the past 5 weeks which element has made the biggest impression on you? What element do you think you can use in future work or school applications?
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