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MTH 221 Week 1 DQ 1

MTH 221 Week 1 DQ 2

- 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?

- 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.
- p = God is loveq = Love is blindr = Ray Charles is blinds = Ray Charles is God

MTH 221 Week 1 DQ 3

MTH 221 Week 1 Individual and Team Assignment Selected Textbook Exercises

- Relate one of the topics from this week's material to a situation in your professional or personal life and discuss how you would solve the issue with the recently acquired knowledge.

- Mathematics - Discrete Mathematics
- Complete 12 questions below by choosing at least four from each section.
- · Ch. 1 of Discrete and Combinatorial Mathematics
- o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b)
- · Ch. 2 of Discrete and Combinatorial Mathematics
- o Exercise 2.1, problems 2, 3, 10, & 13,
- o Exercise 2.2, problems 3, 4, & 17
- o Exercise 2.3, problems 1 & 4
- o Exercise 2.4, problems 1, 2, & 6

MTH 221 Week 2 DQ 1

MTH 221 Week 2 DQ 2

- 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?

- 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.

MTH 221 Week 2 DQ 3

MTH 221 Week 2 DQ 4

- 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.

- A common result in the analysis of sorting algorithms is that for nelements, the best average-case behavior of any sort algorithm—based solely on comparisons—is O(n logn). 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 2 Individual and Team Assignment Selected Textbook Exercises

MTH 221 Week 2 Team Assignment Selected Textbook Exercises

- Mathematics - Discrete Mathematics
- Complete 12 questions below by choosing at least three from each section.
- • Ch. 4 of Discrete and Combinatorial Mathematics
- o Exercise 4.1, problems 4, 7, & 18
- o Exercise 4.2, problems 11 & 16
- • Ch. 4 of Discrete and Combinatorial Mathematics
- o Exercise 4.3, problems 4, 5, 10, & 15
- o Exercise 4.4, problems 1 & 14
- o Exercise 4.5, problems 5 &12

- Complete the 4 questions below and submit on the worksheet provided by Deb.
- · Ch. 4 of Discrete and Combinatorial Mathematics
- o Exercise 4.1, problem 18; p 209
- o Exercise 4.5, problems 2; p 241
- · Ch. 5 of -Discrete and Combinatorial Mathematics
- o Exercise 5.2, problems 27(a & b); p 259
- Exercise 5.8, problem 6; p 301

MTH 221 Week 3 DQ 1

MTH 221 Week 3 DQ 2

- In week 2 we reviewed relations between sets. We will continue that topic this week too. With definitions and examples discuss at least 3 different types of relations.

- Read through sections 7.2 and 7.3 for topics on 0-1 matrices, directed graphs and partial orders. Pick any of the topics (definitions and theorems) that was not already covered by your fellow students and present your understanding. Please provide examples as you discuss.

MTH 221 Week 3 DQ 3

MTH 221 Week 3 DQ 4

- Read through section 8.1-8.2 and discuss your findings.
- Sections 8.1 and 8.2 illustrate the principle of inclusion and exclusion based on conditions for inclusion.

- Disucss how the principle of inclusion and exclusion is related to the rules of manipulation and simplification of logic predicates from chapter 2.

MTH 221 Week 3 Individual and Team Assignment Selected Textbook Exercises

MTH 221 Week 3 Team Assignment Selected Textbook Exercises

- Mathematics - Discrete Mathematics
- Complete 12 questions below by choosing at least four from each section.
- • Ch. 7
- o Exercise 7.1, problems 5, 6, 9, & 14
- o Exercise 7.2, problems 2, 9, &14 (Develop the algorithm only, not the computer code.)
- o Exercise 7.3, problems 1, 6, & 19
- • Ch. 7
- o Exercise 7.4, problems 1, 2, 7, & 8
- • Ch. 8
- o Exercise 8.1, problems 1, 12, 19, & 20

- Complete the 4 questions below and submit on the worksheet provided by Deb.
- · Ch. 7
- o Exercise 7.2, problems 2 &14 (Develop the algorithm only, not the computer code.); pp 354
- · Ch. 8
- o Exercise 8.1, problem 20; p 397
- Exercise 8.2, probles 4; p 401

MTH 221 Week 4 DQ 1

MTH 221 Week 4 DQ 2

- Review section 11.1 of the text and discuss here at least 2 topics from the section along with one exercise problem.

- Review sections 11.2-11.4 of the text and discuss topics (that were not already covered by your colleagues) from the section. Don't forget the examples.

MTH 221 Week 4 DQ 3

MTH 221 Week 4 DQ 4

- 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.

- 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

MTH 221 Week 4 Individual and Team Assignment Selected Textbook Exercises

MTH 221 Week 4 Team Assignment Selected Textbook Exercises

- Mathematics - Discrete Mathematics
- Complete 12 questions below by choosing at least four from each section.
- • Ch. 11 of Discrete and Combinatorial Mathematics
- o Exercise 11.1, problems 3, 6, 8, 11, 15, & 16
- • Ch. 11 of Discrete and Combinatorial Mathematics
- o Exercise 11.2, problems 1, 6, 12, & 13,
- o Exercise 11.3, problems 5, 20, 21, & 22
- o Exercise 11.4, problems 14, 17, & 24
- o Exercise 11.5, problems 4 & 7

- Complete 4 questions below and submit on the sheet provided by Deb.:
- · Ch. 11 of Discrete and Combinatorial Mathematics
- o Exercise 11.4, problem 24; pp 554-555
- o Exercise 11.6, problem 10; p 572
- · Ch. 12 of Discrete and Combinatorial Mathematics

MTH 221 Week 5 DQ 1

MTH 221 Week 5 DQ 2

- In your own words, discuss examples of at least 3 of the ten laws of Boolean algebra.

- With an example, discuss the basic concepts of boolean algebra.

MTH 221 Week 5 DQ 3

MTH 221 Week 5 Individual and Team Assignment Selected Textbook Exercises

- 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?

- Mathematics - Discrete Mathematics
- Complete 12 questions below.
- · Ch. 15 of Discrete and Combinatorial Mathematics
- o Supplementary Exercises, problems 1, 5, & 6
- · Ch. 15 of Discrete and Combinatorial Mathematics
- o Exercise 15.1, problems 1, 2, 11, 12, 14, & 15
- · Ch. 15 of Discrete and Combinatorial Mathematics

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