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MTH 221 Course Extraordinary Success
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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

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• 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

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• 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.

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• 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 algorithmbased
  solely on comparisonsis 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?

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• 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

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• 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.

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• 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.

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• 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

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• 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.

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• 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
  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

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• 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

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• 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.

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• 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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