MTH 221 Week 1 DQ 1 New

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MTH 221 Week 1 DQ 1 New

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 1 DQ 2 New

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MTH 221 Week 1 DQ 2 New

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 love

q = Love is blind

r = Ray Charles is blind

s = Ray Charles is God

MTH 221 Week 1 DQ 3 New

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MTH 221 Week 1 DQ 3 New

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.

MTH 221 Week 2 DQ 1 New

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MTH 221 Week 2 DQ 1 New

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?

MTH 221 Week 2 DQ 2 New

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MTH 221 Week 2 DQ 2 New

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 New

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MTH 221 Week 2 DQ 3 New

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.

MTH 221 Week 2 DQ 4 New

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MTH 221 Week 2 DQ 4 New

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 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?