2. MTH 221 Week 5 DQ 1
MTH 221 Week 5 DQ 2
MTH 221 Week 5 DQ 3
MTH 221 Week 5 Individual Assignment Selected Textbook Exercises
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MTH 221 Week 5 Individual Assignment Selected Textbook Exercises
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
o Exercise 15.1, problems 4, 5, 8, & 9
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3. MTH 221 Week 5 DQ 3
Conjunctive and disjunctive normal forms provide a form of balanced expression.
How might this be important in terms of the efficiency of computational
evaluation?
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MTH 221 Week 5 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?
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MTH 221 Week 5 DQ 1
How does Boolean algebra gets the essential properties of logic operations and set
operations?
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MTH 221 Week 4 Individual Assignment Selected Textbook Exercises
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
4. 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
o Exercise 5.6, problems 9 &10
Ch. 12 of Discrete and Combinatorial Mathematics
o Exercise 12.1, problems 2, 6, 7, & 11
o Exercise 12.2, problems 6 & 9
o Exercise 12.3, problems 2 & 3
o Exercise 12.5, problems 3 & 8
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MTH 221 Week 4 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, sub clauses, nouns, verbs, adverbs, adjectives, prepositions,
and so on. What might be the significance of the depth and breadth of a parse tree
5. 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 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?
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MTH 221 Week 4 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.
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MTH 221 Week 3 Individual Assignment Selected Textbook Exercises
Complete 12 questions below by choosing at least four from each section.
Ch. 7
6. 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
o Exercise 8.2, problems 4 & 5
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MTH 221 Week 3 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?
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MTH 221 Week 3 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?
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MTH 221 Week 3 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.
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MTH 221 Week 2 Individual Assignment Selected Textbook Exercises
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
Ch. 5 of Discrete and Combinatorial Mathematics
o Exercise 5.1, problems 5 & 8
8. o Exercise 5.2, problems 2, 5, 12, & 27(a & b)
o Exercise 5.3, problems 1 & 8
o Exercise 5.4, problems 13 & 14
o Exercise 5.5, problems 2 & 7(a)
o Exercise 5.6, problems 2, 3, 4, & 5
Ch. 5 of Discrete and Combinatorial Mathematics
o Exercise 5.7, problems 1 & 6
o Exercise 5.8, problems 5 & 6
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MTH 221 Week 2 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.
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MTH 221 Week 2 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.
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MTH 221 Week 2 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?
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MTH 221 Week 1 Individual Assignment Selected Textbook Exercises
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
10. o Exercise 2.5, problems 1, 2, & 4
Ch. 3 of Discrete and Combinatorial Mathematics
o Exercise 3.1, problems 1, 2, 18, & 21
o Exercise 3.2, problems 3 & 8
o Exercise 3.3, problems 1, 2, 4, & 5
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MTH 221 Week 1 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
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MTH 221 Week 1 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.
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11. MTH 221 Week 1 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?
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