Outline

1
Outline

• Introductions, why are you here?
• Pair up to complete preliminary survey
• Workshop goals and objectives
• What makes a problem nifty?
• Teaser nifty problems
• Other nifty problems
• Develop present nifty problems
• Evaluation

2
Introductions

• Name institution department
• Educational background (math, eng, other)
• Why taking this workshop?

3
Pair up

• Complete brief preliminary survey to start
  thinking about the issues
• What makes a problem nifty?

4
Thinking Mathematically
A bicycle rides through a puddle of spilled paint
ten inches wide. The circumference of both
wheels of the bicycle is 50 inches. The bike
continues moving in a straight line after
rolling through the paint. Sketch the pattern
the wheels of the bike make on the surface.
5
Paper Folding

• Lay a strip of paper left-to-right in front of
  you. Now fold it by taking the right end to the
  left end. Press flat so it is folded in half.
  How many creases are there?
• How many creases will there be if it is folded
  twice? 3times?
• Fold it 11 times. How many creases?
• Fold it n 0 times. How many creases?
• Looking from the edge, some the peaks of the
  creases point up (U) or point down (D). What is
  the sequence of Us and Ds, going left to right
  of creases for 5 folds?
• Same as above for 6 folds?
• Generalize the above when going from n to n1
  folds.
• Prove that if each crease is set to a 90 degree
  angle then the paper will never cross itself.

6
Row of Square Boxes

• A row consisting of one box can be made from 4
  match sticks
• A row consisting of two boxes can be made from 7
  match sticks
• How many match sticks are required to make a row
  of 11 boxes?
• How many match sticks are required to make a row
  of 64 boxes?
• How many match sticks are needed to make a row of
  n0 boxes?
• Define a join to be a point at which 2 or more
  match stick ends meet. For a row of n 0
  boxes, what is the relationship between the
  number of boxes, the number of matchsticks and
  the number of joins?

7
Counting Diagonals

• A polygon with 3 equal sides has how many
  diagonals?
• A polygon with 4 equal sides has how many
  diagonals?
• A polygon with 5 equal sides has how many
  diagonals?
• A polygon with 7 equal sides has how many
  diagonals?
• If a polygon with n 2 equal sides has k
  diagonals, then
• how many diagonals does a polygon with n1
  sides have?
• 6. How many diagonals does a polygon with n
  2 sides have?

8
Discussion
What is the relevance/importance of these types
of problems for computer science and software
engineering students?
9
Let's say we decided to dispense with men
entirely and boost the number of women in the
world. All women would get together and agree
to the following As soon as a woman gives birth
to a boy, she would have no more children. But,
as long as she gives birth to a girl, she can
have another child. This way, no family would
have more than one boy, but plenty of families
would have several girls. Do you see anything
wrong with this argument?
10
The Turner Triplets have an annoying habit
whenever a question is asked of the three of
them, two tell the truth and the third lies.
When I asked them which of them was born first,
they replied as follows   Werner Virna was
born first.   Virna I am not the
oldest.   Myrna Werner is the
oldest.   Which of the Turner Triplets was born
first? Explain your reasoning.
11
A man and a woman are walking side-by-side and
their right feet touch the ground at the same
time.   The woman takes three steps for each two
steps of the man, and they continue walking
side-by-side.  How many steps does the man
take before their left feet simultaneously touch
the ground the next time? Explain your answer.
12
Assume you travel from point A to a second
point B at a constant speed of 30 miles per
hour.  How fast would you need to travel on the
return trip from point B to point A in order
to average 60 miles per hour for the whole
trip?  Explain your answer.
13
Discussion
What is the relevance/importance of these types
of problems for computer science and software
engineering students?
14
For each of the following predicate logic
formulas, say whether it is a true or false
statement about the natural numbers  0,1,2,3,
... .  In each case explain your reasoning.  
a)     "  x  (x 17  Ú  x x    y  (y x) c)        y  " x  (y
x) d)        y  "  x  (x y)
e)     "  x   (x 17    23 15
Problem Domain

Math logic model

argument
Problem Domain
Logical Conclusion


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Models of Computation
All models of computation can be reasoned about
using mathematics. Assignment rule for
sequential computations r 2i i ß i
1 r 2i-1 r ß 2 r r 2i
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Resources

• Math Thinking Group
• http//www.math-in-cs.org
• SEN Software Engineering Ed ucation (SEED)
• http//blue.butler.edu/phenders/SEEd
• SIGCSE Math CountS
• http//blue.butler.edu/phenders/InRoads
• ITiCSE 2002 materials development group
• http//blue.butler.edu/phenders/iticse2002
• phenders_at_butler.edu

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Resources cont.

• My Foundations of Computing courses
• http//www.butler.edu/csse/cs151 (fall)
• http//www.butler.edu/csse/cs252 (spring)
• Communication of the ACM (Sept 2003 issue on math
  in CS education)
• Keith Devlin viewpoint article CACM The Real
  Reasons Why Software Engineers need Math Oct
  2002
• http//blue.butler.edu/phenders/iticse2002
• Alumni survey of FOCS course at SUNY Stony Brook
• http//www.ic.sunysb.edu/cse113/survey/