Nature of Mathematics Jeopardy

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Nature of Mathematics Jeopardy!

• Produced by the USF Mathematics Program
• Hosted by the ever-affable Jason Douma

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This semesters categories

• The Right Tool for the Job
• Famous Folks
• Give Me a QuestionStat!
• Behind the Curtain
• Geometric Gems
• Choice Cuts

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The Right Tool for the Job 100This is what
the Huntington-Hill method is used for.

• Apportionment.
• Currently used for apportioning the U.S. House of
  Representatives.

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The Right Tool for the Job 200You might
use this method for planning a route that will
allow you to visit each of the thirty Major
League Baseball stadiums and return home.

• Nearest Neighbor Algorithm
• or Sorted Edges Algorithm

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The Right Tool for the Job 300This tool
measures the strength and direction of the
relationship between two variables.

• Correlation (or correlation coefficient)

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The Right Tool for the Job 400This is the
fastest of the following four bin packing
algorithms first fit, first fit decreasing, next
fit, and worst fit.

• Next Fit

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The Right Tool for the Job 500A heuristic
algorithm typically sacrifices some ________ to
allow us to obtain greater _________.

• Optimality
• Speed

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Famous Folks 100His groundbreaking result
in voting theory demonstrated that it is
impossible for a voting system for more than two
candidates to satisfy both the Condorcet Winner
Criterion and the Independence of Irrelevant
Alternatives.

• Kenneth Arrow

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Famous Folks 200He developed a
mathematical abstraction that solved the
Königsberg bridge problem.

• Leonhard Euler

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Famous Folks 300This man was the subject
of A Beautiful Mind and was the pioneer of
nonzero-sum game analysis.

• John Nash

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Famous Folks 400This French mathematician
is widely recognized as an intuitionist,
philosophically, and has his name attached to a
well-known model of hyperbolic geometry.

• Henri Poincaré

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Famous Folks 500These three individuals
each (independently) developed non-Euclidean
geometry.

• Karl Freiderich Gauss
• Janos Bolyai
• Nikolai Lobachevsky

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Give Me a QuestionStat! 100These are two
major forms of bias found in a typical radio
call-in show.

• Voluntary Response Bias
• Convenience Sampling

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Give Me a QuestionStat! 200This is what
(if anything) a correlation coefficient of r
-.893 suggests about the relationship between two
variables.

• The two variables being studied have a strong
  negative correlation. As one quantity increases,
  the other decreases.

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Give Me a QuestionStat! 300This is why
statisticians care about probability.

• The fundamental statistical question is Is this
  result unlikely to have occurred purely by
  chance? Probability theory gives us precise
  mathematical answers to this question.

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Give Me a QuestionStat! 400If a poll
result gives a political candidate 40 support
with margin of error 4, this is what the margin
of error tells us.

• We can be 95 confident that the candidates true
  level of support among the population lies
  between 36 and 44.

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Give Me a QuestionStat! 500In a unimodal
skewed right distribution, the median will be
_____________ (gt, lt, or ) the mean.

• The median will be less than the mean.

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Behind the Curtain 100This is the name of
the method by which mathematical truths are
derived.

• the Axiomatic Method

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Behind the Curtain 200Of the major
philosophies concerning the nature of
mathematical truth, this is the one that would
agree most with the statement Mathematical
truths are like stars in the heavens they had
their form and meaning long before we discovered
them, and will keep their meaning long after we
forget them.

• Platonism

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Behind the Curtain 300When David Hilbert
observed, One must be able to say at all
timesinstead of points, lines, and
planestables, chairs, and beer mugs, what was
he saying about the nature of mathematics?

• He was indicating that since the names we give to
  mathematical objects do not refer to anything
  real, we can call them anything we want. Their
  structure, validity, and meaning (a purely formal
  meaning, to Hilbert) would remain unchanged.

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Behind the Curtain 400In proper Euclidean
geometry, this is what a line is defined to be.

• Ha! Trick question.
• A line is an undefined term.

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Behind the Curtain 500What is ironic (or
even misleading) about the well-intended
suggestion, We need to make mathematics more
concrete.

• Mathematics itself is fundamentally formal its
  application can indeed be concrete.

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Geometric Gems 100This is the symmetry
group of the Pentagon building.

• D5 (the dihedral group of order 10)

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Geometric Gems 200These are two examples
of expressions of the golden ratio in art,
architecture, or music.

• Some examples from class include DaVincis
• Da Divina Proportione and Portrait of St. Jerome,
  
• Le Corbusiers design of the U.N. Headquarters,
• and Debussys Prelude to the Afternoon of a Faun

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Geometric Gems 300In this geometry,
parallel lines do not exist.

• Elliptical/Spherical Geometry

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Geometric Gems 400Suppose we have two
geometrically similar containers. The smaller
one is 2 feet tall the larger one is 6 feet
tall. The smaller one holds 5 gallons of water.
How much water will the larger one hold?

• 135 gallons
• (5 ? 33)

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Geometric Gems 500True or FalseThe sum
of the measures of the angles in a triangle is
always 180 degrees.

• Trick question! It depends on the geometry
  were working in the statement is true in
  Euclidean geometry, but not in hyperbolic or
  spherical geometry.

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Choice Cuts 100A voting system cannot
have more than one dictator. Can it have more
than one person with veto power?

• Yes, e.g. 6 3, 3, 1

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Choice Cuts 200These are the fairness
axioms satisfied by the adjusted winner
procedure.

• Proportional, Equitable,
• Envy-Free, Pareto Optimal

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Choice Cuts 300There are many divisor
methods for apportionment. What basic feature
distinguishes each of these methods from one
another?

• how the quotas are rounded

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Choice Cuts 400At one point in the 2004
Democratic Presidential Primary season, most
polls put Dean on top, followed by Kerry,
followed by Lieberman. Lieberman dropped out of
the race, and just about that time Kerry became
the front-runner. This scenario illustrates a
violation of which fairness axiom?

• Independence of Irrelevant Alternatives

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Choice Cuts 500If, when you calculate an
optimal mixed strategy, you arrive at p 5/4,
you can rest assured that one of these two things
went wrong.

• You either have an error in your
  arithmetic/algebra, or you tried to find a mixed
  strategy when a saddle point was already present.

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Final Jeopardy!

• Category
• Noah Webster, Where are you when I need you?
• Question
• In graph theory, this is what the word valence
  refers to.
• Answer The valence at a vertex on a graph is
  the number of edges emanating from that vertex.