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John Little -- This is a preliminary draft of course descriptions
proposed for the 2015-2016 CHQ Cluster.  As you will see, these are quite heavily slanted
toward the ``origin/journey/destination'' form of the cluster theme.
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{\it Mathematical Journeys}
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Fall -- {\it From the Known to the Unknown}
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Does it surprise you to learn that people are constantly adding to 
what we know about mathematics?  How does that happen, and how do new ideas 
come to be accepted?  Proofs play a key role and mathematicians would say these journeys
into the unknown are often as important as the destinations.  But how are proofs found, 
and how does this relate to practical mathematics?   We will study a number of sources, 
including Euclid's {\it Elements}, and begin to understand how mathematical insights  
are justified and communicated through proofs.  No background beyond high school geometry 
and algebra is required, but openness to new points of view and willingness to think deeply 
will be helpful.  
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Spring -- {\it From the Unknown to the Known}
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How likely is Joe DiMaggio's 56-game hitting streak to be surpassed
in our lifetimes?  Does a high-fat diet increase our risk of cancer? 
Finding patterns and answering such questions can be seen as journeys from the 
unknown to the known.  But does this relate to the mathematical journeys 
recorded in proofs when there is such a large element of chance and randomness involved?  
We will take a detailed and occasionally critical look at the ways reasoning about 
probabilities is used to identify patterns via statistics.  In the process, you will 
develop an appreciation of the power and the limitations of statistical thinking and 
learn to analyze claims backed by statistics.  
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