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.

Mathematical Journeys

Fall – From the Known into the Unknown

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 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.

Spring – From the Unknown to the Known

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.