Teachers As Scholars (Steven J Miller: sjm1 AT williams.edu)

"A-ha!" Moments in Mathematics and the Sciences

Tuesday January 29 and Tuesday February 5, 2013
Harvard Hillel, 52 Mount Auburn Street, Rabb Hall (1st Floor)

Pictures: Here are pictures from the lectures: Day 1 (January 29, 2013)        Day 2 (February 5, 2013)

Description: There are many stages and approaches to solving a problem. Before trying to find a solution, it's often a good idea to determine if one exists, as if it doesn't our search will be fruitless! If we're fortunate enough to know there is a solution, the next step is to find it. Oftentimes we can solve a problem through brute force approaches, but these are inelegant, give us no greater understanding of the problem or why the solution works, and frequently cannot be generalized to related problems. The goal of this seminar is to introduce you to alternatives to brute force. There are many examples throughout mathematics and science where, if you look at the problem the right way, what was originally a long, involved calculation evaporates into a wonderful `A-ha!' moment! We'll draw examples from problems that can be solved by tedious, long computation as well as quick arguments if viewed the right way.

Probable topics, comments and reading:


Math Riddles
I also maintain a math riddles page. Please feel free to share these riddles with your colleagues and your students, and let me know if there is anything I can do to make the site more useful for you and your classes. The goal is to add a student / teacher's corner sometime in the spring to facilitate using these in classrooms. If you're interested in helping, or want updates on the progress, let me know.


Lecture Notes from 2013