Jan 14, 2024

Today we learned about the importance of mathematics historically and in today’s world. Steven Miller of Williams College began the day by discussing how to solve linear equations and quadratic equations, before showing us the very complicated formula for solving third degree equations. He then discussed how to approximate the value of the square root of 3 more accurately than a calculator can. Students on each team were challenged to find their best approximation of the square root of 3 using a simple algorithm that he provided. We eventually found an approximation of the square root of 3 that was accurate to about 20 places. When asked what was the practical value of having such an accurate approximation. Professor Miller explained that when we use Google Maps, the directions would be inaccurate without such approximations.

After Professor Miller completed his morning presentation, Victor Barranca of Swarthmore College spoke to our students about applied mathematics, his field of interest. He began by asking our students, “What Is Mathematics?” This may seem like a simple question to ask, but the answer is a bit more complicated than what you might think. Mathematics is not just numbers or even patterns of numbers. It’s also about shapes and their patterns. Professor Barranca went to discuss the development of mathematics from early civilization to today, from counting, to arithmetic, to measuring/building, to Fibonacci, and eventually to our highly sophisticated mathematics we now have. Dr. Barranca ended his talk discussing the Monty Hall Problem. This is a very well-known problem based on the quiz show called Let’s Make a Deal. In this show, there are three doors. Behind two of these doors is a goat and behind the third door is a car. If you want to learn more about this problem, you can do so at Monty Hall Problem.

After lunch, we all rendezvoused at Bliss Hall for our first contest round of this summer. Today’s contest round was our Team Round in which the students on each team work together to solve 12 difficult questions in 90 minutes. These are very challenging questions that few students at this age level can solve. Amazingly, one team received a perfect score of 1200 points (each question was worth 100 points) and no team scored fewer than 700 points. To say we were all very impressed with these scores is putting it mildly. A great performance by our participants!

After the Team Round, we returned to Decker Social Space to listen to the second half of Steven Miller’s talk. Professor Miller started with a discussion of Pascals triangle, and specifically patterns that appear within it - for example, where are the odd numbers? Using a computer program that showed how the patterns develop over a large number of rows, students were able to see interesting triangular sub-regions within Pascals triangle. From there Professor Miller continued to a discussion of dimensionality and even Newton Fractals. Professor Miller eventually introduced our participants to non-integer dimensions such as the dimension in a Sierpinski triangle. Professor Miller was kind enough to share with us some slides form his presentations. Here are the links he sent to me:

• For more for those just knowing Algebra I:
  
  • From Pascal to Calculus: Part I: https://youtu.be/dv15VTyEWyQ (powerpoint here, pdf here) (3/25/2020): For those knowing Algebra I (equations of lines): 52 minutes
    
  • From Pascal to Calculus: Part II: https://youtu.be/D6OnleQJ1XM (powerpoint here, pdf here) (3/26/2020): For those knowing Algebra I (equations of lines): 40 minutes
    
• For more for those with more comfort with higher mathematics:
  
  • From C to Shining C: Complex Dynamics from Combinatorics to Coastlines, Hampshire College 8/8/2022 (video: https://youtu.be/GO3EbWUesBQ) pdf

This evening was the first night of our two-evening Talent Show. Although I have been told I can be very funny, I’m no match for our master of ceremonies, Adam Raichel. Adam started performing imrpov in New York City in 1999. After moving to Chicago, Adam became a teacher at the Second City Training Center where Alan Arkin, Ed Asner, Nichols and May as well as more recently Chris Farley, Mike Myers, Tina Fey, Amy Poehler, Steven Colbert, and Steve Carell performed. (No, Adam is not old enough to have taught any of them!) Since moving to San Diego, Adam (along with some friends) founded Mockingbird Improv. He performs their regularly hosting their shows. Tonight, we were all privileged to watch Adam in action. Now hosting a talent show may appear to be an easy job, but I can assure you that it takes Adam hours to prepare for this since he has to find the worst jokes in his joke book and refine them so we laugh at them. Yes, some of his jokes are corny, some of them make you think a few seconds before you figure them out, but Adam’s delivery makes us all laugh. Adam introduced a variety of acts this evening---we had singers, pianists, dancers, an harmonicist, and a couple of Rubik’s Cube experts. I am always amazed at the many talents our students possess besides their mathematical talents.