12/2/19: For our last meeting of the semester, we worked on AMC and Putnam problems.
11/25/19: Thanksgiving Break
11/18/19: Dr. deForest presented on the clock and wavefront model that describes the development of the segmented structure of the vertebral column during embryonic development. This is an interesting example demonstrating the roles of both negative feedback and delay in creating oscillations in solutions to a differential equation.
11/11/19: Dr. Daniels discussed careers and opportunities in math. Her presentation can be found at tinyurl.com/mathclub111119.
11/4/19: No meeting this week.
10/28/19: Dr. Richards gave a talk entitled “Statistical Properties of the Risk-Transfer Formula in the Affordable Care Act.”
Abstract: The Affordable Care Act, signed into law in 2010, fostered competitive insurance plans that provide universal health-insurance coverage without regard to pre-existing medical conditions. To assist insurers during an initial period the Act introduced a “risk-transfer formula,” which requires insurance plans with healthier enrollees to pay funds to plans with sicker enrollees, hence discouraging any tendency
for insurers to favor healthier enrollees. In this talk, we study the statistical and probabilistic properties of risk-transfer amounts. We will find that smaller insurance plans have a higher risk of insolvency simply because of their size, and by using Markov chain analysis we discover that smaller plans are at continued risk over the long term.
This research was done with Michelle Li and with Ishan Muzumdar,
undergraduate students at PSU.
10/21/19: For a more laid back meeting, we watched a variety of interesting math videos.
10/14/19: This meeting we discussed some of the computational tools available to people in math. The slides from the meeting can be found here.
10/7/19: Dr. Sadovskaya came and gave a talk about fractals including common examples like the Cantor set, Sierpinski triangles, and the Mandelbrot set.
9/30/19: Professor Russel Miller of Queens College CUNY gave a talk titled “Functions That No Computer Can Compute.”
Abstract: We will introduce computability theory, with twist: the functions to be computed (if possible) are functions on the real numbers. The usual jumping-off point for this topic is functions on N, but with R we will be able to get our hands on some non-computable functions pretty quickly, and discuss what makes them impossible for a computer to handle. (This question also turns on one’s method of representing real numbers, which we will also discuss.) Computability theory is the branch of mathematical logic closest to computer science, but no background in either logic
or computer science will be necessary
9/23/19: In groups, we worked on a set of math problems that came from a mixture of AMC and Putnam problems.
9/16/19: Dr. Hile and her adorable dog came to talk about some dog-themed math centering around the key question: “Do dogs know calculus?”
9/9/19: For our first meeting of the year, we introduced all of the club officers then played a fun game of math Jeopardy.