ORMC Meetings • 2021-2022 Academic Year

We kick off the year by discussing some interesting questions about words! This is a two-week topic.

The handout is the same as last time.

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Nim is a simple combinatorial game in which players take a certain number of elements from a pile. The last person to take an item is the winner. We will play games of Nim with multiple setups in order to determine winning strategies. Eventually, we will define a number system based on Nim.

We continue our exploration of Nim and devise a strategy for general Nim!

This week we'll split into teams and do math competitions.

We take a look at discrete dynamical systems, and how a particular dynamical system known as the logistic map leads to the mathematics of chaos.

We will continue our study of dynamical systems by connecting logistic maps to the Mandelbrot set.

We'll do a competition. It will be the last meeting of 2021.

We will attempt to naively count the number of spanning trees in a graph.

We will introduce two methods for computing the number of spanning trees in a graph: deletion-contraction and the miraculous Matrix Tree Theorem. We will need to take a detour to the land of matrices for the second method.

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers.

Peano axioms provide a rigorous foundation for the natural numbers and arithmetic. We will list the axioms and develop competing systems for the counting numbers. Can we make it all the way to the rational numbers with only a handful of axioms?