|10/7/2018| [Show less]
We will start the school year with an an overview of math problems and puzzles involving a chessboard (with and without chess pieces) and solving techniques including tiling, coloring and invariance principle.
|10/14/2018| [Show less]
In this meeting we will explore the symmetries of different objects like squares, rectangles, and coins. We will see how these symmetries interact with each other to form a structure called a group.
|10/21/2018| [Show less]
Having experimented with the groups of symmetries of the rectangle+string model, we will define groups and explore associated concepts such as subgroups, group actions, isomorphisms, orbits, and stabilizers.
|10/28/2018| [Show less]
In this meeting, our goal is to construct a strange new geometry where straight lines are circles and triangles have angles that sum to less than 180. We start with circle inversions and then introduce the Poincaré disc model.
|11/4/2018| [Show less]
We will continue our exploration of the Poincaré disc and prove facts about hyperbolic lines and shapes.
|11/11/2018| [Show less]
We will keep working in the Poincare disc and discover phenomena peculiar to hyperbolic geometry such as AAA congruence, Lobachevskii's Theorem, and Schweikart's constant.
|11/18/2018| [Show less]
We look at more peculiar hyperbolic facts, like the hyperbolic Pythagorean theorem and the angle of parallelism.
|11/25/2018|| [Show less] |
|12/2/2018| [Show less]
We will have a short review quiz. Then, Aaron Anderson will talk about how electrical circuits correspond to random walks on the vertices of graphs.
|12/9/2018| [Show less]
We will continue talking about the correspondence between voltage, resistance, and current in circuits with random walks on graphs.
|1/13/2019| [Show less]
We will have a competition to solve problems for prizes!
|1/20/2019| [Show less]
We will start a lesson studying algorithms: what are they, and how do they work?
|1/27/2019| [Show less]
We will learn about more aspects of algorithms, such as efficiency and computational complexity.
|2/3/2019| [Show less]
We're going to look at the famous Cantor set, its construction, and some of its oddities.
|2/10/2019| [Show less]
We will continue studying the Cantor set, invesitgating properties such as its cardinality and "dimension." Once we develop some notions of dimension, as a bonus we will also look at other fractal sets and their dimensions.
|2/24/2019| [Show less]
We’ll explore a measure of economic inequality known as the Gini Index. In particular, we’ll learn what it is, how to calculate it, and what some of its strengths and limitations are.
|3/3/2019| [Show less]
In this lesson we will do combinatorial weighing and probability problems, with some related problems about information exchange.
|3/10/2019| [Show less]
To celebrate Pi day, we'll look at some probability questions involving pi. For example: suppose you have equally spaced lines and you drop a toothpick. What is the probability that the tootpick crosses a line?
|3/17/2019| [Show less]
We will continue the worksheet on problem related to pi. We will find the probability that two randomly selected integers are coprime and calculate some continued fractions.