Los Angeles Math Circle

LAMC Calendar // 2018-2019 Academic Year. Jump to:

For meetings prior to Fall 2018, visit the Circle Archive.

AdvancedBeginnersBreaking Numbers into PartsEarly Elementary IEarly Elementary IIHigh School IHigh School IIJunior CircleOlympiad Training

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.

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.
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.
Handouts: Problems
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.
Handouts: Handout | Solutions
We will continue our exploration of the Poincaré disc and prove facts about hyperbolic lines and shapes.
Handouts: Solutions | Handout
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.
Handouts: Section 2
We look at more peculiar hyperbolic facts, like the hyperbolic Pythagorean theorem and the angle of parallelism.
Handouts: Solutions
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.
Handouts: Handout
We will continue talking about the correspondence between voltage, resistance, and current in circuits with random walks on graphs.
We will have a competition to solve problems for prizes!
We will start a lesson studying algorithms: what are they, and how do they work?
We will learn about more aspects of algorithms, such as efficiency and computational complexity.
We're going to look at the famous Cantor set, its construction, and some of its oddities.
Handouts: Handout
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.
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.

Handouts: Handout | Solutions
In this lesson we will do combinatorial weighing and probability problems, with some related problems about information exchange.
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?
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.