Los Angeles Math Circle

LAMC Meetings • 2019-2020 Academic Year

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For meetings prior to Fall 2019, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPIntermediate 1A
Intermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
We start off the new year with some problems from the Moscow Math Olympiad.

Handouts: Handout
We start off probability by introducing some set theory notation and defining sample spaces. Then we apply those to classical probability questions.

Handouts: Handout | Homework
We continue our probability unit with a worksheet on Conditional Probability. This includes the Law of Total Probability and Bayes' Theorem.

Handouts: Handout | Homework

Our third week of probability includes a handout on random variables and expected value, as well as some more interesting conditional probability problems.

Handouts: Handout

We will be working through a fun application of probability and graph theory to electrical circuits. No knowledge of physics is necessary, everything needed is contained in the handout.

Handouts: Handout

We dive further into the connection between random walks and electrical circuits, deriving series and parallel circuits. We then discuss electrical circuits on an integer lattice and its connection to Polya's problem.

Handouts: Handout

We start a new unit: Complex Numbers! We will see that while complex numbers might seem unnatural, they are actually extremely useful and can simplify problems that have seemingly nothing to do with the square root of -1.

Handouts: Handout

We will explore roots of unity and some geometric aspects of the complex numbers.

Handouts: Notes | Handout

For the last meeting of the quarter we will split up into groups and compete!


We start off the new (calendar) year with something you probably haven't seen before: tropical geometry. Throw out everything you know about addition and multiplication; we define new operations and explore polynomials under the new rules.

Handouts: Handout
Handouts: Handout

In the first part of a two (or three) part series on cardinality, we deal with bijections and give a proper definition for the cardinality of a set.

Handouts: Handout | Homework

We continue with part 2 of our Infinity sequence. This time we define cardinality through injectivity and bijectivity.

Handouts: Homework | Handout
Handouts: Handout

We start off our two week unit on Point Mass Geometry. This is a topic that lets you get the nice results of planar geometry without the tedious work!

Handouts: Handout | Solutions
Handouts: Handout | Solutions

We continue working on the second handout on point mass geometry. This gets into negative masses and barycentric coordinates.

Handouts: Handout | Solutions

For our final (virtual) meeting of the quarter, we will be hosting a Kahoot competition over the Zoom application. Please make sure to download the app at https://zoom.us/download and join the meeting from 4-6 pm at the link sent via email. See you there!


Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofs