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
10/6/2019

We start off the new year with some problems from the Moscow Math Olympiad.

Handouts: Week-1
10/13/2019
We start off probability by introducing some set theory notation and defining sample spaces. Then we apply those to classical probability questions.


Handouts: Week-2 | Homework-2
10/20/2019

We are continuing solving probability problems. The topics for this class are Conditional Probability, Law of Total Probability, Bayes' Rule.

Handouts: Week-3 | Homework-3
10/27/2019

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

Handouts: Week-4
11/3/2019

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.

11/10/2019

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: Week-6-Handout
11/17/2019

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: Week-7-Handout
11/24/2019

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

12/8/2019

We're playing a traditional end-of quarter game.

1/12/2020

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

1/19/2020
1/26/2020

In the first part of a 3-part series on cardinality, we deal with bijections and give a proper definition for the cardinality of a set.

Handouts: Infinity-1 | Homework
2/2/2020

In the second part of the sequence, we explore more bijections and prove several surprising facts about the cardinalities about the naturals, integers, and the reals.

Handouts: Infinity 2 | Homework
2/9/2020

This week we are concluding our conversation about infinity with some more challenge problems on constructing bijections.

We also look into some mathematical paradoxes related to infinity and not only.

Handouts: Infinity-3
2/16/2020
2/23/2020

We will learn a new method of solving geometry problems with assigning masses to points and using intuition from physics.

Handouts: Handout | Solutions
3/1/2020
Handouts: Handout
3/8/2020
Handouts: Handout
4/5/2020

We'll go over various proof techniques and practice writing rigorous proofs.

Handouts: FormalProofs
4/12/2020

We'll continue practicing writing formal and rigorous proofs.