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 2BBNPChess class
Intermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
10/6/2019
We start off the new year with some problems from the Moscow Math Olympiad.




Handouts: Handout
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: Handout | Homework
10/20/2019
We continue our probability unit with a worksheet on Conditional Probability. This includes the Law of Total Probability and Bayes' Theorem.




Handouts: Handout | Homework
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: Handout
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.

Handouts: 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: 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: Handout
11/24/2019

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

Handouts: Notes | Handout
12/8/2019

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

1/12/2020

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
1/17/2020
Handouts: Handout
1/26/2020

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
2/2/2020

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

Handouts: Homework | Handout
2/9/2020
Handouts: Handout
2/23/2020

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

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

Handouts: Handout | Solutions
3/15/2020

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!

4/5/2020

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

Handouts: Handout
4/12/2020

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

Handouts: Handout
4/19/2020
Handouts: Handout
4/26/2020

We take a look at the HM-GM-AM-QM inequalities and their applications.

Handouts: Handout
5/3/2020

We continue with more applications of our HM-GM-AM-QM inequalities.

Handouts: Handout | Solutions
5/10/2020
Handouts: Handout
5/31/2020

We will continue studying backward reasoning.