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
What kinds of patterns can be used as wallpaper? What are their groups of symmetries, and how can we classify them? How many are there? We will attempt to answer some of these questions and learn how to use Thurston's "orbifold notation" for wallpaper patterns.






10/13/2019
We will continue to answer some of the questions posed about wallpaper symmetries. For those that finish the worksheet on wallpaper symmetries, we started discussing the origins and early properties of the p-adic numbers.






10/20/2019

We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns.

10/27/2019

We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns.


11/3/2019

We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics.

Handouts: Formal Proofs
11/10/2019

We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics.

11/17/2019

We work on Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory.

11/24/2019

We do further Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory.

12/8/2019
1/12/2020

We motivate the study of metrics by introducing the taxicab metric (the distance traveled by a taxi in a city with a grid layout). How would you define a circle, line segment between points, or a parabola with a new notion of distance?

1/19/2020

Using the taxicab metric as a guide, we define the general notion of metric and give numerous examples.

Handouts: Metrics
1/26/2020

We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension?

2/2/2020

Happy Groundhog Day! With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers.

2/9/2020

We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins.

2/23/2020

In the first week of a three week sequence, we introduce basic probability concepts such as conditional probability, Bayes' Rule, and tower property

3/1/2020

We will continue our study of probability by introducing random variables and distributions.

3/8/2020

We will continue our study of random variables by introducing the Bernoulli, geometric, and binomial distributions. As a final surprising example, we construct a famous example of a non-measurable set.

3/15/2020
4/5/2020

We review the material from last quarter.

Handouts: Time Travel
4/12/2020
4/19/2020
4/26/2020
5/3/2020
5/10/2020
5/17/2020
5/31/2020
6/7/2020