LAMC Meetings • 2019-2020 Academic Year

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.

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.

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

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

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

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

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?

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

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?

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

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.

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

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

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.

We review the material from last quarter.