LAMC Meetings • 2019-2020 Academic Year

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

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

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

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.

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.

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.

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

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

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.

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.

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.

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.

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

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

We'll continue practicing writing formal and rigorous proofs.