LAMC Meetings • 2019-2020 Academic Year

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.

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

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.