ORMC Meetings • 2024-2025 Academic Year

Students will study polynomials with real and integer coefficient.

Students will explore deeper properties of functions having the form F(x)=(ax+b)/(cx+d).

Students will continue studying the topic they started on 9/29.

For handout, see https://circles.math.ucla.edu/circles/lib/data/Handout-2826-2424.pdf

In this week, we will rediscover cross ratios, anharmonic group, and j-invariants using what we have learned about fractional linear transforms.

We explore how financial markets combine and influence each other, especially through the role of arbitrage - the process of finding and taking advantage of price differences across markets. We describe how markets share striking similarities to thermodynamic systems. This perspective helps us see how the process of combining markets can lead to a "market entropy," a measure of lost liquidity when markets aggregate quantifying price uncertainty. Finally, we examine how this theory unifies two perspectives of a market: one as an exchange mechanism and the other as a venue for interaction among traders. The talk is aimed at a general audience.

We will talk about various counting problems about permutations.

We will discuss some more advanced aspects of permutations.

The class will prepare students for the 3/9 guest lecture by Prof. Lara Dolecek.

Deletion-error correcting codes, construction and modern applications.

Students will study the game of Nim and other two-player impartial combinatorial games.

We will dive deeper in the theory of nim games!