U.C. Davis Math Circle

Mathematical Finance

Jeff Anderson

How can you learn to apply mathematics to model real world phenomena, understanding investing, and solve problems creatively? Where can you meet interesting people, express yourself and improve your ability to think critically? Answers to these questions are waiting for you to experience in Math Circle's six part series: Mathematical Finance: Understanding Options.

Under the direction of Jeff Anderson, we will discover topics in mathematical finance including:

The Options Market: What are options and how do they work
Options and Arbitrage: European Call and Put Options and Arbitrage Examples
The One Step Binomial Model: Pricing European Options using a one period binomial model
Multiperiod Binomial Model: Replication in the Multiperiod Binomial Model
Advanced Options Strategies: The Butterfly Spread
Using Linear Programming to Detect Arbitrage: Optimization Applied to Finance

Geometry

Yvonne Kemper

Despite being one of the oldest mathematical sciences, geometry is home to a large number of open problems which are easy to state...but difficult to prove! We will explore some of the open problems relating in particular to polyhedra, and discuss relevant notions and real-world applications, such as:

Triangulations
Polynomials
Lattice Points
Voting Theory
Graph Theory

Quantum Information Theory

Amanda Back

Quantum information processing refers to the science of communicating and computing through quantum systems. As a field of study it has developed rapidly in the last few decades and continues to do so today. We will learn the mathematical underpinnings of quantum information and computation along with some applications. Topics to be discussed include: