# Applied mathematics

There have been 4 completed talks and 4 topic suggestions tagged with applied mathematics.

## Completed Talks

### Social Choice Functions

Delivered by Sidhant Saraogi on Wednesday November 8, 2017

Social choice functions help aggregate the opinions of many agents. Social choice problems arise in examples as varied as citizens voting in an election, committees deciding on alternatives, and independent computational agents making collective decisions. We aim to study social choice theory through the lens of boolean functions, and study concepts such as influence and noise stability, which provide analogues for natural concepts in the study of social choice. We will finish off by looking at the famous Arrow’s Theorem often popularly stated as “the only voting method that isn't flawed is a dictatorship”.

### Markov Chain Monte Carlo

Delivered by Jacob Jackson on Wednesday October 4, 2017

The talk will introduce Markov chain Monte Carlo methods as a means of sampling from a distribution. The Metropolis-Hastings algorithm will be discussed as well as applications of Markov chain Monte Carlo for Bayesian inference and optimization.

Will expect familiarity with basic probability theory, especially conditional probability.

The slides for this talk are available at Jacob Jackson’s website.

### Cantor Set and Dynamical Systems

Delivered by James Bai on Friday March 31, 2017

The talk will be begin on the cosnstruction of the most commonly used tenary Cantor set. The talk will then talk about the common properties of Cantor set and methods of evaluating the size of the set. Then, depending on time, a brief introduction will be given on the dynamical system and chaos.

A summary of this talk is available here.

### Brachistochrone

Delivered by Manas Joshi on Friday March 24, 2017

In the late 1600’s, Johann Bernoulli came out with a problem to challenge the world’s greatest mathematicians. The problem, known as the Brachistochrone, had garnered some interest and eventually was solved by Johann, Jacob Bernoulli and Newton amongst others. In this talk, we will analyze the solution given by Leonard Euler (and Lagrange), which started a new field of Calculus, called the Calculus of Variations. We will prove the most fundamental equation, Euler-Lagrange, and see how this can be applied to solve the Brachistochrone problem.

## Talk Suggestions

### Gillespie Algorithm

The Gillespie Algorithm for stochastic equations is used heavily in a number of fields of applied mathematics, in particular computational systems biology.

Possible reference materials for this topic include

### Molecular Set Theory

In 1960, A.F. Bartholomay wrote about a mathematical model of chemical reaction mechanisms using set theory.

Possible reference materials for this topic include

### The Stochastic Lotka-Volterra Equation

The famous Lotka-Volterra equations model the population of a predator and a prey, which are of course closely related. Stochastic variations on the Lotka-Volterra equations can be an illuminating introduction to the methods used to solve stochastic differential equations.

Possible reference materials for this topic include