Category Archives: Both

Frobenius algebras – Supervisor: Dr A Ros Camacho

2021/2022, Both, Double, Yr 3 Descriptions 2021/2022

Title of Project: Frobenius algebras

Code: ARC2122A

Supervisor: Dr A Ros Camacho

Project Description: Frobenius algebras are an interesting family of algebras
that play a crucial role in research topics of mathematical physics. In this
project, we will study them and its properties, compute several examples
of these and see how they arise in the study of topological and conformal
eld theory.

Project offered as a Double module.

Prerequisite: 2nd year modules: Linear Algebra II, Algebra 1: Groups

Prerequisite: 3rd year modules for concurrent study: Algebra 2:
Rings, Algebra 3: Fields

Maximum number of students: 2

Type: algebra, mathematical physics

The Arithmetic-Geometric Mean and Elliptic Integrals – Supervisor: Prof. K.M. Schmidt

2021/2022, Both, Yr 3 Descriptions 2021/2022

Title of project:
The Arithmetic-Geometric Mean and Elliptic Integrals

Code:
KMS2122A

Supervisor: 
Prof. K.M. Schmidt

Project description:
The Arithmetic-Geometric Mean is a function, defined via a limit process by Gauss after playing with the two concepts of mean which compose its name. This function turns out to be intimately connected with elliptic integrals and, since its defining limit converges with breathtaking speed, provides an efficient method for the calculation of such integrals, which resist application of the usual techniques of calculus. Moreover, the connection of elliptic integrals with the number pi gives rise to very fast converging algorithms for the calculation of this number to millions of decimal digits.

In the project, the properties of the arithmetic-geometric mean and its relation to elliptic integrals are reviewed, working towards an understanding of the Salamin algorithm for pi.

Prerequisite 2nd year modules:
MA2006 Real Analysis

Number of students who could be supervised for this project:
1