Difference Galois Theory For The "Applied" Mathematician

TL;DR

This paper introduces difference Galois theory tailored for applied mathematicians, emphasizing applications like differential transcendence, and provides accessible explanations with a focus on practical implications rather than proofs.

Contribution

It presents an accessible overview of difference Galois theory with a focus on applications in number theory and differential transcendence, omitting detailed proofs for clarity.

Findings

Simplified explanations of difference Galois theory for applied contexts

Application-focused statements useful in differential transcendence

Omission of proofs to emphasize practical understanding

Abstract

The lecture notes below correspond to the course given by the author in occasion of the VIASM school on Number Theory (18-24 June 2018, Hanoi). We have chosen to omit the proofs that are already presented in details in many references in the literature, although they were explained during the lectures, and we have devoted more space to statements useful in the applications, in particular to differential transcendence.