Lecturer in Mathematics,

University of South Wales.

Honorary Lecturer in Mathematics,

University of Bristol

dan (dot) fretwell (at) southwales (dot) ac (dot) uk

daniel (dot) fretwell (at) bristol (dot) ac (dot) uk

# Dr. Dan Fretwell

###### Teaching

Here are the notes for part one of the module "Topics in Discrete Mathematics" for 2021/22 in Bristol. These notes present a basic course in mathematical cryptography. Exercise Sheet, Solutions.

Here are the notes for part one of the module "Topics in Discrete Mathematics" for 2017/18 in Bristol. These notes present a basic course in coding theory. Exercise Sheet 1, Solutions 1, Exercise Sheet 2, Solutions 2, Practice Exam, Practice Exam Solutions.

During my PhD in Sheffield I lectured the module MAS430 - Analytic Number Theory. Here are the course notes, exercises and solutions.

I also gave many tutorials and group sessions in a wide variety of pure maths modules. While tutoring the module MAS208 - Topics in Number Theory I wrote a short revision aid for proving infinitude of primes in arithmetic progressions for small parameters.

As part of the module MAS328 - Codes and Cryptography I offered two cipher challenges on classical techniques (Challenge 1, Challenge 2). I also created a sheet on simple RSA weaknesses. Here are the solutions.

Here are the notes for an unofficial set of Galois theory lectures that I gave. Here are some (incomplete) exercises.

Here are some exercises on group theory that I prepared for some of my undergrad students.

###### Notes

A short note on the inversion formula for Hilbert-Siegel theta series.

A short note on modular forms.

A short note on how to solve the cannonball problem using elliptic curves.

My masters thesis on Global Class Field Theory. Part 1 is an introduction to the main theorems. Part 2 contains all of the proofs and some applications. Here is a short overview of the theory in terms of ideals.