Lecturer of Mathematics,
University of Lancaster
Honorary Research Fellow,
University of Bristol
d (dot) fretwell (at) lancaster (dot) ac (dot) uk
daniel (dot) fretwell (at) bristol (dot) ac (dot) uk
Dr. Dan Fretwell
Teaching
Current:
I am currently teaching the following modules at Lancaster:
I am also currently developing the new module:

MATH320  Introduction to Mathematical Cryptography
Previous:
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 HilbertSiegel 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.