# MAU23101 - Introduction to number theory

### Course information

Lecturer: Nicolas Mascot

Assessment: 15% homework assignments, 85% final exam.

Because of the current situation, all the lectures will be prerecorded and available online on this page, see below.

### Suggested textbooks

Unfortunately, I do not know any book which covers exactly the topics of this module, here are a few suggestions:
• A course in computational number theory, by D. Bressoud and S. Wagon
• The higher arithmetic, by H. Davenport (up to chapter VI)
• A classical introduction to modern number theory, by K. Ireland and M. Rosen (up to chapter 5)
• Primes of the form x²+ny², by D. Cox (up to section 2.B)

### Recorded lectures

This section will be regularly updated until the end of the term.

The course contents are available as prerecorded videos and as PDF notes. You can save these files by right-clicking on the links and clicking on "Save link as".

The PDF notes for the current chapter will be updated regularly as the chpter progresses. During this time, they will be marked as "Incomplete - in progress". Once the chapter is complete, the final version of the notes will be marked as "Complete".
• Chapter 0: Introduction - Diophantine equations
Video - Notes (Complete)

• Chapter 1: Divisibility and factorisation
Notes (Complete)
Videos:

• Chapter 2: Congruences and Z/nZ
Notes (Complete)
Videos:

• Chapter 3: Power residues, Legendre symbols, and quadratic reciprocity
Notes (Complete)
Videos:

• Chapter 4: Sums of squares
Notes (Complete)
Videos:

• Chapter 5: Binary quadratic forms
Notes (Complete)
Videos:

• Chapter 6: Continued fractions
Notes (Complete)
Videos:

### Homework

You must submit your homework assignments before the deadline, by emailing it to me.

Typesetting your work in LaTeX will increase your mark by 20% (but it will still be capped at 100/100).

The solutions will be made available immediately after the deadline, so late submissions will not be accepted.

Exercise sheet Due date Solutions LaTex source
Sheet 1 Friday October 16th, 2PM Solutions 1 Source 1
Sheet 2 Monday October 26th, 2PM Solutions 2 Source 2
Sheet 3 Wednesday November 4th, 2PM Solutions 3 Source 3
Sheet 4 Friday November 20th, 2PM Solutions 4 Source 4
Sheet 5 Wednesday December 2nd, 2PM Solutions 5 Source 5
Sheet 6 Monday December 14th, 2PM Solutions 6 Source 6

### Exam

The final exam will take place on Wednesday January 13th, 2021, from 12PM till 6PM, in the form of a take-home exam.

Here is a mock exam paper to practice on, and here is its solution.