MAU22103/MAU33101 - Introduction to Number Theory
Course Information
Lecturer: Adam KeilthyMAU22103 Assessment: 20% homework assignments, 80% final exam.
MAU33101 Assessment: 10% homework assignments, 90% final exam.
The course will not follow any particular textbook, but students may find the following options helpful. Be aware that most of these contain far more than we can realistically hope to cover in this course.
- A course in computational number theory, by D. Bressoud and S. Wagon
- A classical introduction to modern number theory, by K. Ireland and M. Rosen
- An Introduction to the Theory of Numbers by I. Niven, H. S. Zuckerman and H. L. Montgomery
Lecture notes
This section will be populated with notes from the lectures as the course goes on. Please report any errors or typos you find so that I can correct them quickly.The current (mostly complete) lecture notes can be found here, last updated 19/11/24
Homework problems
You must submit your homework assignments before the deadline, preferably by emailing it to me, but you are welcome to submit a physical copy after a lectureWhere possible, please submit your assignment as a single PDF file, with your name in the filename, e.g. adam_keilthy_NTHW1.pdf or similar. Please also ensure that your name is visible on the first page of the assignment.
I encourage you to typeset your work in LaTeX. Doing so will increase your mark by 20% (but it will still be capped at 100/100). A rough template that does not reflect best practice or prettiest practice can be found here.
The solutions will be made available immediately after the deadline, so late submissions cannot be accepted
| Exercise sheet | Due date | Solutions | Tutorial date |
|---|---|---|---|
| Sheet 1 | Friday September 27th, 2PM | Solutions 1 | Thursday September 19th |
| Sheet 2 | Friday October 11th, 2PM | Solutions 2 | Thursday October 3rd |
| Sheet 3 | Friday October 25th, 2PM | Solutions 3 | Thursday October 17rd |
| Sheet 4 | Friday November 8th, 2PM | Solutions 4 | Thursday October 31st |
| Sheet 5 | Friday November 22th, 2PM | Solutions 5 | Thursday November 14th |
Sheets will be released approximately two weeks prior to the deadline.
The sixth exercise sheet is entirely optional, and has a relatively short deadline. If you choose to complete and submit it, your continuous assessment will be based on the best 5 out of 6 homeworks submitted.
| Exercise sheet | Due date | Solutions | Tutorial date |
|---|---|---|---|
| Sheet 6 | Friday November 29th, 23:59 | Solutions 6 | N/A |
A note about tutorials
The current plan is to replace every second Thursday lecture with a tutorial, assuming there is sufficient time. In these tutorials, we will discuss a number of the extra exercises from the current homework sheet, specifically those marks with a star.If there is another problem you would like to discuss, please email me in advance of the class. In multi-part exercises, not every part will necessarily be addressed.
Sample Exams
Below are two sample exams, with complete solutions for one of them. The actual exam will be the same format. Be aware that some of the questions in these sample exams are more time consuming than is reasonable for an actual examSample exam 1 and its solutions
Sample exam 2 and its solutions