MAS114: Numbers and Groups,
Semester 1, 2019 – 2020

Lecturer: Dr James Cranch

frivolous course picture

Here's the official information on this module.

Exams are looming…

I have a page of exam advice and also some revision notes for you.

Easter Challenge Problems

If you like hard problems, then here are a few to keep you going through the Easter break.

Online revision tool

Here is Number Theory as a Service, an online revision tool for the number theory sections of the course.


There are two of these a week:

Here, are the lecture notes from the course up until now, in one big file.

Here are the slides as used in the lectures. Please don't print these: they have zillions of pages! There is more material in the full notes above, anyway: these might just be nice to click through on screen.

Lecture slides:

If you miss a lecture, then read the notes online. They should be online a good amount of time before each lecture. If there are any gaps which I've left to fill in during the lecture, see for yourself if you can do them. If you still don't understand, come to a surgery hour!

Problem classes

At problem classes you can ask for help with things you're stuck on. You will also be given exercises to work on in small groups.

Here are those sheets, and comments and solutions on the problems:

Class sheets:


Here is the booklet of exercises. Here also are the solutions of exercises so far.

You work on these on your own, and hand them at the beginning of each problems class (starting in week 2). At the next problems class, the staff will give you it back, with helpful comments.

One exercise each week is the challenge problem. If you attempt it, hand it in on a separate sheet of paper. I'll showcase one solution each week, if a nice one makes it to me!

Here is a list showing which problems I'm setting as homework:

Homework 1 (due in Week 2)Questions 1 and 2; challenge problem 4
Homework 2 (due in Week 3)Questions 5 and 7; challenge problem 8
Homework 3 (due in Week 4)Questions 9 and 12; challenge problem 13
Homework 4 (due in Week 5)Questions 14 and 15; challenge problem 17
Homework 5 (due in Week 6)Question 18; challenge problem 21
Homework 6 (due in Week 8)Questions 22 and 23; challenge problem 25
Homework 8 (due in Week 9)Questions 26 and 29; challenge problem 31
Homework 9 (due in Week 11)Questions 32 and 34; challenge problem 35

Challenge problem writeups:

Online tests

These constitute 20% of the total course mark. Here is the link to the system:

You will need to use your usual login (something like JDCranch1), but get the system to send you a special password.

Each week's test will be available immediately after the Thursday lecture, at 6pm. The deadline is at 3am on Tuesday morning (that is, very very late Monday night).

Please try it as soon as you can. If you experience technical difficulties, please email me early on so that we will have a chance to fix it in time: I definitely won't be able to help you shortly before the deadline.

Surgery hours

If you have a problem, you can see me in my office (G39c, Hicks Building) on Fridays between 2pm and 3pm.

If those times are no good for you, then you can:

  1. catch me after lectures (though I may be in a hurry) or
  2. ask me by email, or
  3. ask me for an alternative time.


This will be at the end of the year, and will constitute the other 80% of the total course mark.

Suggested reading

There are no required books for this module. Some recommended books are listed on the official information page.

Contact Details

Dr James Cranch
G39c Hicks Building

Some useful links: