# MAS114: Numbers and Groups, Semester 2, 2017-2018

## Lecturer: Dr Sam Marsh

Strike action paused! The strike action which caused significant disruption to the first half of the semester has been paused to allow for a Joint Expert Panel to be convened to make an in-depth assessment of the pension fund. It is highly unlikely that strike action will resume this academic year, although nothing is certain.

You can read more about the reasons for the dispute here, and you can also read an article I was asked to write for the Times Higher Education Supplement here.

This is the 2017-2018 course web page for MAS114: Numbers and Groups, Semester 2, which will be updated as the module progresses. For official course information, including timetabling and syllabus, please consult the list of current modules.

## Course Information

The notes for this semester will be distributed in the first lecture, and consist of a booklet with blank sections. The full notes, with blanks filled in, can also be downloaded below.

I have an office hour at Friday, 12 midday in my office (G9, Hicks Building). No appointment necessary.

## FAQs

• Can I change tutorial group? (show)
• Where do I get a copy of the notes and problem booklet? (show)

## Tutorial Classes

The worksheets used by the tutors in the tutorial classes are below.

WeekSheet
1Modular arithmetic
2Functions
3Surjectivity injectivity and bijectivity
4No class
5Countability and permutations
6Cycle decompositions parity and order
7Cycle decompositions parity and order
8Groups
9Subgroups
10Cyclic groups and group actions
11Orbit counting theorem

An additional sheet of questions on equivalence relations and Lagrange's theorem can be found below.

## Problem Booklet and Homeworks

The problem booklet, given out in Week 1 of Semester 2, can be downloaded below. The problems are for working on outside of classes. The solutions can also be downloaded below, but solutions to homework problems will not appear until after the hand-in.

Below are the details of which problems were set as homework.

Week Homework Solution
1 Chapter 1, Q1 Model answer
2 Chapter 1, Q5 Model answer
3 Chapter 1, Q9 Model answer
4 (None set, no class)
5 (None set, no class)
6 (None set, probably no class)
7 Chapter 2, Q9 & Q10 Model answer
8 Chapter 3, Qs 4 & 5 Model answer
9 Chapter 3, Q7 Model answer
10 Chapter 5, Q3 Model answer
11 None -

Due to strike action, some intended homework questions were never set. The solutions to these questions are below.

## Videos

Below is a video on how to approach the colouring problems that feature in the course.

## Online Tests

The online tests continue as in Semester 1. Please follow the link below. The tests will appear by Friday midday, and close at the end of the following Thursday at midnight.

## Lecture Recordings

As with most of your modules, the lectures will be recorded using the university's Encore system. You can find the lectures by logging into MOLE, or using the link below.

## Past Exams

The 2016-17 and 2015-16 papers, with solutions, are below. In line with departmental policy, further past papers can be found on the School of Mathematics and Statistics' website but solutions will not be provided. If you want to ask about a question from one of these past papers, please use the discussion board.

Prior to 2011-12 this course was taught in two halves; the relevant code for the second semester material was MAS175.

• 2016-17 exam and solutions
• 2015-16 exam, solutions and feedback

### Course Recap and Exam Advice

I have prepared a summary sheet with the main definitions and results from Semester 2 of the course (which may be helpful for revision purposes), along with some advice for the exam.

• MAS114 Semester 2: a summary
• Do the natural numbers contain $0$?

## Interesting Extras

Below are things related to material covered in the course which may be of interest to you.

• Java applet for squares in a grid (as mentioned in the notes) Oops! This appears to no longer work.
• How many triangles in a triangle? (related to Problem Booklet Chapter 1, Q2)
• Proof that 0.9999... = 1 (show)

## Contact Details

Dr Sam Marsh
Room G9, Hicks Building
Telephone: 0114 2223792 (internal extension: 23792)
email: s.j.marsh@shef.ac.uk