# MAS114: Numbers and Groups, Semester 2, 2016-2017

## Lecturer: Dr Sam Marsh

This is the 2016-2017 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 available below.

WeekSheet
1Modular arithmetic
2Functions
3Surjectivity injectivity and bijectivity
4Countability and permutations
5Cycle decompositions parity and order
6Groups
7Subgroups
8Isomorphism and orders
9Cyclic groups and group actions
10Orbit counting theorem
11Equivalence relations and lagrange

## 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 Chapter 1, Q11 Model answer
5 Chapter 2, Q9 & Q10 Model answer
6 Chapter 3, Qs 4 & 5 Model answer
7 Chapter 3, Q7 Model answer
8 Chapter 4, Q2 Model answer
9 Chapter 5, Q3 Model answer
10 None -
11 None -
12 No class -

## 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

I am experimenting with using the university's MyEcho system for recording lectures. I can't guarantee every lecture will appear, but I hope those that do will be useful. Please follow the link below, or log in to MOLE.

## L3cture app

The L3cture app can be downloaded for Android or iOS (Apple) smartphones for free from the relevant app store: search for 'L3cture' from Walsh Tech Solutions Ltd. (Show registration instructions)

## Past Exams

The 2015-16 and 2014-15 papers, with solutions and the feedback sent to students after the exam, 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.

• 2015-16 exam, solutions and feedback
• 2014-15 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 $0$?