## MTH5100 |
## Algebraic structures I |

Course Material |
Spring 2010 |

**11/05/10:**Solutions to Exercise sheet 10 are now available, from the link below.**31/03/10:**Revision lecture scheduled for Wed 28th April, 10-11, in PUG1. Come prepared to ask questions.**31/03/10:**Exercise sheet 10 is now available, as are the solutions to sheet 9.**24/03/10:**The feedback question on Exercise sheet 9 has been made easier, by removing the words "and only if" from part (a)(ii). (The "only if" part of the question requires something we have not covered in the lectures.) The revised version is on the link below.**23/03/10:**Exercise sheet 9 is now available, as are the solutions to sheets 7 and 8.**17/03/10:**Exercise sheet 8 is now**really**available. I will have some copies available at the tutorial for those who were not able to print it out in time.**16/03/10:**Exercise sheet 8 is now available.**09/03/10:**Exercise sheet 7 is now available, as are the solutions to sheet 6.**02/03/10:**Model solutions to the mid-term test are posted below, along with a sample exam and a couple of exams from previous years. Marked scripts can be collected from the exercise classes this week.**01/03/10:**Exercise sheet 6 now available from the link below.**16/02/10:**Exercise sheet 5, and solutions to sheet 4, are now available from the links below.**12/02/10:**Modification to Sheet 4 below. Hopefully this will make the question easier. Deadline extended to 5pm on Monday.**10/02/10:**Solutions to Exercise sheet 3 are now available below.**09/02/10:**Exercise sheet 4 is now available from the link below.**02/02/10:**Exercise sheet 3 is now available from the link below.**26/01/10:**Solutions to Exercise sheet 1 are now available below.**26/01/10:**Exercise sheet 2 is now available from the link below.**19/01/10:**Exercise sheet 1 is now available from the link below.**15/01/10:**Apologies for the cancelled lecture on Wednesday. Due to snow and several cancelled trains I was not able to make it to the campus.**10/08/09:**Course information in preparation. In the meantime, Prof. Cameron's Notes for MAS201 from 2006 (Notes 2006) provide the best guide as to what is likely to be in the course.

- Lectures: 10-11 Tue (Geog 226); 10-11 Wed (PUG1); 10-11 Fri (PP2).
- Lecturer: Professor Robert Wilson, Room G51. For office hours, see my homepage.
- Exercise classes: 11-12 Wed (Queens EB2) or 9-10 Fri (Queens FB1), starting in week 2.
- Solutions to exercises to be handed in to the BLUE box on the GROUND floor by 12 noon Monday.

- Prerequisites: MTH4104 Introduction to algebra. If you need to revise the material from this course, you may find Prof. Cameron's notes useful.
- Course Description from the Maths UG Handbook.
- Description and syllabus.
- Organisational details.
- Key objectives/learning outcomes.
- Sample exam paper.

**Notes**

**Exercise sheets**

- Exercises 1, and Solutions
- Exercises 2, and Solutions
- Exercises 3, and Solutions
- Exercises
4. Revision to feedback question: omit the part which says "construct the
quotient ring R/I". Hint for the last part: construct a ring homomorphism from R to the
complex numbers which has I as its kernel.

Solutions - Exercises 5, and Solutions
- Exercises 6, and Solutions
- Exercises 7, and Solutions
- Exercises 8, and Solutions
- Exercises
9, and
Solutions. Misprint in Q. 1(b): K should also
contain the identity element.

Error in solution: the cosets listed as left cosets are actually right cosets, and vice versa. - Exercises 10, and Solutions

**Other course material**

- Mid-term test and model solutions are here.
- Exams from 2007 and 2008. Note however that, due to changes in the School regulations, this year's exam is in a different format. Other past exams can be found on the library web-site.
- Sample exam here.
- Some thoughts on the overall aims of the course, my teaching strategy, and study skills, are collected here.

The recommended course text is
*P. J. Cameron, Introduction to Algebra. Oxford University Press.*

- Prof. Cameron's Notes for MAS201 (the previous version of MTH5100) from 2006 Notes 2006.

- General:

Robert A. Wilson

Created 10 August 2009

Updated 3 June 2010