Algebraic structures I

Course Material Spring 2011
Important notice
No revision lecture has been scheduled for this course during the revision "week".
If you want help with your revision, you are welcome to visit me during my office hours, or email for an appointment.
I believe the exam is from 10-12 on Thursday 2nd June, in York Hall (for most people), but YOU SHOULD CHECK YOUR PERSONAL TIMETABLE.
I am unlikely to be available for last-minute questions after Tuesday 24th May, as I have another exam to mark.

News | Info | Lectures | Tutorials | Exams | Other material | FAQs

  • 26/04/11: Selected solutions to Exercises 10 are now available from the link below.
  • 29/03/11: Solutions to Exercises 9 are now available from the link below.
  • 18/03/11: I have now finished marking the mid-term test. Marked scripts, and model solutions, will be available in the tutorial today.
  • 18/03/11: The slides for lecture 25 (Monday 14/3/11) can be found from the link below.
  • 11/03/11: Exercises for week 9: details below. Hand in Q.50.
  • 11/03/11: An example of a PID that is not a Euclidean domain: sketch of proof.
  • 08/03/11: Solutions to Exercises 5 and 6 are now available below.
  • 21/01/11: At your request, the deadline for handing in coursework has been extended to Monday at 4pm.
  • 20/01/11: Summary notes of the first five lectures are available from the link below.
  • 20/01/11: Friday tutorial now confirmed as 11am, in Eng 324.
  • 17/01/11: Exercises for this week are listed below.
  • 13/01/11: Subject to being able to find a suitable room, the tutorial scheduled for 9am on Friday will be moved to 11am on Friday, to avoid the clash with Number Theory.
  • 13/01/11: The lecture at 4pm on Thursday will from now on be in the new Mathematics Lecture Theatre (on the right immediately as you enter the basement entrance of the mathematics building).
  • 11/01/11: Exercises for the whole term are available from the link below, as are summary notes for the first lecture.
  • 10/09/10: 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.

    General information


    Administrative information

    Course descriptions and syllabus

    Your working week

    Each module is designed to fill one-quarter of a full-time working week. That is, you are expected to work roughly ten hours a week on each module. Only four hours are timetabled. The rest is your responsibility. It should include, at the very least:

    Lectures, notes, and books


    What is the purpose of lectures, if the notes are available online? Experience has shown that it is actually quite difficult to learn mathematics by reading notes or books, even if you are conscientious about doing the exercises (which most people are not). If you are studying music, it is much better to hear it in real time, rather than read the score. A mathematical proof is like a piece of music: there is really no substitute for seeing it develop in real time.


    If I have time, I may put up some summary lecture notes here from time to time. A summary of Lectures 1-29 is currently available. For the rest of the course, or for an alternative view, you are recommended to look at Prof. Cameron's Notes for MAS201 (the previous version of MTH5100) from 2006 Notes 2006.

    An example of a PID that is not a Euclidean domain: sketch of proof.

    Lecture 25 slides.

    Exercises, tutorials, and feedback

    Exercises and tutorials

    These should be regarded as compulsory. Mathematics is not about learning facts ("know-what"), it is about learning methods ("know-how"). Methods and techniques cannot be learnt without practice. As Confucius (551-479BCE) said:

    "I hear and I forget;
    I see and I remember;
    I do and I understand."

    Mathematics is about doing, not about hearing or seeing.

    Exercise sheets

    Here are some Exercises, which are intended to last the whole semester. Not all of these questions will be set formally, but they are provided for your benefit anyway. Each week's set of exercises is structured so that there are:
    (a) practice questions, which you can get help on in tutorials,
    (b) one feedback question, to be handed in and marked for feedback, for which help is not generally available in tutorials, since this defeats the purpose of feedback,
    (c) extra questions for those who want to deepen their learning.
    Marked work will normally be returned for feedback in the tutorials 3/4 days after handing in.

    Assessment and examinations

    Note: this is a change from last year
    20% of the assessment for this course is based on the mid-term test.
    80% of the assessment is on the final exam in May/June.
    Note: this does not mean that the weekly exercises are optional! They are still compulsory, and anyone not making a genuine attempt at them may be excluded from the course, including from the exam.

    Model solutions

    I will not provide model solutions to past examination papers, because they encourage poor quality learning. If you wish to use past exam papers as an aid to your revision, you may bring your solutions to one of my office hours, and I will give you feedback on them as far as time allows.

    Other course material

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

    Web Resources Further reading

    Frequently asked questions

    Robert A. Wilson

    Created 10 August 2009
    Updated 26 April 2011