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MATH2008 home page

An Introduction to Modern Algebra

This page refers to the unit of study MATH2008 "Introduction to Modern Algebra" as it was given in 2nd Semester 2003. This unit of study was abolished in the change from 4 credit point units to 6 credit point units that was implemented in 2005.

The page was updated weekly throughout the semester, as links were added for tutorial solutions and lecture summaries. This material was also made available for purchase from KopyStop.

The information sheet for Math2008 in 2003 is still available here.

Please report any problems you have with this web site by email to

Page contents

* Objectives
* Assessment
* Classes
* Consultations
* Books
* Tutorials and assignments
* Lecture summaries
* Past exam papers

Course objectives

  • To gain proficiency in dealing with abstract concepts, with emphasis on clear explanations of such concepts to others.
  • To understand the theory of inner product spaces, including concepts such as the orthogonal projection onto a subspace, and its use in finding the best polynomial model for a data set, and finding the best approximation, by polynomials or by sines and cosines, to a continuous function over an interval.
  • To see how group theory can be used to study symmetry in geometric and abstract contexts.
  • To understand the basic group theoretic concepts such as subgroup, coset and homomorphism, and their elementary properties.
  • To learn how to use the computer algebra package MAGMA (to a small extent).

Assessment details

The examination is two hours in length and carries 85% of the assessment. The other 15% is made up as follows: assignments 10%, tutorial participation 5%. Tutors will record attendance and participation in the standard tutorials; attendance at the computer tutorials will be monitored via computer login records.

There will be two assignments: the first will be distributed near the end of Week 4, and its due date will be the first Tuesday in Week 6. The second will be due on the first Tuesday after the mid-semester break – that is, at the start of Week 10. The questions will be distributed two weeks before that.


Lectures are at 9:00 am Tuesdays in Carslaw 175 and 9:00 am Thursdays in Carslaw 275. Students should also attend one computer tutorial and one standard tutorial each week, starting in the 2nd week of the semester. Note that you will benefit more from the tutorials if you attempt the questions beforehand. The times and locations for computer tutorials are as follows: Monday 10:00 am, 2:00 pm in Carslaw 610/611, Tuesday 10:00 am in Carslaw 729/730.

The times and locations for standard tutorials are as follows: Tuesday 11:00 am in Eastern Avenue 312, Thursday 10:00 am and Friday 11:00 am in Carslaw 350.

Please attend the tutorial to which you have been timetabled. If exceptional circumstances force you to miss your scheduled tutorial class then you may attend another instead.

In the computer tutorials we shall be using the computer algebra package MAGMA to investigate inner product spaces and to learn about group theory. There will be problems for you to solve each week: these are complementary to the problems in the standard tutorials and are designed to help you understand the theory of lectures. You will be expected to learn some basic MAGMA commands: the assignments may require the use of MAGMA and there will be questions in the examination about the use of MAGMA.


The lecturer is A/Prof Bob Howlett, whose room is Carslaw 523. Office hours: 12:00 – 2:00 Mondays and 1:00 – 2:00 Tuesdays. (Possibly also available for consultation at other times: click here to see his timetable, to find the best times to try.)

Stewvac consultation times:

I shall be in my room between 2:30 and 3:30 on Wednesday 5th and Thursday 6th. But I shall be in every day between now and the exam, and you are welcome to ask questions any time.


The following are useful reference books.

  • Carol Whitehead, A Guide to Abstract Algebra, MacMillan Mathematical Guides, 1988.
  • H Anton, Elementary Linear Algebra, Fifth Edition, Wiley, 1987.
  • G Strang, Linear Algebra and its Applications, HBJ, 1988.
  • J A Green, Sets and Groups, Routledge and Kegan Paul.
  • J R Durbin, Modern Algebra, an Introduction, Second Edition, Wiley, 1985.

Tutorials and assignments

Tutorial and assignment solutions will be made available from Kopystop, 55 Mountain Street, Ultimo. They will also be available for web download. Links will be provided here in due course.


Instructions relating to computer tutorials.


Lecture summaries

Notes on each week's lecture material will also be available via KopyStop and the internet.

The lecture summaries are available from KopyStop in book form. Individual weekly summaries will not be sent to KopyStop, but will remain available via the web. Any corrections that are made to the KopyStop versions will be announced here.

*Week 1 *Week 5 *Week 9 *Week 13
*Week 2 *Week 6 *Week 10
*Week 3 *Week 7 *Week 11
*Week 4 *Week 8 *Week 12

Examination papers from previous years

The exam paper from 2000 (extended answer section only) is available for download.

The solutions to the 2000 exam are also available.

If you want to look at exam papers from other years, you can download them from the library's website: