Welcome to 620-222

Linear & Abstract Algebra

Second Semester 2007

Your lecturer is

Craig Hodgson

Email: cdh AT ms.unimelb.edu.au
Room 172, Richard Berry Building

Contents

NEWS Feedback

The Course

Course Notes and Other Materials

Assessment

Books

Practice Class

Some Course Related Links

NEWS

Solutions to Assignment 2 available here

Help available during swot vac and the exam period is listed here

Some old exams: 2006 2005 2004

Others are available here

Assignment 2 is available here

Lectures on Euclidean Isometries:

My approach to Euclidean isometries differs from the notes. Therefore I will upload each lecture shortly after giving it. Please CLICK HERE to view the lectures.

Solutions to mid-semester test are available here

Solutions to assignment 1 are available here

Consultation hours

  • Monday, 12-1, room 172
  • Wednesday, 2.15-3.15, room 172
  • Thursday, 3.15-4,15, room 172

Class Rep

  • Thomas Werner
 

 

The Course

The course will discuss various aspects of modern algebra  concentrating on extending the linear algebra that you have already done and introducing some new abstract algebra in the form of group theory.

Generic skills

In addition to learning specific technical skills that will assist you in your future careers in science, engineering, commerce, education or elsewhere, you will have the opportunity to develop in this subject, generic skills that will assist you whatever your future career path.

  • You will develop problem-solving skills including engaging with unfamiliar problems, and identifying relevant strategies.
  • You will develop analytical skills - the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of the analysis.
  • Through practice classes and other interactions with fellow students, you will develop the ability to work in a team. The department distinguishes between ethical collaboration, which is strongly encouraged, and plagiarism, which is prohibited.

 

Assessment

There will be a three hour examination in the usual examination period at the end of the course.

There will also be

  • a mid-semester test which will take the form of a 50 minute test during the lecture time on Wednesday September 12.

and

  • two take-home assignments, one to be given out on Wednesday August 22 and the other on Wednesday October 17.

The final mark will be calculated as the maximum of

E and 0.1T+0.1A+0.8E

where T, A and E are the marks (out of 100) for your test, assignment and examination, respectively. That is, we will count the test and assignment marks if they improve your final mark but not otherwise.

 

Books

There is a set of lecture notes for the course; this includes some answers and solutions to exercises as well as solutions to old examination papers. These will be on sale at the Melbourne University Bookshop. I recommend that you consider buying a copy. It is not essential, however, as the topics are covered by many books both in the Library and for sale.

For those who do not want to buy a copy of the notes, the exercises will be available (free, of course) separately. The first set of exercises will also be available at the first lecture so that you can get started before obtaining the notes.

For those who do not buy the notes or who want more than the notes there are many books that make suitable reading.  If you are browsing in a library, look for books on Linear Algebra (but not a `first course') or Abstract Algebra or Group Theory.  The books listed below are recommended and will be on reserve in the mathematics library.

`Algebra' by Michael Artin (Prentice Hall, 1991)

`Finite dimensional vector spaces' by Paul R. Halmos (Springer, 1974)

`Groups and symmetry', by M. A. Armstrong (Springer, 1988)

'Abstract algebra' by Thomas Hungerford (Saunders College, 1990)

'Linear Algebra Done Right' by Sheldon Axler (Springer, 2002)

 

Practice Class

There will be weekly practice classes, starting in week 2 as given on your timetable from Allocate.

These are intended to give a more informal approach to the material of the course with more chance for discussion and questions. They will not introduce new material. It is expected that most students will want to come to only one class.

 

Feedback

If you have any comments about how the course is going, please let me know. If you want to see me at any time (outside consultation hours), please contact email me (cdh AT ms.unimelb.edu.au).

Course Notes and Other Materials

You can view the notes on the internet from this screen. While the mathematical details may
not be as clear, there are some advantages in the form of links both within and without the document.

To view the notes, you will need the Adobe Acrobat Reader. If there is not one already on the machine you are using, it can be obtained free from Adobe. It is simple and convenient to use and you can print out any part of the notes if you wish.
 
The notes are available either as a single (long) document

 Notes for 620:222 Linear and Abstract Algebra

or in shorter parts. You will probably find it more convenient to take only the part you need at the time.

 

These electronic notes are actually from a previous year -- they are isomorphic to this year's notes.

Assignments will be handed out in class.
If you miss class please obtain one from my office (Room 172).

 

 

Some Course Related Links

History of Mathematics archive (Mactutor)
A very good (and award winning) collection of material on the history of mathematics.  This has been referred to at several places in the electronic version of the notes.
Highly recommended.

MathWorld  A concise and comprehensive mathematics encyclopaedia on the web.

3D-XplorMath  A program for various sorts of mathematical visualisation. It includes curves, surfaces, conformal maps, ODEs and, of particular relevance to us, polyhedra.
Highly recommended.

The French Mathematician
A review of an Australian novel based on Galois, the (young) father of modern abstract algebra.

An encyclopaedia of polyhedra
A collection of over 1000 images of polyhedra. To view them properly, you will need a vrml viewer; but the page explains how to obtain one.

Seventeen Kinds of Wallpaper Patterns
Wallpaper patterns in Japanese weaving; the source for the patterns in the notes.

Wallpaper patterns in oriental carpets
Similar to the previous one, but carpets.

Kali
A computer program that lets you draw symmetrical patterns based on any of the 17 tiling groups; worth exploring. (For Windows and Macintosh computers.)

Kaleidotile
A computer program to create tessellations of the sphere, Euclidean plane and hyperbolic plane. (For Windows and Macintosh computers.)

Two-dimensional geometry
A detailed discussion of symmetries, plus a treatment of wallpaper groups; worth exploring.

The Discontinuous Groups of Rotation and Translation in the Plane
A treatment of wallpaper groups.

Wallpaper groups
A very good source on wallpaper groups.
Highly recommended.

Symmetries of polygons
A lovely website for messing around with the symmmetries of polygons and getting an intuitive feel for the dihedral group.

 
 

 

Created by: Craig Hodgson, Department of Mathematics & Statistics.
Maintained by: Craig Hodgson, Department of Mathematics & Statistics.
Email: cdh at ms.unimelb.edu.au