MATH2902 Linear Algebra (Advanced)

An introduction to the theory of vector spaces and linear transformations

First Semester 2003

This page will be updated periodically through the semester. See below for links to weekly tutorial problems and solutions.

First Quiz Announcement:

The first quiz was held on Thursday 10 April. Marked quizzes have been returned in lectures.

Second Quiz Announcement:

The second quiz was held on Thursday 15 May. Click here to see what that quiz entailed. Marked quizzes were returned in the lecture on Thursday 22 May.

Third Quiz Announcement:

The third quiz was held on Thursday 12 June. Click here to see what that quiz entailed. The third quiz will be marked and then returned in the Carslaw Lecture Theatre 275 at 9.15 am on Thursday 19 June. Marked quizzes may also be collected at the consultation time later that day. Afterwards any uncollected quizzes will be placed in the assignment boxes for second year.

Lecturer

The lecturer is David Easdown, whose office is Carslaw 619 (phone 9351 4217). David plans to be available for lunchtime consultations each Thursday from Week 2 between 1.00-2.00 pm. If you need to make an appointment to see him at some other time, try ringing first or emailing him. Click here to see David's timetable.

Classes

Lectures are held on

Students should also attend one tutorial each week, starting in week 2.

The times and locations for tutorials are

Text/Reference

David Easdown's notes A Course in Linear Algebra will be a comprehensive text for all of the course. These notes may be purchased for $9 in book form from Kopystop, 55 Mountain Street, Broadway.

An excellent reference for further material and reading on exponentials of matrices and solving differential equations is ``Differential Equations, Dynamical Systems, and Linear Algebra'' by Morris Hirsch and Stephen Smale. The authors write elegantly, simply and clearly, and include (in an appendix) a proof of the Fundamental Theorem of Algebra, which students in this course will find quite accessible. The call number for that book, in the Fisher Library and the Mathematics Library (level 8 Carslaw), is 517.382 92 (several copies).

These libraries have many books, too numerous to mention here, on elementary linear algebra and related topics. A very fine resource also is Bob Howlett's MATH2902 webpage for 2001, which has a link to his own lecture notes and a list of further references.

Assessment

Your final mark for this option may be calculated as follows:

One assignment will be set, but not collected. The assignment does not count towards your final grade, but will be excellent preparation for written exam questions. The purpose of the assignment is to gain practice and skill at writing mathematics and presenting clear concise arguments.

Three quizzes will be given during lecture times, announced the week before. These are an opportunity for you to get quick feedback from the lecturer how well you are coping with the material, and help the lecturer fine-tune the pace of lectures and rectify obvious difficulties.

The exam will comprise two sections, the first requiring short answers, similar to the quizzes, and the second requiring longer written answers. Click here to see more detailed information about the exam.

Tutorial and Assignment Problems

Solutions to Tutorial and Assignment Problems

Paper copies of tutorial solutions may also be purchased from Kopystop, from the Friday before the week for which the tutorial is held.

Handouts

Tutorial sheets and any other handouts will usually be distributed in lectures. Spare copies may be collected also from the Carslaw seventh floor corridor.

The Course

We will study linear algebra, one of the most fundamental branches of mathematics and an essential part of the background required of mathematicians, engineers, physicists and other scientists. Linear systems, which are related in a precise sense to simple arithmetic operations, arise naturally everywhere and can be used to approximate phenomena with arbitrary precision. We study abstract vector spaces, the correct general setting for understanding linear systems, and develop tools for understanding and analysing linear transformations, the means by which objects from different vector spaces are related. This involves developing the classical theory of matrices, determinants and canonical forms. We expect the order of topics to be

Pre-examination consultations

Consultation times in Room 619, Carslaw:

Past Exam papers

The following examination papers from previous years are available electronically. The Library may have others. Be aware that the course has changed and not all the material in previous exam papers is relevant. Also notation may be different from that used by the present lecturer.

David Easdown
13 June 2003