MATH2902 Online Resources
This was the home page for Math2902 for first semester 2001.
Note that the syllabus has subsequently been modified slightly.
This lecture course introduces students to pure mathematics,
via the theory of vector spaces. The principal objectives
can be summarized as follows.
- To gain proficiency in dealing with abstract concepts, with
emphasis on clear explanations of such concepts to others,
and especially to acquire the ability to write down proofs of
the elementary theorems of the subject.
- To understand the axiomatic development of the theory of vector spaces,
learning basic concepts such as linear independence of vectors,
spanning sets and bases of vector spaces.
- To learn the basic properties of linear transformations,
and their relationship with matrices.
- To understand eigenspaces, generalized eigenspaces and
diagonalizability for matrices and linear transformations.
See below for links to
week-by-week lecture summaries and
Examination papers from previous years
The following examination papers from previous years are available
for your perusal. The library may have others too.
Note that the syllabus of the course has not changed significantly
in the years 1988–2001, although its title has. (For example, it
was 292F in 1997. But it has always been "2nd year advanced linear
algebra".) Different lecturers sometimes use slightly different
notation; so some of the questions in the
past exam papers may use notation that you are not familiar with.
The lecturer in 2001 was A/Prof Bob Howlett,
whose room is Carslaw 523.
The lecture notes "Vector Space Theory" by R. B. Howlett
are available on-line, and I also
have a few hard copies left. I sometimes donate copies to
Some reference books:
- Beaumont, R. A.: Linear Algebra
2nd ed. (Harcourt, Brace, Jovanovich, N.Y. 1972).
- Curtis, C. W.: Linear Algebra: an introductory approach
4th ed. (Springer-Verlag, N.Y. 1984).
- Halmos, P.: Finite-dimensional Vector Spaces 2nd ed.
(Van Nostrand, Princeton, 1958).
- O'Nan, M.: Linear Algebra 2nd ed.
(Harcourt, Brace, Jovanovich, N.Y. 1976).
Summaries of each week's lecture material are provided here.
There was no Week 13 summary.
Another pdf file is available containing a discussion of
the Fundamental Theorem of Algebra.
(This material was not examinable.)
There is also an animated display illustrating
the approach to the Fundamental Theorem that is taken in the document
referred to above.
Tutorials and assignments