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MATH2902 Online Resources

Introduction

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 tutorial solutions.

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.

Lecturer

The lecturer in 2001 was A/Prof Bob Howlett, whose room is Carslaw 523.

Books

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 deserving people.

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).

Lecture summaries

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

Questions onlyQuestions and solutions