MAT 2141 (Fall 2010)

Linear Algebra I

About The Course

In this course, we will take a more abstract approach to linear algebra than the one taken in MAT 1341 (the prerequisite for this course). Instead of working only with real or complex numbers, we will generalize to the setting where our coefficients lie in a field (the real numbers and complex numbers are both examples of fields, but there are others as well). We will revisit familiar topics such as matrices, linear maps, and determinants, but now in this more general setting. Compared to MAT 1341, this course will concentrate more on justification of results and mathematical rigour as opposed to computation. Almost all results presented in class will be accompanied by a proof and students will be expected to do proofs on assignments and exams.

MAT 2141/2541 versus MAT 2342/2742: MAT 2342 (and its French equivalent MAT 2742) covers similar material to MAT 2141 (and its French equivalent MAT 2541) but is more applied and less abstract and aimed at students studying economics or statistics. Depending on their program, students may have the option of taking either MAT 2141 or MAT 2342. Students in the MAT-ECON program and in statistics are especially encouraged to take MAT 2342 instead of MAT 2141. If you're unsure of which course you should be taking, you can discuss your options with the professor.

Official Course Description

Vector spaces over arbitrary fields, linear maps, representation of linear maps by matrices, quotient spaces, the isomorphism theorem, multilinear mappings, determinants, inner products, orthogonal projections, the Gram-Schmidt algorithm.

Prerequisites

MAT 1341 (Introduction to Linear Algebra).

Course Text

Official course text:

This book is out of print. The author and publisher have been kind enough to grant permission for students in this course to purchase photocopies of the text. Students registered in MAT 2141 can purchase a copy of the text for $22.38 at University Centre, Room 0024. If you have any difficulties when trying to purchase the text, it is useful to know that it is in Bin C40.

Optional text:

This book is very well suited to this course. It has not been selected as the official course text because of its high price. However, if students wish to purchase it, it is available at the university bookstore (listed as a "recommended text").

DGDs

DGDs will be taught by the professor. In these sessions we will supplement the course material with extra problems and applications. The DGD is also an excellent opportunity for students to ask further questions about any course topics they are having difficulty understanding, to discuss homework and exams, etc.

Private tutors

Students who are finding the course difficult and are interested in hiring a private tutor can take advantage of the tutor referral service of the Peer Help Centre.

Course Outline

A more detailed syllabus can be found here.

Course Webpage

There are two main online locations for information regarding the course: