Linear
equations, matrices, determinants, vector spaces and inner product
spaces. This course covers material similar to that
in AS/SC/AK/MATH 2221 3.0 but at a more
advanced level. It is required in Honours Mathematics degrees.
Linear algebra is the study of vectors, matrices and linear
transformations. These concepts are used in all areas of
mathematics, in all branches of science and in the quantitative
aspects of the social sciences. The content of this course is
similar to that of MATH 2221 3.0. This course, however, is more
theoretical and covers additional topics in linear algebra and
its applications. It therefore provides a solid background not
only for courses in linear programming and statistics which use
linear algebra but also for advanced theoretical mathematics
courses such as abstract algebra and functional analysis.
The course begins with concrete topics such as the solution of
linear systems of equations by GaussJordan reduction, matrices
and determinants. We then proceed to study
the more abstract concepts of vector spaces, basis, dimension and
eigenvalues.
This is a rigorous mathematics course in which all definitions
and proofs are presented in class. In addition, all concepts
will be illustrated with examples and reinforced through
computational homework problems. Moreover, students are expected to
learn to construct proofs as the course progresses. Theoretical
homework problems will be assigned; however, most
exam questions will be computational in nature.
This is an honours course intended primarily for students
intending to earn an honours degree in mathematics (other than
Honours Mathematics for Commerce). However, all students who meet the
prerequisites are welcome.
The text is W. Keith Nicholson, Linear Algebra with
Applications (3rd Ed.), PWS Publishing Co., 1995.
The marking scheme has yet to be determined.
(Note from the Undergraduate Office:
MATH 1540 3.0 may not be taken for credit by anyone
who is taking, or anyone who has taken, MATH 2021.)
Prerequisite: OAC algebra or any university mathematics course.
Exclusions:AS/SC/MATH 1025 3.0,
AS/SC/AK/MATH 2221 3.0, AK/MATH 2220 6.0.
