AS/SC/MATH 2021.03F

Linear Algebra I (Honours)

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 MATH2221.03. 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 Gauss-Jordan reduction, matrices and determinants. Applications are made to graph theory, economics and polynomial interpolation. We then proceed to study the more abstract concepts of vector spaces, basis, dimension and inner products.

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, graded and counted towards the final grade. Most exam questions, however, 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.

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The final mark will be based on the homework (20%), two in-class tests (40%) and a final examination (40%).