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%).