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MATH-UA-140
Linear Algebra
Instructor Information
TBD
Course Information
● Normal prerequisite: Calculus 1 with a C or higher (or equivalent)
Course Overview and Goals
This is an introductory course on linear algebra, one of the most important and basic
areas of mathematics, with many real-life applications. The course introduces students to
both the theory of vector spaces and linear transformations and the techniques such as
row-reduction of matrices and diagonalisation, which can be applied to problems in areas
such as engineering, economics, and mathematical biology.
As well as mastering techniques, it is important that the students get to grips with the
more abstract ideas of linear algebra, and learn to understand and write correct
mathematical arguments. Taking an active approach to problem-solving is also important.
The class will consist of a mixture of lectures, working on problems and class discussions.
Each class will correspond to two or three sections of the recommended text, which
students will be expected to read. There will be weekly assignments, which are a very
important part of the learning process: actively engaging with the mathematics is crucial.
Upon Completion of this Course, students will be able to:
● Understand the basic theory of vector spaces: linear independence, spanning,
bases, dimension, subspaces.
● Understand the basic theory of linear transformations: matrix representation,
diagonalisation, orthogonal diagonalisation
● Carry out the basic techniques of the following: row-reduction and LU
decomposition to solve systems of linear equations; calculating determinants;
finding eigenvalues and eigenvectors and diagonalising matrices; orthogonally
diagonalising matrices.
● Apply linear algebra to solve some real-life problems.
● Be able to work with formal mathematical arguments.
Course Requirements
