Linear algebra is one of the most widely used and fundamental areas of mathematics. Linear algebra is an important tool in virtually all physical sciences, in economics and other social sciences, and in engineering. It is an important companion to calculus, but the flavor of the subject is different, as you will see in this course.
We will study matrices, rectangular arrays of numbers, and see how they are used in a variety of ways. First, matrices are used to solve systems of linear equations. They are an efficient means for recording the steps that are used to solve the system. Second, matrices are used to define functions, which we call linear transformations. An n x m matrix defines a function from m -dimensional space to n -dimensional space. From this perspective, solving a system of equations is essentially finding the preimages for an element of the n -dimensional space. Third, matrices are used to define a change of coordinate system.
The core material is in Chapters 1-4, which we will cover thoroughly. Chapters 5-7 develop the geometry of linear tranformations and change of coordinates. That is where it gets very interesting!
The main prerequisite is high school algebra.
|Ch 1-2||Solution of Equations and Transformations||3 weeks|
|Ch. 3||Subspaces of R^n||2 weeks|
|Ch. 4||Abstract linear algebra||2 weeks|
|Ch. 5||Orthogonality and projection.||2 weeks|
|Ch. 6||Determinants||2 weeks|
|Ch. 7||Eigenvalues and Eigenvectors||3 weeks|
Written assignments should be carefully and neatly presented.The expected weights of the work are given below, but this is subject to change.