Linear Algebra is the study of linear equations in several variables and related topics. The word "linear" here means the variables appear only with exponent 1 and do not appear inside other "nonlinear" functions, such as exponentials or trigonometric functions. Indeed, a linear equation in two variables describes a straight line (hence the name "linear"). Though this simple description makes the subject sound elementary, linear algebra is quite involved since typical applications require the solution of many equations with many unknowns (often numbering in the thousands). Thus, much of the subject involves finding efficient techniques for solving systems of linear equations, and other related tasks.
The specific list of topics we will cover include the following:
In terms of level of coverage of the topics, this course will be about a 50/50 mix between theory and computation. Certainly it is important to learn how to compute and manipulate matrices and related operations in linear algebra. You should also have access to the software package, Matlab from MathWorks, either by purchasing the student version or having access to it from a university or library site. Although you could use other forms of software (e.g. Maple), guidance will only be given for Matlab. Proofs of theorems will be covered and some proofs will be expected of you on assignments.
The official prerequisite for the course is Math 304, which is an undergraduate linear algebra course. However, the assumption here is that many students enrolling in the distance section of Math 640 will not have had linear algebra for quite some time, and thus quite a bit of the material in Math 304 will be reviewed.
The required textbook is Applied Linear Algebra by Olver and Shakiban, published by Prentice Hall, 2006 (ISBN number is 0-13-147382-4). We will cover most of chapters 1-5 and chapters 7 and 8.
This is a "distance class" which means there is no classroom or class meetings in the traditional sense. All course materials, assignments and grades will be disseminated through WebCT starting the week before classes begin. There will be two types of lecture notes: 1) static notes in .pdf format 2) dynamic notes in the form of streaming videos. These lectures will be "asynchronous", which means that you can view them anytime (i.e. they are not live video cams that require you to be viewing them at any particular time). Assignments from the textbook will be posted on WebCT and you will be required to send your assignments to me electronically through WebCT preferably in pdf, postscript or .doc format. I prefer you type your assignments, but neatly handwritten assignments which are scanned and then sent electronically will be accepted. Additional information on how to do this on WebCT (and other WebCT features pertaining to this course) will be given in the link to "Use of WebCT in This Course" available from the course home page on WebCT.
Course grades will be determined by homework (40%); a technology project/assignment (25%) and a final exam (35%). The technology project/assignment will require using computer software (Matlab is recommended) to solve various problems that are too difficult to solve by hand, and that relate to the course material (e.g. least squares analysis, fast Fourier transform with data analysis, eigenvalues/eigenvectors, ill-conditioned matrices). More details on the project will appear later. You may collaborate with other students on the homework. No collaboration with any humans is allowed on the final exam, but you may use books and notes. Grades will be made available through WebCT.
As mentioned above, you are recommended to purchase the Matlab software package from Mathworks. Many of the problems will be easier with this software package (at least as a check of your answers). The software will be essential for doing your technology/project. I will be giving you some instruction and hints on the use of Matlab, but not on the use of other software packages.
When this course is loaded onto WebCT (the week before classes begin), you should be able to view the following three items from the course home page on WebCT: