Linear algebra, as a field of mathematics, can be approached both theoretically and as a useful tool. Our major goal this semester is to learn the mathematics that makes linear algebra work, but it is also important to see how the subject works for other fields of study. We will see at least four applications of linear algebra during the semester. I will lecture on two of them, and you will do projects on another two. Each project consists of reading a section of the text, distilling the information into your own words, and organizing the topic into a 5-10 page paper.
Each paper should be 5-10 pages, typed, single spaced, with 10- or 12-pt type and approximately 1" margins. Mathematica is a reasonable word processor as well as a useful computer program for linear algebra, but any technology is acceptable. It must be converted to a file format that I can read and sent through Blackboard. The paper should contain your own title, introduction, conclusion, references, and other labeled sections as needed. You are encouraged to include pictures, computer output, and an outside reference. Each of the two papers counts 5% of your semester grade. The topics and due dates are:
|Lecture 1||Games of Strategy, section 11.8||Friday 9/13, in class|
|Project 1||Graph Theory, section 11.7||Due Monday 9/23, 11:59 pm|
|Lecture 2||Cubic Spline Interpolation, section 11.5||Friday 10/11, in class|
|Project 2||Curve Fitting, section 11.1||Due Monday 10/21, 11:59 pm|
|Lecture 3||Computed Tomography, section 11.13||Monday 12/2, in class|
There are three papers available to you in both hard and soft copies. You should read these for several reasons. First, they contain examples of applications of linear algebra. I hope it will be interesting to find out how the math you are studying is used. Second, the papers contain Mathematica code that you may find useful. Third, you can change and execute the code in the soft copy to see what happens. This is a good way to learn both the topic and Mathematica. Fourth, each is an example of an acceptable paper for this class.
Feel free to cut and paste examples of code or text formatting that you want to use in your own paper. But please do not copy text content from these or any other sources. Keep in mind the policy on Academic Honesty designed to help you avoid plagiarism and other forms of cheating.
To save a file to disk, right click on the link and choose Save Link As.... Then open the file from Mathematica.
Matrices and Game Theory (4 Jul 02, 27 kb)
Curve Fitting with Splines (4 Jul 02, 619 kb)
CAT Scans (16 Aug 02, 169 kb)
I knew very little about game theory before I started that paper, so perhaps my experience will be somewhat like yours.
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