Guidelines for the Projects
You can work together in groups of up to 3 people (though each person will have to turn in their own individual report). If you do work in groups, you should not write your project collectively, but you should feel to use the members of your group as sounding boards and to assist you in finding resources or solving the problems. If you want to form a group, I recommend posting to the message board or hooking up with friends from class. You should also cite the other members of your group in your bibliography.
I'll be glad to answer any questions you have about your project and to help you find references, etc. I highly recommend Applications of Linear Algebra and Elementary Linear Algebra: Applications Version by Anton and Rorres as starting points in researching these topics.
The basic sections that you'll need to include in your report are listed below, together with what portion of your project grade each is worth. The total number of points available is 80.
Nota Bene: you don't have to put your report in the order that the following sections appear. One possibility is to use the assigned problems to illustrate how the ideas of the subject fit together with the mathematical ideas that you will be using, in which case Background and Solutions would be interwoven. Just make sure that these aspects appear in your report.
Background (20) This is mostly a discussion of how the linear algebra fits in with your topic. In other words, you need to talk about what you needed to know about your topic in order to do the associated problems and how linear algebra fits into the picture. So you might include the definitions of the words I've given you, the linear algebra ideas you used (e.g. matrix multiplication, solving linear systems, etc), and some explanation about why these ideas were useful.
Solutions (40) You need to include solutions to the problems in the project description. Don't just give the answers, however. Include a full, detailed explanation of what you're doing at each step. You'll want to use words and write in full sentences, though you can also have the occasional formula or sequence of equalities.
Evaluation (10) I'd also like you to include your take on these projects. Answer the following questions, and include any other comments that you'd like to make: Were they worth it? Did you enjoy your project? How much time did you spend on it? Do you think that this is something you may use in the future? How could the projects be improved?
You'll notice that there are still 10 points unaccounted for. The remaining 10 points are for style: clarity, neatness, flow, design, organization and creativity--it's important to be able to communicate your ideas.
Your project should be written in clear language, and you should use complete sentences, adequate spelling and proper grammar. While you should cite any references you use, I don’t have any particular preferences about bibliography formatting. Your project should contain a complete solution to whatever problems are involved in the project descriptions I gave you, and an explanation of the techniques and methods used in solving the problems. An appropriate model for your audience is one of your fellow classmates who hasn’t done this particular project. The idea is to provide an explanation which would make it clear to someone who is somewhat knowledgeable of linear algebra what you did and why it worked, so that they could attempt similar problems with a reasonable chance of success. On the other hand, don’t go completely overboard. Be succinct, to the point and most importantly clear. It is not necessary to re-derive from scratch in the paper any mathematics you use, but a brief explanation of any new tools or ideas used is necessary.
While it isn’t necessary to type your papers, it is necessary to write clearly enough that I don’t ever find myself squinting at something and wondering what the heck you meant to say. Diagrams should likewise be clearly labeled.