Course Syllabus - Fall 2008

From the College Catalog :Synthetic and algebraic development of projective spaces. Collineation groups, representation theorems, quadratic sets and applications. Emphasis will be on finite projective spaces.

Prerequisites: Math 3191(Linear Algebra)

A comment on prerequisites: We will use Linear Algebra heavily, so Math 3191 (or a more advanced Linear Algebra course) is a real prerequisite. I will emphasize the finite aspects of the subject, so a background in Combinatorics will be useful (say, Math 4409 Applied Combinatorics), but not essential, as we will not be using any of the real heavy-duty combinatorial techniques. There is a bit of algebra (in particular, groups and fields) involved in the course, but these topics will be reviewed. No geometry background is assumed.


Meets: M,W 2:30 - 3:45
Room: SO - 111


Text: R. Casse, Projective Geometry: An Introduction, Oxford Univ. Press, 2006

Exams: There will be two exams, a midterm and a final. These are both likely to be take-home exams. The midterm will cover the material in Chaps. 1-5 (inclusive) and should be expected in early-October. The final will cover Chaps. 6-8 and special topics (see below) and will be on or due Dec. 8.

Homework: All problems in the text are to be considered assigned homework unless I say otherwise. As many topics are introduced in the problem sets, we will work most problems in class (student presentations), and some questions will be handed in for grading.

Projects: Each student will be assigned a special topic in projective geometry. All students are to prepare an hour lecture on the topic and give it to the class. Also, the student is to prepare a set of lecture notes on the topic, these will be given to everyone and posted on the web in the section devoted to special projects of the course web page. The topics will appear on the final exam. It is expected that all projects are to be completed during October and November. If not done before November 5, there will be a grade penalty.

Grades: The final grade will be determined as follows:


               Exams                    60%
               Project                  30%
               Homework, Classwork      10%

There's no curving of exam grades : A(100-90) B(89-80) C(79-70) D(69-60) F(<60)

Plusses and minuses may be used in final grades at my discretion.

Syllabus: My intention is to cover all of the text and some additional topics (there will be notes for these). An approximate schedule is given below:

DateSection     DateSection
8/11Chap. 2     10/8Chap. 7
8/13Chap. 3     10/13Chap. 7
8/18Chap. 3     10/15Chap. 8
8/20Chap. 3     10/20Chap. 8
8/25No Class     10/22Special Topics: Hyperovals
8/27No Class     10/27Special Topics: Hyperovals
9/1No Class     10/29Special Topics: Figueroa Planes
9/3Chap. 4     11/3Special Topics: Figueroa Planes
9/8Chap. 4     11/5Special Topics: Tits Ovoid
9/10Chap. 4     11/10Special Topics: Tits Ovoid
9/15Chap. 4     11/12Student Presentations
9/17Chap. 4     11/17Student Presentations
9/22Chap. 5     11/19Student Presentations
9/24Chap. 6     11/24No Class
9/29Chap. 6     11/26No Class
10/1Chap. 6     12/1Student Presentations
10/6Chap. 7     12/3Student Presentations
Note: Any and all of the above is open to negotiation.


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Last updated July 25, 2008