Interactive Course on Projective Geometry


The course MA1127 is a discovery-based, interactive course on projective geometry. Among its aims are: to exercise the student in the visualization of mathematical concepts, to present a unified view of basic geometry as the study of group actions, to develop and exercise problem-solving techniques, and to give the student a sense of the unity of mathematics by relating projective geometry to other fields such as special relativity, integral geometry, topology, and hyperbolic geometry.

At each meeting, the instructor will propose definitions which will be motivated and discussed, and he will proceed to develop the theory through problems, which the students are expected to solve by passing to the board. Although this may seem hard for the students, last year's experience shows that it is not only possible, it is fun! Of course, the intellectual freedom that such a course provides the students comes at a price: it is harder to take notes than in a regular course and students which are poorly motivated or prepared risk lagging behind in a very visible way (In a regular course, these students usually lag behind without the instructor or themselves noticing it). Nothing can replace personal responsablity or a good preparation, nevertheless there will be plenty of office hours and these notes, together with Berger's book, contain all that will be covered in the course.

The evaluation, following the rules of our university, will take the form of a single exam. This exam will contain five or six problems and will last about three hours. The problems will not be problems previously solved in class and learning by rote is violently discouraged. Because this seems to be a break with tradition that causes the students some anxiety, I have prepared some sample exams and interactive quizes (coming soon!). The students are encouraged to try to solve these exams at the earliest possible date and to hand them in for evaluation. The students are also encouraged to go to the library and check out other books beside Berger's (see the list of recommended reading). They are also encouraged to make use of the applets and animations in this site.