This course uses the classical Euclidean plane geometry as an anchor point to study some of its natural outgrowth: affine, projective, spherical, and non-Euclidean geometries. The study of these geometries will, in turn, deepen our appreciation for the classical Euclidean geometry. The unifying theme in approaches to these geometries is Klein's transformation groups. Technically we will use a lot of analytic methods (setting up and analyzing equations in approriate coordinates, matrix manipulations), so it would be beneficial for the students to review the material in Math 250. However, our approach will not be purely computational. We will emphasize the geometric flavor of the subject, and whenever possible and beneficial, will provide direct geometric argument. In particular we will blend in fair amount of deductive proofs (also called axiomatic or synthetic proofs). The hope is that, after the course, you will have an appreciation for the liveliness, diversity and connectedness of mathematics, and the excitement and pleasure of discovering mathematics, and that you would be comfortable to attack geometric problems using a combination of methods learned in this course. Emphasis will be placed on geometric understanding and logical reasoning. As such, mere memorization of facts would be of little help. Nor can you complete most regular assignments by simply looking up a magic formula on a page from the texts. Instead, you should be prepared to fully participate in the discussions (in-class and out-class), do extra readings and research, develop and communicate your ideas. You are also encouraged to try to use a combination of geometric exploration, model making, and thought experiments to help you in the learning process. Group discussions and brainstorms will be strongly encouraged. An important aspect of the course is to help you sort out your ideas and present them in a logical way. So it is expected that you present your work in a coherent way, using compelte English sentences. More guidelines are given below.

Course Catalogue Description.

Exams There will be two mid-term exams and a cumulative final. The final will count 200 points. Each midterm will count 100. They will be closed book exams and student-prepared formula sheets will not be permitted. Missing one exam will result as immediate failure for the class

Homework and Quizzes: You will have weekly regular assignments. The regular assignments are to help you work through the ideas discussed in class and gain a fuller understanding of the technical aspect of the ideas. Discussion and cooperation with each other is strongly encouraged at every stage of the course work, except at the writing-up. In your submitted work, ideas that come from other people should be given proper attribution. If your work has emerged from work with other people, write down whom you have worked with. If you have referred to some sources, cite them. Short quizzes may occasionally be given to test basic understanding on concepts.

Make-up exams/quizzes and late homework policy: There will be no make-up quizzes or exams, except in case of documented emergency. Late Homework will not be accepted.

Attendance: I will record attendance each class, but it will not count for the final grade.

In summary, here are the components of the term grade with their maximum possible points: