# 640:435:01 Geometry

Class meets: MTh2(10:55 -- 12:15), RAB-204.
Instructor: Dr. Zheng-Chao Han
Office Hour: Th9:30-10:30, Chem. Bldg(R.B.Heldrich Science Bldg)-101A; T3:30-4:30pm, Hill-230.
Email: zchan at math dot rutgers dot edu (I prefer to answer math questions in person during office hours, not through emails; I try to process my emails once per day ).
Text: The following is the required text for this course:
• David A. Brannan, Matthew F. Esplen & Jeremy J. Grayd; Geometry (first edition); Cambridge University Press, 1999 (510 pp.); (ISBN 0-521-59787-0)
Additional supplementary material will be provided/recommended as the course progresses. Later in the semester, we will do some reading and discussion of the classic The Thirteen Books Of The Elements, by Euclid (translated with introduction and commentary by Sir Thomas L. Heath), which contains rich information about our subject from its birth more than two thousand years ago until the nineteenth century. Dover publishes an economical edition: The Thirteen Books Of The Elements, Vol. 1 (Books I and II) (second edition, ISBN 0-486-60088-2); 1956. There is also an online version of Euclid's Elements .

Note: Do not forget to "reload" the assignments pages - if you visited them before, your browser may be showing you only the old cached page.

## General Comments on the Course

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. One unifying theme in this course's approach 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 (Linear Algebra). 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).

Out 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 most regular assignments be completed 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 Material

You may find a copy of our section's syllabus and homework assignment posted on line. Both are subject to adjustment. Any updated information should be posted on this web page. However, the most accurate information will be from the lectures. I am also planning to post some notes and outlines for our lectures.

## Structure of Assignments

Homework and Quizzes: You will have weekly regular assignments(due each Monday). 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.

## Assignment Grading Guidelines

Attendance and Make-up Policy: Class attendance is expected. Poor attendance will be used to decide borderline grade situations. Any changes to the syllabus, homework assignment and any announcement for the midterms and final exam will be made in the lectures. No late work will be accepted. There will be no make-ups for quizzes. A make-up midterm will be given only if you have a valid reason such as serious illness (not a slight cold) or a family emergency, and provide an acceptable, written excuse (not an email message), or you will receive a grade of zero. If possible (particularly if you want to be sure that your excuse is an acceptable one), contact me before missing an exam.

## Course Grading Policy

Your course grade will be determined on the following basis:

• Regular assignments and Quizzes: 20%
• Midterms(first one tentatively scheduled on Monday, Oct. 16): 20% each
• Final Exam: 30%
• In-class presentation and participation: 10% (Each student will be asked to do a short presentation towards the end of the semester; To encourage students' participation in discussions, each round of volunteer response to questions, formulating own questions, will contribute towards extra credit; extra work in making models or bringing and presenting geometry related information may also be awarded credit from this category.)

For comments regarding this page, please send email to zchan at math dot rutgers dot edu.