640:435:01 Geometry

Class meets: MTh2, RAB-204.

Text: There will be two required texts for this course:

Euclid; The Thirteen Books Of The Elements, Vol. 1 (Books I and II), (second edition); Translated with introduction and commentary by Sir Thomas L. Heath, Dover, 1956. (ISBN 0-486-60088-2)
David A. Brannan, Matthew F. Esplen & Jeremy J. Grayd; Geometry (first edition); Cambridge University Press, 1999 (510 pp.); (ISBN 0-521-59787-0)

Instructor: Dr. Zheng-Chao Han

Office Hour: TTh8:30pm-9:30am, Chem. Bldg-102.

Email: zchan@gauss.rutgers.edu (I try to process my emails once per day ).

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

The central issues to be dealt with in this course are

Comparison of axoimatic, analytic, and mixed points of view of studying Geometry
Development of Euclidean Geometry through the study of Book 1 of Euclid's Elements, and some additional interesting theorems in Euclidean Geometry; Briefly examine some foundational issues in classical Euclidean Geometry and the significance of non-Euclidean Geometry.
Introduction to some modern geometries, including affine and projective geometries.

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 may also 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 at http://math.rutgers.edu/~zchan/435syllabus.txt. It is subject to adjustment. Any updated information should be posted on this web page. However, the most accurate information will be from the lectures.

Some reference books will be put on reserve in Mabel Smith Douglass Library. You are encouraged to explore our libraries, the bookstores and the internet to find more readings.

List of References on Reserve:

Robert Bix, Topics in Geometry, Academic Press, 1994. (ISBN 0-12-102740-6)
Robin Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
Marvin Jay Greenberg, Euclidean and non-Euclidean geometries: development and history, San Francisco: W.H. Freeman, 1980.

Here is an online version of Euclid's Elements.

Structure of Assignments

Homework and Quizzes: You will have weekly regular assignments(due each Thursday), and one or two writing assignments, of term paper nature. 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. The writing assignments are to provoke you to think more of the ``big" pictures of our subject, its connections with your real experience and other subjects, and to help you organize your mathematical thinking in a coherent way and communicate with others effectively. See the Assignment Grading Guidelines below for what constitutes good/poor writing assignments. 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.

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.

Assignment Grading Guidelines

The grading of both regular and writing assignments will be based on correctness and depth of understanding of concepts and content, soundness of logical structure in your arguments, and exposition. You should present your work just as you would do for a writing assignment in any other subject, giving the necessary background information, definition of terms you are about to explain, logical arguments, and your conclusions. More specifically, if you are presenting the solution to a problem, explain first what the problem is; if you are going to use some terms o r concepts, try to give as clear a definition as possible(because mathematical concepts in a typical student's mind are often vague and may change from context to context, but in scientific discussions preciseness of concepts is needed); if you are giving an argument, try to explain the point before you launch into it. This may seem hard in the beginning. But you can improve quickly if you keep a journal to record what you have been thinking and doing in your work, and then try to organize the ideas in a coherent way as if you wanted to explain your ideas to a friend or to convince him/her of your arguments. It is important that you learn to explore geometry on your own, instead of limiting youself to answering the questions raised by the instructor. It is good practise to raise further questions of your own at the end of each assignment(as simple as questions like `what if we are in a different situation like...'). Writing assignments will be given two gradings. The first version will be graded and returned with comments for rewriting. The initial grading will take up 25% of the weight, and the second grading will take up 75% of the weight. Since writing assignments need rewriting and second grading, I request that all your writing assignments be typed using a word processing software. You may do the drawings or mathematical symbols by hand. No late work will be accepted.

Course Grading Policy

Your course grade will be determined on the following basis:

Regular assignments: 20%
Midterm/Writing assignments: 30%
Final Exam: 35%
Quizzes and in-class participation: 15% (Short quizzes may be given randomly; To encourage students' participation in discussions, each round of volunteer response to questions, formulating own questions, presentation, demonstration, and report will get one point credit; extra work in making models or bringing geometry related information may also be awarded credit from this category.

Here are links to dated material, as our course progresses.

Some notes and homework for week 1.

Here is the homework for week 2, due in class on Thursday, September 19.

Here is the homework for week 3, due in class on Thursday, September 26.

Here is the homework for week 4, due in class on Thursday, October 3. Here is the solution.

Here is the homework for week 5, due in class on Monday, October 14. Here is the solution.

The midterm exam is scheduled on:

Thursday, October 17

Here is the list of problems used on midterm1.

Here are some notes on the parallel postulates and the homework assignment, due Thursday, October 31.

Here are some notes on several foundational issues in Euclidean Geometry and an additional homework problem, also due Thursday, October 31.

Here is the writing assignment, with first draft due on Monday, November 18.

Here are some reading guides to the text "Geometry" by Brannan et al, and dated assignments.

Here are some suggestions for reviews and some supplementary problems.

The final exam is scheduled on Tuesday, December 17, 12-3pm, RAB204

For comments regarding this page, please send email to zchan@gauss.rutgers.edu.