640:435:01 Geometry
Class
meets: MTh2, RAB204.
Instructor:
Dr. ZhengChao Han
Office Hour:
M11:1512:15, Chem. Bldg102;
T3:004:00pm, Hill230.
Email:
zchan@math.rutgers.edu (generally not for answering math questions.
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 0521597870)
Additional supplementary material will be provided/recommended as the course progresses. The classic
The Thirteen Books Of The Elements, by Euclid (translated with
introduction and commentary by Sir Thomas L. Heath)
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 0486600882); 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 nonEuclidean 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(inclass and outclass), 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 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.
Here are
 Solutions to Homework 1.

Solutions to Homework 2.
 Notes on Key Concepts and Properties
of Projective Geometry.
 Solutions to Homework 3.
 Here are some practice
problems for our midterm, to be given in class on Oct. 28.
 Here are solutions to our
midterm.
 The writing assignment First draft due Dec. 2.
 here is the revised
writing assignment.
 here are some notes on
nonEuclidean geometry, which may be helpful to your writing projects. You won't need all
the technical discussions in the notes. For those interested in the subject, the notes
can serve as an entry into the subject. Due to the time contraint, I was not able to supply any
diagrams to help your reading. You should supply them when reading the technical discussions. We hope
to cover some of these by the end of the semester.
 Here are solutions to
the Homework of Chapter 7.
 Here are solutions to
the first homework on Euclidean proof.
 Here are solutions to
the second homework on Euclidean proof.
 Here are some notes
on orthogonally intersecting circles and the interpretation of hyperbolic geometry.
 Here are review
guides for the final exam ( and solutions to select problems),
which is to be held on Dec. 23, from 811am, in RAB204.
Structure of Assignments
Homework and Quizzes:
You will have weekly
regular assignments(due each Thursday), and one or two writing assignments,
of term paper