640:435:02 Geometry
Class
meets: TF1(8:40am  10:00am), ARC207.
Instructor:
Dr. ZhengChao Han
Office Hour:
Wednesday 9:30am11:30am in 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. Gray;
Geometry (2nd edition); Cambridge University Press, 2011 (602 pp.);
(ISBN10: 1107647835, ISBN13: 9781107647831)
Additional supplementary material will be provided/recommended as the course progresses.
Later in the semester, we will do some reading and discussion of Books IIII 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 0486600882); 1956.
There is also an
online version of Euclid's Elements .
Another useful source is
Geometry by Its History by
Alexander Ostermann and Gerhard Wanner. A free electronic version can be obtained for free via the Rutgers
Springer Mathematics Ebooks packageRutgers affiliated users
can also order each print copy for $24.95 (Shipping and handling are included). The specific Springer link
for the book is here.
This book will not be used
systematically in this course, but it provides a lot of interesting geometric arguments which complement
the more algebraic approach of the David A. Brannan, Matthew F. Esplen & Jeremy J. Gray text, and one
can browse through and work on specific topics without too much difficulty.
Sakai
The course will use Sakai for all material during the semester.
All enrolled students should have automatic access to the site after logging in to Sakai.
Current information about syllabus and homework will be found there.
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.
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 appropriate coordinates, matrix manipulations), so it is essential that
students review the material in Math 250 (Linear Algebra) most of the material will be needed
starting in the second week! You can find a list of review problems
from our sakai course site.
On the other hand, 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(inclass and outclass), 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 complete
English sentences. More guidelines are given below.
Course Material
This course uses a fair amount of linear algebra, especially in chapters 1, 2, 3 and 7. The attached file
here
contains a list of review problems for the relevant material. Problems 1, 2, 3, 6, and 7 will be needed
starting in the first two weeks. Please review these topics on your own in the first week.
You can focus your review to 2x2 or 3x3 matrices.
Structure of Assignments
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 writingup. 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.
Here is a link to the
homework assignment
site.
Assignment Grading Guidelines
The grading of the regular
assignments will be based on correctness 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 or
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 precision of concepts is
needed); if you are giving an argument, try to explain the main points before you
launch into the details. 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 yourself 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...').
Attendance and Makeup 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 makeups for quizzes.
A makeup 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: 20% each (first one is tentatively scheduled on Friday, Oct. 9, and second one is tentatively
scheduled on Tuesday, Nov. 17).

Final Exam: 40% (Wednesday, December 16, 8am  11am). See
here for the full final exam schedule.
For comments regarding this page,
please send email to zchan at math dot rutgers dot edu.