Syllabus for Math 334634 Differential Geometry by sparkunder16


									           Syllabus for Math 334/634:
             Differential Geometry
1    Contact Information
 Professor: Stephen Robinson
 Office: 127 Manchester
 Phone: 758-4887

2    Office Hours
I hope that you will make a habit of visiting me during office hours, which
are listed below. No appointment is needed. Just stop by. This time with
students is one of the most pleasant parts of my job. I certainly hope that
you find it helpful, and I know that I find it helpful. If you need help at
another time, then it is usually best to call or send email before stopping by.
 M,W,F 10-12, or by appointment

3    Text
Differential Geometry of Curves and Surfaces, by Manfredo P. Do Carmo

4    Course Content and Goals
We will follow the author’s suggestion for a short course, which are
 Chapter 1: 2,3,4,5
 Chapter 2: 2,3,4,5
 Chapter 3: 2,3
 Chapter 4: 2,3,4,5

with occasional excursions that go deeper into, or beyond, the text. We will
be finishing the course by studying the Gauss-Bonnet Theorem, a truly deep
and beautiful theorem.

5     Homework
Homework is very important. During most class meetings I will point out
which problems you should be working on. Every Monday I will collect two

    1. One solution from the previous weeks’ material. This should represent
       your best possible effort. I will announce which problem to prepare
       during class on the previous Friday.

    2. A list of three specific questions about current or past material.

My primary goal in doing this is to promote communication. I need to know
how well you are understanding the material, and I need to know what your
questions are. You need to know what I am looking for when I am grading.
Homework grading is based primarily on effort, and is on a one point scale.
I will either accept it and give you a point, or I will ask you to rewrite it.
I will also provide a good indication of how the problem would have been
graded on an exam. Your total homework score will be worth 10% of your

6     Exams
There will be two equally weighted exams. One exam is based upon chapters
1 and 2, and one exam is based upon chapters 3 and 4. Each exam comes in
two parts:

 Part A: Contains standard problems and must be done in a two hour period
     with no help from the text, notes, or other aids.

 Part B: Contains problems that require more time and thought and must be
     completed in a three day period. You are allowed to use the textbook
     and your class notes. This part is very likely to contain a problem, or
     two, taken from the text.

   For undergraduates, each exam is worth 45% of your grade. For gradu-
ates, each exam is worth 40% of your grade.

7    Projects
There are a number of ways to complete a short independent project. Most
often they are based upon a section of the book that we did not cover, but
they may also be based upon a journal article, or perhaps on creating a
Maple Worksheet. All project topics must be approved by me ahead of time.
I prefer projects that emphasize proof and mathematical insight. Surveys of
cool material with lots of pictures are fun, but will not receive credit unless
they contain some proof. To receive credit for a project you must make an
oral presentation for me during office hours. I will either accept your project
for credit, or ask you to do some more work.
    Undergraduates are not required, but are encouraged, to do these projects.
A successful project will allow you avoid one 5-point problem on the next
    Graduate students must complete at least one project before each exam.
The projects are worth 10% of your grade. Graduate students may complete
additional projects to receive credit on the next exam in the same way that
undergraduates can.

8    Grading Policy
If you consistently demonstrate an ability to perform standard computations
and solve standard problems, then you have a good chance of earning a C or
better. If you can also solve some more difficult problems and provide some
insight as to why the methods work, then you have a good chance of earning
a B or better. If you become adept at solving standard and nonstandard
problems, and if you can clearly justify all of the methods that you use, then
you have a good chance of earning an A. Hard work is a prerequisite for
earning a good grade (A, B, or C), but no amount of work will guarantee
you a particular grade. Just do the best that you can, and then be proud
of the grade that you have earned. If you are ever unsure about a grading
policy, or if you are not sure where you stand, then you are welcome to ask.
    Here is the grading scale that I will use at the end of the semester. I

reserve the right to make adjustments to this scale, but I will not adjust the
boundaries to anything higher than those listed below. Pluses and minuses
are assigned to grades that are within three points of a cutoff.

 A: Total ≥ 90%

 B: 80% ≤ Total < 90%

 C: 65% ≤ Total < 80%

 D: 50% ≤ Total < 65%.


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