INTRO TO DIFFERENTIAL GEOMETRY SYLLABUS

MATH 4391/6391 (PHYS 4391/6391)

SPRING 2006

 

 

CRN 16509/16511, MW 3:00 pm – 4:15 pm, Sparks Hall 430

 

Instructor:          Alexandra Smirnova

Office:              702-College of Education

Phone:               (404) 651-0641

E-mail:              smirn@mathstat.gsu.edu

Web page:            http://www.mathstat.gsu.edu/~matabs/

Office hours:        MW 4:30 pm – 5:15 pm, TR 11:00 am – 11:45 am

 

Description: Theory of curves and surfaces in parametric and implicit form. Curvature and torsion of a curve. Differential forms of a surface. Topological properties of surfaces. The Shape operator, Normal curvature and Gaussian curvature. Special curves in a surface. Surfaces of revolution. The Fundamental equations. Isometries and local isometries. The Gauss - Bonnet Theorem. Applications to physics.

 

Textbook: Elementary Differential Geometry, 2th edition by Barrett O’Neill, Elsevier (USA) 1997.

 

Prerequisite: Grade of C or higher in MATH 2215.

 

Administrative Drop Policy: During the first two weeks of the semester the Department of Mathematics and Statistics checks the computer records to determine whether or not each student has met the prerequisites for the course. If you do not have the prerequisites, please inform your instructor and change to another course right away. If our computer search finds that you do not have the prerequisite, you must drop this course or you will be dropped automatically. If you do not attend the class during the first two weeks you will be administratively dropped.

 

Withdrawal: Friday, March 3, is the last day to withdraw and receive a possible grade of W except for hardship withdrawal. A grade of W will only be assigned to a withdrawing student, if the student is passing at the time of withdrawal.

 

Procedures: Class meets twice a week. Taking good notes during the class is of paramount importance. Homework will be assigned in each class. After the class read the book, read your notes and do as many of the homework problems as you can prior to the next class. Try to get the remaining problems explained in the beginning of the next class or during the next office hours. You are responsible for all material covered in class, whether or not you attended this class.

 

Grading: There will be a total of 530 points possible for this course. The points are distributed as follows

 

Five quizzes

50 = 10*5

Three exams

270 = 90*3

Final exam

180

Extra Credit

30

 

Having 320 points or more BEFORE the final exam, will result in a grade of A in this course, and being excused from the final. Otherwise you must take the final exam and your total accumulated points will determine your final letter grade

  

A                 450-530

B                 400-449

C                 350-399

D                 300-349

F                   0-299

 

Quizzes: There will be 5 quizzes during the semester. The purpose of these quizzes is to keep you up-to-date in the course. Usually you will have a quiz in the end of a class. Make-up quizzes will not be given, except when special conditions exist.

 

Examinations: There will be 3 hourly exams and the final exam (two hours). All hourly exams will be taken during the regular class time and in the regular classroom. Books and notes will not be allowed on all tests. There will be no make-up exams except in an extreme verifiable emergency. Absence from the final exam will result in a grade of F for the course unless arrangements are made PRIOR to its administration. The tests and the final for graduate students (Math 6258/Phys 6510) will contain additional problems.

 

Exam dates: February 15, March 22 and April 19. Final Exam: Wednesday, May 3, 2:45 pm – 4:45 pm.

 

Academic Dishonesty: Plagiarism and cheating are serious offenses and may be punished by failure on the exam. Repeated cheating will result in a grade of F for the course.

 

Studying: You must work on this course every week. The pace is hectic and allowing yourself to fall behind will end in disaster.

 

This course syllabus provides a general plan for the course; deviations may be necessary.

 

                                  GOOD LUCK!