Math 412 Differential Geometry

Spring 2003  UAF

Instructor: Ed Bueler
Office: Chapman 301C. 
Office hours are online and on the back of many assignments.
Phone: 474-7693, eMail: ffelb@uaf.edu 		Class Time:  TTh 3:40 -- 5:10 pm   Chapman 107
Text: do Carmo, Differential Geometry of Curves and Surfaces
Web Site: www.math.uaf.edu/~bueler/

The Course and Grade:  
Differential geometry of curves and surfaces leading toward an abstract view of spaces.  The first fourth of the course will be the geometry of curves, which was introduced in calculus III--we will do a more complete job.  The next half of the course will be the geometry of surfaces.  We will see the contributions of Gauss and Riemann and lay the foundations for the geometry of curved manifolds of any dimension.  The last fourth of the course will be a survey of, and introduction to, manifolds, Riemannian geometry, Maxwell's equations and gravitation.

You will need to do both calculations and proofs.  You need to review multivariable calculus (that is, Math 202 and especially that part related to parameterized curves, curvature of curves, arclength and surface area).   With those tools you will get a quite complete understanding of the geometry of curves and surfaces, and an introduction to the general theory of Riemannian geometry.

An hourlong in-class midterm exam will be given as well as a two-hour final.  Weekly homework makes up the remainder of the grade:
Part
Midterm Exam
Final Exam
Homework		 Grade-Fraction
25%
35%
40%		 Dates

3:15--5:15 pm Thurs. May 8 (Final Exam time)
nearly weekly

The following represents a guarantee of grade---I reserve (and will surely exercise) the right to increase your grade above this schedule:

 Percent
90 - 100 % 
79 - 89 % 
68 - 78 % 
57 - 67 % 
0 - 56 % 		 Grade
A
B
C
D
F

Topics:
Policies:   The department has reasonable policies on incompletes, late withdrawals, early final examinations, etc.  See www.dms.uaf.edu/dms/Policies.html .  Note that you are covered by the UAF Student Code of Conduct (p. 22 of the catalog and at www.uaf.edu/catalog/current/undergrad/regs3.html#Student_Code_of_Conduct ).

Prerequisites: