To faculty and graduate students,
 
There will be a new topics course offered this spring:
 
MTG 5932-01 Differential Topology.
 
This course will cover multi-variable calculus, differential forms,
vector bundles, and differentiable manifolds.   The course is open to
all graduate students who have taken the equivalent of Advanced Calculus,
or Topology I.
 
Topics include:  inverse and implicit function theorems;
change of variables;  vector fields and vector analysis;  constrained
extrema and Lagrange multipliers;  tangent bundles and more general
fiber bundles;  differentiable manifolds and differential forms.
 
If there is time I would also like to cover some basics of Riemannian
geometry.
 
Eventually, this course will become one of the three qualification
courses in Topology, in addition to Topology I offered concurrently
this spring, and Topology II offered next fall.  The topics covered
in this course will be included in the Topology qualifying exam
offered in August 2006.

Here is a list of sample texts:

Rudin's Principles of Mathematical Analysis (Ch. 9,10)
Marsden's Elementary Classical Analysis (Ch. 6,7)
Singer and Thorpe's Lecture Notes on Elementary Topology and Geometry (Ch. 5)
Boothby's An introduction to differentiable manifolds and Riemannian geometry
(Ch. II, parts of III and IV)

If you have questions, feel free to come by my office, or email me.

Eriko Hironaka