Mathematics 425/525, Section 101

Introduction to Modern Differential Geometry

Department of Mathematics,  University of British Columbia

Instructor

Joel Feldman

Text

• Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, 1983.

I will post all handouts, problem sets, etc. on the web here.

Topics

1. Manifolds (§1):
       Definition, examples
       Tangent and cotangent vectors
       Submanifolds
       Frobenius theorem
2. Tensors (§2):
       Tensor and exterior algebras
       Tensor fields and differential forms
3. Integration on Manifolds (§4):
       Orientation of manifolds
       Integrals of forms
4. Another topic, like "Lie Groups" or "Geodesics and Curvature"

Grading

• There will be weekly problem sets accounting for about 50% of the final mark.
• The final exam will account for about 50% of the final mark.
• Grades will probably be scaled.

Policies

• The final examination will be strictly closed book: no formula sheets or calculators will be allowed.
• There is no supplemental examination in this course.
• Late homework assignments normally receive a grade of 0. Missing a homework normally results in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency.