Course Information for Math 7590:
Riemannian and Symplectic Geometry
|Time and place:
||M/W/F, 1:40--2:30p.m., 135 Lockett Hall
|Monday and Wednesday 12:00-1:30p.m., or by appointment.
224 Lockett Hall
Textbook: Do Carmo, Riemannian Geometry (Birkhauser,
ISBN: 0-8176-3490-8) and Introduction to Symplectic Geometry
by Dusa McDuff and Dietmar Salamon (Oxford University Press,
ISBN: 0-1985-0451-9 ) will be useful.
Prerequisites: Math 7510.
Assessment: Students will present at least one topic
in front of the class during the semester. Assessment will be
based on the preparation and delivery of this presentation, and
on observed effort in learning the material of this course.
Topics covered by the course: This course is an
introduction to Riemannian geometry: manifolds, metrics, Levi-Civita
connections, and curvature. Riemannian geometry is key to
understanding Einstein′s general relativity and plays an
important role in gauge theory and invariants of smooth
4-manifolds. We will use this technology to introduce and
investigate symplectic geometry, another important topic in
mathematics that also comes from physics.
Homework: The purpose of the exercises is to give you a
chance to practice and refine the theory learned in class. As
homework is assigned, try them, and feel free to stop by office
hours to ask questions. All homework problems will be announced
Written work: We write to communicate. Please bear
this in mind as you complete homework assignments and take
exams. Work must be neat and legible to receive consideration.
You must explain your work in order to obtain full credit; an
assertion is not an answer. For specific suggestions see
A guide to writing in mathematics classes.
Disabilities: Students with disabilities who will be
taking this course and may need disability-related classroom
accommodations are encouraged to make an appointment to see the
instructor as soon as possible.