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 in class.
 

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.