Math 5510 – Introduction to Topology and Geometry

Room: LCB 225

Time: MWF 10:45-11:35

Office: JWB 210

Office Hours: M 9:30-10:30 or by appointment.

Textbooks: Allen Hatcher's notes. This is a good text for general topology. 
The standard book for general topology is Munkres: Topology (amazon), but it is very expensive and we won't go 
into the subject in the same detail, as we will also study geometric aspects of topology. So you are not required to purchase it.

Prof. Toledo's notes for this class. The beginning has more information about metric spaces than we talked about in class.

A proof that compactness and sequential compactness are equivalent in metric spaces.

Bent Petersen's notes  on the contraction principle.

Michael Mueger's notes for a general topology course.

John Stillwell: Geometry of Surfaces (amazon). We'll cover chapters 1 and 2. Chapter 1 is about the classification of Euclidean isometries, and an alternative reference is:

Classification of Euclidean isometries: notes

You can contact me by email.

• Metric spaces, isometries, Lipschitz mappings.

• Surfaces as metric spaces.

• Groups of isometries of the plane and of the sphere.

• Topological spaces and continuous mappings.

• Construction of topological spaces. Identification topology.

• Compact spaces. Connected spaces.

• Surfaces as identification spaces.

Homework: It will be assigned and collected in class roughly every 2 weeks.

Exams: There will be two midterms, on Sep 30 and Nov 11. The comprehensive final exam is on Friday, Dec. 20, 2013, 10:30 am - 12:30 pm

Grading: Homework (drop lowest 2): 35%, Midterms: 40%, Final 25%.

ADA: The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, cognitive, systemic, learning, and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations you may require.