MAT 531 
Geometry/Topology II 
Spring 2015 

TuTh 11:30-12:50
Physics P-125 

Prof. Claude LeBrun       
Math Tower 3-108
TuTh 2:00--3:30 pm,
or by appointment.

Grader:  Xuemiao Chen
Math Tower 3-104
M 5:00--6:00 pm,
or by appointment.

This course will offer an introduction to the elementary theory of smooth manifolds.
Topics will include: vector fields, differential forms, vector bundles, Lie derivatives, Stokes' theorem, and de Rham cohomology.

Enrollment in this class is strictly limited to mathematics graduate students, except by explicit permission of the instructor.


John M. Lee,
Introduction to
Smooth Manifolds,

Second edition,
Springer, 2012.

Click here for Homework Page

Remark. The first edition of the text is still available in paperback, and costs considerably less than the second edition. It is perfectly fine to use this older edition if you so choose. However, students who make this choice should carefully compare their book with a class-mate's copy of the newer edition before beginning each homework assignment.

Important Dates

Midterm Exam Thursday, Mar 12 11:30 am--12:50 pm
Final Exam Wednesday, May 13 5:30--8:00 pm

Solution Guide for Mid-Term Exam

Your grade will be based upon your performance on the homework, the mid-term, and the final exam. Each exam is worth 25% of your grade, while the homework will determine the remaining 50% of your grade.

Incompletes will be granted only if documented circumstances beyond your control prevent you from taking the final exam.

Homework assignments and other useful information regarding the course will be posted regularly on this web-site.

You may e-mail Prof. LeBrun by This is the best method for making appointments outside normal office hours.

Stony Brook University expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws as well as University regulations; and to respect the rights, privileges, and property of other people. Faculty must notify the Office of Judicial Affairs of any disruptive behavior that interferes with their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information regarding any disability will be treated as strictly confidential.

Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.