MAT 531 
Geometry/Topology II 
Spring 2024 

TuTh 11:30-12:50 pm
Math Tower P-131 

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

Grader:  Daniel Brogan
Math Tower 2-106
Office hours:
W 2:30pm - 3:30pm,
or by appointment.


This course provides 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 the course is strictly limited to mathematics graduate students, except by explicit permission of the graduate program director.


Textbook:

John M. Lee,
Introduction to
Smooth Manifolds,
Second edition,
Springer, 2012.

☞ Click here for the Homework Page ☜

☞ Click here for Lecture Slides from 2020 ☜


Remark. The first edition of the text may still be available as a used book, but using this earlier version is not recommended, in light of the many significant differences between the two editions.

Important Dates

Midterm Exam Tuesday, Feb 27 11:30--12:50 pm
Final Exam Tuesday, May 14 11:15--1:45 pm

Your grade will be based upon your performance on the homework, the mid-term, and the final exam.

The midterm will determine 25% of your course grade, while the final exam will be worth 35%. Your homework will then determine the remaining 40% of your overall course 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.

STUDENT ACCESSIBILITY SUPPORT SERVICES (SASC) STATEMENT: If you have a physical, psychological, medical, or learning disability that might impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, at (631) 632-6748 or https://www.stonybrook.edu/sasc/. They will determine, with you, what accommodations are necessary and appropriate. All information and documentation will be treated as confidential.

ACADEMIC INTEGRITY STATEMENT: Students must pursue their academic goals honestly, and everyone must be personally accountable for all submitted work. Representing another person's work as your own is always wrong. The Academic Judiciary requires faculty members to report any suspected instances of academic dishonesty. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at https://www.stonybrook.edu/commcms/academic_integrity/.

CRITICAL INCIDENT MANAGEMENT: Stony Brook University expects students to respect the rights, privileges, and property of other people. The Office of Judicial Affairs requires faculty members to report to any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.