MAT 362 Differential Geometry, Spring 2011
Syllabus in pdf format
Introduction to the course
This course is an introduction to the theory of curves and surfaces
in Euclidean space, from the differentiable viewpoint. Our main goal
is to cover "the local and global geometry of surfaces: geodesics,
parallel transport, curvature, isometries, the Gauss map, the
Gauss-Bonnet theorem." We will first spend some time (about 3-4 weeks)
studying local and global properties of curves; these give insight into
analogous results about surfaces, as well as tools for analyzing
surfaces via the curves they contain.
The main prerequisites for this material are linear algebra, calculus
in several variables, and the topology of R^n (such as one can get in
an analysis course). These topics will be reviewed as needed, according
to the students' background.
This is one of the most advanced courses offered by the math department
at the undergraduate level. You are expected to spend about 10-15 hours
each week outside of class working on the material.
Grading will be based on homework, exams, and a final project.
- 30% Weekly homework (due each Tuesday, except following an exam)
- 15% First exam: Thursday, February 24
- 15% Second exam: Thursday, March 24
- 15% Third exam: Thursday, May 12 (last day of class)
- 15% Final project: papers due Tuesday, May 10, presentations on Thursday, May 19 (scheduled exam period)
- 10% Take-home final exam (distributed last day of class, collected at presentations on May 19)
We will use two texts as references for this class:
Here are a few other books about classical differential geometry, which I will be using:
- Differential Geometry of Curves and Surfaces, by Thomas Banchoff and Stephen Lovett, available in the bookstore.
Here is the site containing the authors' applets.
- Differential Geometry: A First Course in Curves and Surfaces, by Theodore Shifrin,
available for (free) download here.
Many other resources are available, both in the library and online.
- Differential Geometry of Curves and Surfaces, by Manfredo P. do Carmo
- Differential Geometry: Curves -- Surfaces -- Manifolds 2nd ed., by Wolfgang Kühnel
- Elementary Differential Geometry, by Andrew Pressley
- Lectures on Classical Differential Geometry 2nd ed., by Dirk J. Struik
Disability Support Services
If you have a physical, psychological, medical, or learning
disability that may impact your course work, please contact
Disability Support Services at (631) 632-6748 or
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and
Disability Support Services. For procedures and information go to
the following website:
Each student must pursue his or her academic goals honestly and
be personally accountable for all submitted work. Representing
another person's work as your own is always wrong. Faculty are
required to report any suspected instances of academic dishonesty
to the Academic Judiciary. For more comprehensive information on
academic integrity, including categories of academic dishonesty,
please refer to the academic judiciary website at
Critical Incident Management
Stony Brook University expects students to respect the rights,
privileges, and property of other people. Faculty are required to
report to the Office of Judicial Affairs any disruptive behavior
that interrupts their ability to teach, compromises the safety of
the learning environment, or inhibits students' ability to learn.
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