MAT 362 Differential Geometry, Spring 2011

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.

Grading

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)

Textbooks

We will use two texts as references for this class:

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.

Here are a few other books about classical differential geometry, which I will be using:

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

Many other resources are available, both in the library and online.

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 http://studentaffairs.stonybrook.edu/dss/. 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: http://www.sunysb.edu/facilities/ehs/fire/disabilities.

Academic Integrity

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 http://www.stonybrook.edu/uaa/academicjudiciary/

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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