### MAT 362  Differential Geometry of Surfaces   Spring 2013  TuTh 1pm - 2:20pm Physics P117

Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: Wed 4 - 6 pm in Math 3-115, Wed 1:30 - 2:30 pm in the MLC
Grader: Ye Sle Cha (ycha at math dot sunysb dot edu)
Grader's office hours: Tue 5-6pm in Math Tower 4-118, Tue 6-7 pm in the MLC, Wed 10-11 am in the MLC

The Instructor may be reached by e-mail at kamenova@math.sunysb.edu.

Course Description: The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of surfaces in Euclidean space. For this, you'll need a solid background in multivariable calculus and linear algebra. We hope to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.

Prerequisites: MAT 205 (Calculus III) and MAT 210 (Linear Algebra).

Text: M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall (1976)

Other books:
• A. Pressley, Elementary Differential Geometry, Springer, 2001.
• B. O'Neill, Elementary Differential Geometry.
• Millman and Parker, Elements of Differential Geometry.

Grading: There will be two midterm exams (on 3/14 and 4/18 in class) and a final exam (on 05/20, 5:30 - 8 pm). There will be regular homework assignments, due roughly once per week. Your grade will be determined via the following percentages: homework: 30%, midterms: 20% each, and final: 30%.

Homework:

HW 1 (due on Feb 7): [Do Carmo] Section 2.2. Problems 1, 4, 10, and 16

HW 2 (due on Feb 14): [Do Carmo] Section 2.3. Problems 2, 3, 4 and 5

HW 3 (due on Feb 21): [Do Carmo] Section 2.4. Problems 1, 2, 3 and 7

HW 4 (due on Feb 28): [Do Carmo] Section 2.5. Problems 3, 4, 5, 9 and 10

HW 5 (due on March 7): [Do Carmo] Section 2.6. Problems 1, 2 and 4

HW 6 (due on March 28): [Do Carmo] Section 3.2. Problems 2, 3, 8 and 17

HW 7 (due on April 4): [Do Carmo] Section 3.3. Problems 1, 2 and 13

HW 8 (due on April 11): [Do Carmo] Section 3.4. Problems 1, 2 and 3

HW 9 (due on April 25): [Do Carmo] Section 3.5. Problems 1, 5 and 12

HW 10 (due on May 2): [Do Carmo] Section 4.2. Problem 14, Section 4.3. Problem 3, Section 4.4. Problem 4.

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