Math 42: Differential Geometry

M, W, F 12:30-1:35pm

X-hour Tuesday 1-1:50pm

Location: 104 Gerry

Professor: Craig J. Sutton

Office: 313 Bradley Hall

 

Syllabus/Homework Extras

• Course Description: Utilizing our knowledge of multivariable calculus, differential equatioins and linear algebra we will explore the geometry of n-dimensional surfaces. In particular, we will consider vector fields, orientation, covariant differentiation, parallel transport, geodesics, curvature, parameterized surfaces, volume, surfaces with boundary, the Gauss-Bonnet theorem and minimal surfaces. As time permits we will also discuss the exponential map, isometries and Riemannian metrics.
• Text: Elementary Topics in Differential Geometry, J.A. Thorpe
• Target Audience: This course should serve as a nice introduction to beautiful topics in geometry for pure math majors or for students in other disciplines which use techniques and ideas from geometry.
• Prerequisites: This course is the confluence of ideas from linear algebra, multivariable calculus and differential equations. Consequently, it is imperative that you be at peace with these topics. In addition, as this course will require you to understand and construct proofs a fair degree of "mathematical maturity" and committment is also required.
• e-mail: craig.j.sutton@dartmouth.edu