Math 439.500
Differential Geometry of Curves and Surfaces
Fall 2014
Math 439.500
Differential Geometry of Curves and Surfaces
Course Description
Math 439 is a comprehensive introduction to the geometry of curves and surfaces in the plane and Euclidean
three-dimensional space. In recent years geometrically inspired methods have gained wide acceptance in
many areas of mathematics and applications. Math 439 provides necessary background for understanding
these methods.
Topics covered: Parametrized curves including regular curves, arc length, local theory, local canonical form,
and global properties of plane curves; regular surfaces including change of parameters, tangent planes, functions and their differentials, first fundamental form, and area; the Gauss map including definition, fundamental properties, and coordinate representation; intrinsic geometry of surfaces including isometries, Gauss
theorema egregium and equations of compatibility, parallel transport and geodesics, and Gauss-Bonnet theorem; selected applications in surface theory according to taste of class.
Catalog Description.
From the catalog: Local and global theory of parameterized curves; regular surfaces, local coordinates,
first fundamental form, orientation, area; Gauss map, second fundamental form; Gauss Bonnet theorem;
additional topics to be selected by the instructor.
Prerequisites.
Prerequisites: MATH 221/251/243 or equivalent; MATH 308 or equivalent; MATH 304 or MATH 323 or
equivalent; and basic knowledge of matrices.
Instructor and Class Information
Jon Pitts
Office: BLOC 607
E-mail: j-pitts at tamu.edu
Homepage: http://www.math.tamu.edu/ jon.pitts/
Class meets in Zach 227A at MWF 1:50–2:40 p.m.
Office hours are MW 11:30 a.m.-12:20 p.m. and by appointment.
Text
Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo, Pearson; first edition (February
11, 1976) ISBN-10: 0132125897, ISBN-13: 978-0132125895.
Course Information
c 2014 by Jon Pitts
Copyright Page 1 of 2
Math 439.500
Differential Geometry of Curves and Surfaces
Fall 2014
Basis for Grading
Your grade will be determined by assigned homework (30%), two midterm examinations (20% each), and
the final examination (30%). A total score of 85% or more guarantees an A, 75% or more a B, 65% or more
a C, and 55% or more a D.
Attendance and Make-up Policy
Attendance is mandatory. Makeups are subject to university policy. In accordance with university regulations, make-ups for missed exams and assignments will be allowed only for a university approved excuse in
writing. Whenever possible, students should inform the instructor before any work is missed.
Americans with Disabilities Act (ADA) Policy Statement
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that
all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact
the Department of Student Life, Disability Services Office, in Room B118 of Cain Hall or call 845-1637.
Academic Integrity Statement
An Aggie does not lie, cheat, or steal or tolerate those who do. The Honor Council Rules and Procedures
are available on the web at http://aggiehonor.tamu.edu.
Course Information
c 2014 by Jon Pitts
Copyright Page 2 of 2