Courses: Geometry (MATHB315001)

Fall 2011

Class Number: 3061
An introduction to geometry with an emphasis that varies from year to year. Prerequisites: MATH 201 and 203 (or equivalent) or permission of instructor.
Div: II
Differential geometry is a deep area of mathematics which focuses on
using the tools of integral and differential calculus to study
geometric and topological properties of objects and spaces. By
restricting ourselves to "low-dimensional" objects -- curves
andsurfaces in 3-space -- we can easily adapt techniques familiar from
multivariable calculus to explore the rich structure underlying them,
while taking a glimpse into the goals and approaches of the field as a
whole.This course will have two underlying themes: to extend the
notions of calculus so it can be done on curves and surfaces (instead
of just on lines and planes), and to use this new calculus to
understand the inherent shapes of these objects. Fundamental to both
is also the development of an understanding of when exactly two such
objectsare the "same". The course will begin with a brief review of
the necessary calculus, and the introduction of a powerful tool - the
differential form -- which will reappear throughout the semester as we
examine various topics. We will discuss how to use the Frenet frame of
a curve to study its curvature and torsion, and how to use the
shapeoperator of a surface to study different notions of its
curvature. We will look at how all of these ideas contribute to a
deeper understanding of the geometry of 3-space, and examine
applications to areas of physics (e.g., trajectories and Maxwell's
equations from electrodynamics) and mathematics (e.g., cohomology and
contact structures).Prerequisite: Math B201 or permission of instructor.

Fulfills: Class Nbr: 3061 Div: II

Department

Mathematics (Web site)

Taught By

Schneider,Gregory R.

Location

Bryn Mawr, PK336

Meeting Times

MW 2:30pm-4:00pm