MATH 433 - Introduction to Differential Geometry
Winter 2014, Section 001
Instruction Mode: Section 001 is (see other Sections below)
Subject: Mathematics (MATH)
Department: LSA Mathematics
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Details

Credits:
3
Requirements & Distribution:
BS
Waitlist Capacity:
10
Advisory Prerequisites:
MATH 215 (or 255 or 285), and 217.
Other Course Info:
F.
BS:
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
Repeatability:
May not be repeated for credit.
Primary Instructor:

Description

This course is about the analysis of curves and surfaces in 2- and 3-space using the tools of calculus and linear algebra. There will be many examples discussed, including some which arise in engineering and physics applications. Emphasis will be placed on developing intuitions and learning to use calculations to verify and prove theorems. Students need a good background in multivariable calculus (215) and linear algebra (preferably 217). Some exposure to differential equations (216 or 316) is helpful but not absolutely necessary. Topics covered include (1) curves: curvature, torsion, rigid motions, existence and uniqueness theorems; (2) global properties of curves: rotation index, global index theorem, convex curves, 4-vertex theorem; and (3) local theory of surfaces: local parameters, metric coefficients, curves on surfaces, geodesic and normal curvature, second fundamental form, Christoffel symbols, Gaussian and mean curvature, minimal surfaces, and classification of minimal surfaces of revolution. 537 is a substantially more advanced course which requires a strong background in topology (590), linear algebra (513), and advanced multivariable calculus (551). It treats some of the same material from a more abstract and topological perspective and introduces more general notions of curvature and covariant derivative for spaces of any dimension. Math 635 and Math 636 (Topics in Differential Geometry) further study Riemannian manifolds and their topological and analytic properties. Physics courses in general relativity and gauge theory will use some of the material of this course.

Schedule

MATH 433 - Introduction to Differential Geometry
Schedule Listing
001 (LEC)
 In Person
27201
Open
7
 
-
MWF 11:00AM - 12:00PM

Textbooks/Other Materials

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Syllabi

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