Differential Geometry and Knot Theory

General Information
General description: The differential geometry part of this course involves the study of curves and surfaces in three-dimensional Euclidean space. Using vector calculus and moving frames of reference on curves embedded in surfaces we can define quantities such as Gaussian curvature that allow us to distinguish among surfaces. The knot theory part of the course is concerned with various ways to embed a circle in Euclidean space and how two knots can be distinguished from one another.
Course description: Tangent vectors, vector fields, differentiable maps, curves, Frenet frames, surfaces, shape operator, Gaussian and mean curvature, knots, knot groups, Alexander polynomials.
See the online documents relating to this course: Curves , Surfaces , Knots .
Author: Professor C.T.J. Dodson Homepage--You can email me for any further information at: ctdodson@manchester.ac.uk Other On-Line Mathematical Materials:

• Mathematical Formulae and Tables (PDF format).
• Revision Notes on Series (PDF format).
• Revision Notes on ODES (PDF format).
• Basic and C Programs for solving algebraic equations, ODEs and PDEs (HTML format).
• Revision Notes on Laplace Transforms (PDF format).
• Elementary Curves and Surfaces (PDF format).
• More Advanced Geometry: Curves , Surfaces , Knots .
• Pre-Calculus and Calculus Courseware using Mathematica and Maple for A-Level mathematics and first year university calculus.
• Solving Ordinary Differential Equations using Mathematica.
• Beginning Mathematica.
• Back to Dodson's homepage
• General Mathematica information: Mathematica website.