Publication Date

2012-04-25

Availability

Open access

Embargo Period

2012-04-25

Degree Type

Doctoral Treatise

Degree Name

Doctor of Arts (DA)

Department

Mathematics (Arts and Sciences)

Date of Defense

2012-03-19

First Committee Member

Shulim Kaliman

Second Committee Member

Michelle Wachs Galloway

Third Committee Member

Alexander Dvorsky

Fourth Committee Member

Edward K. Baker

Abstract

In this treatise we present an introduction to the concepts of curves and embeddings in Euclidean spaces. We discuss what it means for embeddings to be equivalent, and present the most recent findings in the field. The survey is meant to be appropriate for first year graduate mathematics students to grasp, given the appropriate prerequisite knowledge of calculus and abstract algebra. Exercises for student practice are given throughout, and solutions to selected exercises are offered as an appendix. Glossaries of terms and notation, including entries considered part of the prerequisite knowledge and therefore not defined in the text itself, are also available as appendices.

Keywords

embeddings of curves; algebraic automorphism; equivalence of maps

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