Embeddings of Curves into Euclidean Spaces

Publication Year:
2012
Usage 205
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Repository URL:
https://scholarlyrepository.miami.edu/oa_dissertations/760; https://scholarlyrepository.miami.edu/cgi/viewcontent.cgi?article=1741&context=oa_dissertations
Author(s):
Zohar, Dahlia M
Tags:
embeddings of curves; algebraic automorphism; equivalence of maps; embeddings of curves; algebraic automorphism; equivalence of maps
artifact description
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.