Theses, Dissertations, and Articles of my Students

Tinka Davis

Forty-two Problems of First Degree From Diophantus' Arithmetica
Master's Thesis, December 2010

This work brings to the audience Diophantus' problems of first degree in a literal word for word English translation from Ver Eecke's French translation of Arithmetica. In addition, these problems are accompanied by commentary in modern notation, as well as some modern and general solutions to appropriate problems. [PDF]

Kamielle Freeman

A Historical Overview of Connections in Geometry
Master's Thesis, May 2011

This thesis is an attempt to untangle/clarify the modern theory of connections in Geometry. Towards this end a historical approach was taken and original as well as secondary sources were used. An overview of the most important historical developments is given as well as a modern look at how the various definitions of connection are related.

I hope to clear up some of the confusions surrounding a connection in Differential Geometry; or, at least some of the things that confused me when I was trying to figure out just what exactly a connection is. In particular, 1) How is a covariant derivative operator related to a connection? 2)How is parallel transport related to the previous two notions? 3) What was the first definition of a connection? 4) What is a connection in the most general sense? I hope that I answer all of these questions satisfactorily in the following pages. I have also provided a chart of the heirarchy of connections via the use of Lie subgroups. [PDF]

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