Project Director

Kuhn, Stephen; Davies, Joshua

Department Examiner

Darken, Betsy; Van der Merle, Lucas

Department

Dept. of Mathematics

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

The major focus of this departmental thesis was to complete t he first English translation of E271 Arithmetic Theorems Proven by a New Method, a mathematical treatise published by Leonhard Euler in Latin in 1761. Most importantly, E271 contains Euler's generalization of Fermat's Litt le Theorem and an exploration of the properties of (n). Altogether, this paper includes an Abstract, Introduction, Note to the Readers, Translation of Arithmetic Theorems Proven by a New Method, Epilogue, and References. More specifically, the Introduction is about the historical background of the mathematics and applications leading up to E271 and the key corresponding mathematicians. Then t he Note to the Readers discusses the t ranslation process. Further, the Epilogue consists of the historical background of the mathematics and applications which arose after E271 was published and the key corresponding mathematicians. As the author of E271, Leonhard Euler is the mathematician most relevant to this project. However, before Euler, the mathematician Pierre Fermat also played a significant role in the development of number theory. Thus, the Introduction contains details surrounding the life and mathematics of both Fermat and Euler. Following Euler, Gauss was another major figure in the history of number thenrv, especially its notation. There are various applications, one of which is the FlSA algorithm, which utilize Euler's work as well. As a result , details on Gauss and the RSA algorithm, completing a fascinating path from the 18th Century to the 21st Century, are included in the Epilogue.

Degree

B. A.; An honors thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Bachelor of Arts.

Date

5-2011

Subject

Mathematics -- History -- 18th century

Name

Euler, Leonhard, 1707-1783

Keyword

Mathematics

Discipline

Intellectual History | Mathematics

Document Type

Theses

Extent

49 leaves

Language

English

Rights

Under copyright.

License

http://creativecommons.org/licenses/by-nc-nd/3.0/

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