Master's Theses

e

Department

Math

Degree Name

Master of Science (MS)

Abstract

The meteoric splendor of the transcendental constant e is an intriguing mystery. It rises unexpectedly from nowhere, brilliantly illuminates some obscure mathematical concept, points to its solution, and abruptly fades into oblivion. Its unheralded visitation leaves the student wiser but wondering, tantalized by its omnipotence in apparently unrelated fields. Ever since his first introduction to e in elementary logarithms it has seemed to the writer that all the authors of textbooks are in a conspiracy to defeat any real knowledge of e. They say "2.71828… , called e, is the base of Naperian logarithms." Why? "The derivative of eX is eX." Why? "Placing y - eX, the solution is evident." Why? To answer these interminable "why's" is the object of this thesis; to conquer this phantom in a field of logic. The laconic title, e, is perhaps too all-inclusive. It tends to connote an absolute knowledge of everything pertaining to e. The writer does not pretend to that knowledge. Rather he has attempted to gather from all available sources a little of everything concerning this constant. In this attempt he hopes to justify the title e.

Keywords

Euler's number, Mathematical constant, Napier's constant, Jacob Bernoulli, Euler's identity, Irrational numbers, Transcendental numbers

Advisor

Dr. Edward E. Colyer

Date of Award

Spring 1935

Document Type

Thesis

Rights

© The Author(s)

Comments

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