P. Laborde Montaner's Thesis--New York University, 1951. / Includes bibliographical references (p. 43).

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 100-104).

Thesis (Ph.D.)--University of California, 1909. / Vita.

Thesis (Ph. D.)--University of North Texas, May, 2007. / Title from title page display. Includes bibliographical references.

This paper is devoted to the development of transcendental numbers and to proofs that e and Pi are transcendental. Chapter I presents a brief account of the historical development of transcendental numbers. Chapter II is composed of the existence proof of transcendental numbers which is based on a proof due to G. Canto, and also a method of construction for transcendental numbers. Chapter III is devoted to the proof of the transcendency of e and chapter IV, to the proof of the transcendency of Pi. / Typescript. / "August, 1955." / "A Paper." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Dwight B. Goodner, Professor Directing Paper. / Includes bibliographical references.

"One inexperienced in higher mathematics may very well question the necessity of irrational numbers since all numbers used in computation are rational. For example, one computes the area of a circle by using the formula A = [pi]r² and substituting 22/7 or some other approximate value for [pi]. Furthermore, the rational numbers are dense on the straight line, and so physical means can be used to determine whether a given length or ratio is rational. However, in theoretical mathematics there is a need for a real number system to give all limiting values. Calculus, as we know it, could not exist without the irrational numbers. The purpose of this paper is to make a careful study of the real number system, to develop some criteria for the irrationality of certain numbers, and to analyze the proofs of the irrationality of a few simple irrational numbers"--Preface. / "January 1959." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 36).

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Explains properties of mathematical sets, algebra of sets, and set order types.

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