The purpose of this paper is to present a discussion on the basic fundamentals of the theory of sets. Primarily, the discussion will be confined to the study of cardinal and ordinal numbers. The concepts of sets, classes of sets, and families of sets will be undefined quantities, and the concept of the class of all sets will be avoided.

Honors thesis (B.A.)-Ithaca College Dept. of Mathematics, 2008. / Title from abstract page. "April 15, 2008." includes abstract Includes bibliographical references (leaf 33). Also available in print form in the Ithaca College Archives.

Master of Science / Department of Mathematics / Todd Cochrane / Polygonal numbers are nonnegative integers constructed and represented by geometrical arrangements of equally spaced points that form regular polygons. These numbers were originally studied by Pythagoras, with their long history dating from 570 B.C, and are often referred to by the Greek mathematicians. During the ancient period, polygonal numbers were described by units which were expressed by dots or pebbles arranged to form geometrical polygons. In his "Introductio Arithmetica", Nicomachus of Gerasa (c. 100 A.D), thoroughly discussed polygonal numbers. Other Greek authors who did remarkable work on the numbers include Theon of Smyrna (c. 130 A.D), and Diophantus of Alexandria (c. 250 A.D). Polygonal numbers are widely applied and related to various mathematical concepts. The primary purpose of this report is to define and discuss polygonal numbers in application and relation to some of these concepts. For instance, among other topics, the report describes what triangle numbers are and provides many interesting properties and identities that they satisfy. Sums of squares, including Lagrange's Four Squares Theorem, and Legendre's Three Squares Theorem are included in the paper as well. Finally, the report introduces and proves its main theorems, Gauss' Eureka Theorem and Cauchy's Polygonal Number Theorem.

Thesis (doctoral)--Ruprecht-Karls-Universität zu Heidelberg, 1917. / Cover title. Vita. Includes bibliographical references (p. [63]-68).

Inaug.-diss.--Zürich.

This report explores the historical development of three areas of study regarding prime numbers. The attempt to find an efficient and useful function to generate primes could be a helpful tool in the improvement of encryption. The difficulty of factoring large numbers allows the Rivest, Shamir and Adleman algorithm to be effective for public key cryptography. The distribution of primes is examined through discussion of the prime number theorem and the Riemann hypothesis. A brief case for integrating elementary number theory in secondary curriculum is also included. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

In this dissertation we show that the Giulietti-Ughi arc is not complete for large primes. This arc is complete for primes which are congruent to three modulo four and less than thirty one. The cardinality of this arc has the same order as the Lunelli-Sce bound. We use two powerful theorems, one on the classifications of Galois groups of quintic polynomials and the other, the Čebotarev density theorem for function fields to show that there exist points on a certain curve which are not covered by the arc. We then outline a technique which could be used to extend the arc to a complete arc.

No description available.

[Please see thesis for abstract.] / vi, 114 leaves ; 29 cm