Dissertation/Thesis Abstract

On algebraic and transcendental numbers
by Silva, Nicole, M.S., California State University, Long Beach, 2009, 67; 1466152
Abstract (Summary)

The complex numbers which are roots of rational polynomials are known as algebraic numbers while their counterparts are known as transcendental. In the first part of the thesis, properties of algebraic numbers are explored including the perhaps surprising fact that a number is algebraic if and only if it is the eigenvalue of a matrix made up only of zeroes and ones. The main tool for this theorem will be a type of containment which involves the direct sum of block matrices.

The second part of the thesis looks into transcendental numbers including some of their general properties. The proof of the irrationality of π is given, and then Hermite's Theorem concerning the transcendality of e is explored.

Indexing (document details)
Advisor: Mena, Robert
School: California State University, Long Beach
School Location: United States -- California
Source: MAI 47/05M, Masters Abstracts International
Subjects: Mathematics
Publication Number: 1466152
ISBN: 978-1-109-16606-4
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