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.
|School:||California State University, Long Beach|
|School Location:||United States -- California|
|Source:||MAI 47/05M, Masters Abstracts International|
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