Thesis Title

Transcendental Numbers

Author

Fan Zhou

Date of Graduation

Summer 2005

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Kishor Shah

Keywords

transcendental number, algebraic number, Galois group, Lindemann's Theorem, Liouville number, Liouville Theorem

Subject Categories

Mathematics

Abstract

In our thesis, we study the proof of the Lindemann-Weierstrass Theorem from Jacobson’s Algebra book. In particular, the transcendence of e and is deduced. We also study the proof of Lindemann’s Theorem from a research paper by Eugene Schenkman. We also study Liouville’s Theorem and Liouville’s construction of a transcendental number and a class of transcendental numbers from Joseph Lipman’s Transcendental Numbers monograph. We have filled in various details in these proofs. We have also provided examples to make the proofs easier to understand.

Copyright

© Fan Zhou

Citation-only

Dissertation/Thesis

Share

COinS