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Full-Text Articles in Number Theory
The Kronecker-Weber Theorem: An Exposition, Amber Verser
The Kronecker-Weber Theorem: An Exposition, Amber Verser
Lawrence University Honors Projects
This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …
Comparing The Algebraic And Analytical Properties Of P-Adic Numbers With Real Numbers, Joseph Colton Wilson
Comparing The Algebraic And Analytical Properties Of P-Adic Numbers With Real Numbers, Joseph Colton Wilson
Theses Digitization Project
This study will provide a glimpse into the world of p-adic numbers, which encompasses a different way to measure the distance between rational numbers. Simple calculations and surprising results are examined to help familiarize the reader to the new space.
The Fibonacci Sequence And Hosoya's Triangle, Jeffrey Lee Smith
The Fibonacci Sequence And Hosoya's Triangle, Jeffrey Lee Smith
Theses Digitization Project
The purpose of this thesis is to study the Fibonacci sequence in a context many are unfamiliar with. A triangular array of numbers, similar looking to Pascal's triangle, was constructed a few decades ago and is called Hosoya's triangle. Each element within the triangle is created using Fibonacci numbers.