Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity

<p>This project investigates the development of four different proofs of the law of quadratic reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem published in 1991 by Rousseau. Through this investigation we aim to analyze the different strategies used in the development of each of these proofs, and in the process gain a better understanding of this theorem.</p>

Name thesis:degree_name

Master of Arts in Mathematics

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2016

Author dc:creator

• Mittal, Nitish

Contributors dc:contributor

• Vicknair, James Paul

• Gauss
• Congruence
• Legendre
• Quadratic
• Reciprocity
• Rousseau
• Number Theory
• Set Theory

Repository record dc:identifier

https://scholarworks.lib.csusb.edu/etd/282

OAI identifier oai:identifier

oai:scholarworks.lib.csusb.edu:etd-1324