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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Mittal, Nitish"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Vicknair, James Paul"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-06-01T07:00:00Z","date_published":"2016-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:53Z","subjects":["Gauss","Congruence","Legendre","Quadratic","Reciprocity","Rousseau","Number Theory","Set Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/282","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Vicknair, James Paul"]},{"key":"dc:creator","label":"Author","values":["Mittal, Nitish"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-09T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Gauss","Congruence","Legendre","Quadratic","Reciprocity","Rousseau","Number Theory","Set Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/282"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity"]}]}],"canonical_facts":{"dc:contributor":["Vicknair, James Paul"],"dc:creator":["Mittal, Nitish"],"dc:date.available":["2016-05-09T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/282"],"dc:subject":["Gauss","Congruence","Legendre","Quadratic","Reciprocity","Rousseau","Number Theory","Set Theory"],"dc:title":["Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:53Z"}