{"id":{"repo_id":"mo-state","oai_identifier":"oai:bearworks.missouristate.edu:theses-1867"},"canonical_url":"https://search.dev.ndltd.org/etd/mo-state/oai:bearworks.missouristate.edu:theses-1867","repository":{"repo_id":"mo-state","name":"Missouri State University","base_url":"https://bearworks.missouristate.edu/do/oai/"},"display":{"title":"A Survey of Galois Theory","abstract":"In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem which shows the connections between solvability of polynomials and groups and work a few examples demonstrating how to use groups to solve polynomials. In Chapter 3, we briefly consider the Inverse Problem of Galois theory where we consider arbitrary groups and try to find extensions for which they are the Galois group.","abstract_html":"In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem which shows the connections between solvability of polynomials and groups and work a few examples demonstrating how to use groups to solve polynomials. In Chapter 3, we briefly consider the Inverse Problem of Galois theory where we consider arbitrary groups and try to find extensions for which they are the Galois group.","abstract_has_math":false,"creators":["Daniel, Christina L."],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Les Reid"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995-07-01T07:00:00Z","date_published":"1995-07-01T07:00:00Z","updated_at":"2026-07-24T03:15:54Z","subjects":["Mathematics"],"languages":[],"rights":["© Christina L Daniel"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bearworks.missouristate.edu/theses/866","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Les Reid"]},{"key":"dc:creator","label":"Author","values":["Daniel, Christina L."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© Christina L Daniel"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://bearworks.missouristate.edu/theses/866"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem which shows the connections between solvability of polynomials and groups and work a few examples demonstrating how to use groups to solve polynomials. In Chapter 3, we briefly consider the Inverse Problem of Galois theory where we consider arbitrary groups and try to find extensions for which they are the Galois group."]},{"key":"dc:title","label":"Title","values":["A Survey of Galois Theory"]}]}],"canonical_facts":{"dc:contributor":["Les Reid"],"dc:creator":["Daniel, Christina L."],"dc:description.abstract":["In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem which shows the connections between solvability of polynomials and groups and work a few examples demonstrating how to use groups to solve polynomials. In Chapter 3, we briefly consider the Inverse Problem of Galois theory where we consider arbitrary groups and try to find extensions for which they are the Galois group."],"dc:identifier":["https://bearworks.missouristate.edu/theses/866"],"dc:rights":["© Christina L Daniel"],"dc:subject":["Mathematics"],"dc:title":["A Survey of Galois Theory"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T03:15:54Z"}