Torsion and Rank: Navigating the World of Elliptic Curves

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ac.comp.abstractThis thesis introduces elliptic curves to readers new to the topic, covering foundational concepts, key historical developments, and carefully including proofs of often-omitted results. Emphasis is placed on the group structure, elliptic curves over the rational and complex numbers, and the computation of ranks and torsion points, alongside connections to current research.
ac.comp.awardMathematics, 2025
ac.comp.firstreaderWerner, Caryn
ac.comp.languageEnglish
ac.comp.permissionformPublicen_US
ac.comp.secondreadersCarswell, Brent
dc.contributor.authorBorsh, Ethan
dc.contributor.departmentMathematics
dc.date.accessioned2024-12-17T14:22:40Z
dc.date.available2024-12-17T14:22:40Z
dc.date.issued2024-12-11
dc.description.majorMathematics
dc.identifier.urihttps://hdl.handle.net/10456/58274
dc.subjectAlgebraic Geometry
dc.subjectGeometry
dc.subjectNumber Theory
dc.subjectElliptic Curve
dc.subjectRank
dc.subjectDiophantine Equations
dc.subjectProjective Geometry
dc.titleTorsion and Rank: Navigating the World of Elliptic Curves
dc.typeSenior Project Paper
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