Torsion and Rank: Navigating the World of Elliptic Curves
Project Author
Issue Date
2024-12-11
Authors
Borsh, Ethan
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First Reader
Werner, Caryn
Additional Readers
Carswell, Brent
Keywords
Algebraic Geometry , Geometry , Number Theory , Elliptic Curve , Rank , Diophantine Equations , Projective Geometry
Distribution
Abstract
This 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.
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Chair
Major
Mathematics
Department
Mathematics
Recorder
License
Citation
Version
Honors
Mathematics, 2025