Torsion and Rank: Navigating the World of Elliptic Curves

Borsh, Ethan

Torsion and Rank: Navigating the World of Elliptic Curves

Author(s)

Borsh, Ethan

Date Issued

December 11, 2024

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.

Major

Mathematics

Honors

Mathematics, 2025

First Reader(s)

Werner, Caryn