Graduation Year

Spring 2014

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts



Reader 1

Lenny Fukshansky

Reader 2

David Krumm

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.


  • Best Senior Thesis in Mathematics