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dc.contributor.advisorHerden, Daniel
dc.contributor.authorKing, Brian
dc.date.accessioned2018-05-21T15:44:20Z
dc.date.available2018-05-21T15:44:20Z
dc.date.copyright2018
dc.date.issued2018-05-21
dc.identifier.urihttp://hdl.handle.net/2104/10231
dc.description.abstractDiophantine approximation is a topic of number theory concerned with rational approximations of real, typically irrational, numbers. In other words, we seek q∈Z for a given α∈R such that ||qα|| (the distance from qα to the nearest integer) is small. This thesis serves as a primer on many of the famous results in this field. First, the fundamental result of Diophantine approximation, Dirichlet's theorem, is presented along with several methods of proof. Other theorems involving limits of accuracy are given before moving into inhomogeneous approximations (of the form ||qα- β|| for some β∈R). Finally, recent results in the inhomogeneous case are used to prove a theorem on irrational circle rotations with connections to ergodic theory.en_US
dc.language.isoen_USen_US
dc.rightsBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.en_US
dc.titleInhomogeneous Diophantine Approximationen_US
dc.typeThesisen_US
dc.rights.accessrightsWorldwide accessen_US
dc.contributor.departmentStatistics.en_US
dc.contributor.schoolshonors collegeen_US


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