An Invitation to Modern Number Theory : Steven J. Miller and Ramin Takloo-Bighash

by Steven J. Miller, Ramin Takloo-Bighash

In a manner accessible to beginning undergraduates, An Invitationto Modern Number Theory introduces many of the central problems,conjectures, results, and techniques of the field, such as theRiemann Hypothesis, Roth's Theorem, the Circle Method, and RandomMatrix Theory. Showing how experiments are used to test conjecturesand prove theorems, the book allows students to do original work onsuch problems, often using little more than calculus (though thereare numerous remarks for those with deeper backgrounds). It showsstudents what number theory theorems are used for and what led tothem and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce theproblems and the computational skills required to numericallyinvestigate them, providing background material (from probabilityto statistics to Fourier analysis) whenever necessary. They guidestudents through a variety of problems, ranging from basic numbertheory, cryptography, and Goldbach's Problem, to the algebraicstructures of numbers and continued fractions, showing connectionsbetween these subjects and encouraging students to study themfurther. In addition, this is the first undergraduate book toexplore Random Matrix Theory, which has recently become a powerfultool for predicting answers in number theory. Providing exercises, references to the backgroundliterature, and Web links to previous student research projects, AnInvitation to Modern Number Theory can be used to teach a researchseminar or a lecture class.

Genres: Mathematics

161 pages, Kindle Edition

First published March 6, 2006

Reviews

[Thomas Ray]

QA241 M5344 2006 AMP Library