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

Book Description | Table of Contents
Preface [in PDF format] | Chapter 1 [in PDF format] | Chapter 3 [PDF only] | Chapter 12 [PDF only] | Chapter 15 [PDF only]


"The book provides a much-needed introduction to modern number theory that emphasizes analytic number theory. It should serve remarkably well as an advanced undergraduate textbook and its latter parts would be suitable for a beginning graduate course. Some of the material covered, such as the circle method and random matrix theory, is not readily available elsewhere in book form. These topics provide terrific examples of areas in number theory of great current interest that can be penetrated by students. I would seriously consider using this book in my own classes and recommend it with enthusiasm for highly motivated students."--William Duke, University of California, Los Angeles

"Having this selection of material available in essentially self-contained form is fantastic. Reading the book (or taking a class based on it) might easily decide the future endeavors of many a neophyte mathematician. I have yet to discover a clearer exposition of the works of the circle method. The inclusion of exercises and, especially, of problems for further research and theoretical or numerical exploration is extremely valuable. I would dare to compare the book to Hardy and Wright's classic An Introduction to the Theory of Numbers in that Miller and Takloo-Bighash expose readers to the lively work of number theory, to its proofs, ideas, and methods, assuming only a very modest background."--Eduardo Dueñez, University of Texas, San Antonio

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File created: 4/17/2014

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