{"product_id":"an-invitation-to-modern-number-theory-hardcover","title":"An Invitation to Modern Number Theory - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eSteven J. Miller\u003c\/b\u003e (Author), \u003cb\u003eRamin Takloo-Bighash\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn a manner accessible to beginning undergraduates, \u003ci\u003eAn Invitation to Modern Number Theory\u003c\/i\u003e introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. \u003cp\u003e\u003c\/p\u003e Providing exercises, references to the background literature, and Web links to previous student research projects, \u003ci\u003eAn Invitation to Modern Number Theory\u003c\/i\u003e can be used to teach a research seminar or a lecture class.\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"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.\"\u003cb\u003e--William Duke, University of California, Los Angeles\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\"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.\"\u003cb\u003e--Eduardo Dueñez, University of Texas, San Antonio\u003c\/b\u003e\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eSteven J. Miller\u003c\/b\u003e is an Assistant Professor of Mathematics at Brown University. \u003cb\u003eRamin Takloo-Bighash\u003c\/b\u003e is an Assistant Professor of Mathematics at Princeton University.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 528\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.56 x 9.44 x 6.34 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 26, 2006\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704552550707,"sku":"9780691120607","price":195.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/VkdGenZ4YWZwWDlzYXMrcDZxWVBoUT09.webp?v=1763359089","url":"https:\/\/www.vysn.com\/products\/an-invitation-to-modern-number-theory-hardcover","provider":"VYSN","version":"1.0","type":"link"}