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Elliptic Curves
Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Introduction to Cyclotomic Fields
This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
An Introduction to Number Theory with Cryptography
Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, proje...
Elementary Number Theory
Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments. The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.
Introduction to Cryptography
This text is for a course in cryptography for advanced undergraduate and graduate students. Material is accessible to mathematically mature students having little background in number theory and computer programming. Core material is treated in the first eight chapters on areas such as classical cryptosystems, basic number theory, the RSA algorithm, and digital signatures. The remaining nine chapters cover optional topics including secret sharing schemes, games, and information theory. Appendices contain computer examples in Mathematica, Maple, and MATLAB. The text can be taught without computers.
Poorly Understood
What if the idealized image of American society—a land of opportunity that will reward hard work with economic success—is completely wrong? Few topics have as many myths, stereotypes, and misperceptions surrounding them as that of poverty in America. The poor have been badly misunderstood since the beginnings of the country, with the rhetoric only ratcheting up in recent times. Our current era of fake news, alternative facts, and media partisanship has led to a breeding ground for all types of myths and misinformation to gain traction and legitimacy. Poorly Understood is the first book to systematically address and confront many of the most widespread myths pertaining to poverty. Mark Ro...
Thirteen Days in September
A dramatic, illuminating day-by-day account of the 1978 Camp David conference, when President Jimmy Carter convinced Israeli Prime Minister Menachem Begin and Egyptian President Anwar Sadat to sign a peace treaty--the first treaty in the modern Middle East, and one which endures to this day. With his hallmark insight into the forces at play in the Middle East and his acclaimed journalistic skill, Lawrence Wright takes us through each of the thirteen days of the Camp David conference, delving deeply into the issues and enmities between the two nations, explaining the relevant background to the conflict and to all the major participants at the conference, from the three heads of state to their...
The Plague Year
'A virtuoso feat ... a book of panoramic breadth' New York Times Book Review 'A devastating analysis ... Wright is a master of knitting together complex narratives' The Observer Just as Lawrence Wright's The Looming Tower became the defining account of our century's first devastating event, 9/11, so The Plague Year will become the defining account of the second. The story starts with the initial moments of Covid's appearance in Wuhan and ends with Joseph Biden's inauguration in an America ravaged by well over 400,000 deaths - a mortality already some ten times worse than US combat deaths in the entire Vietnam War. This is an anguished, furious memorial to a year in which all of America's gre...
Modular Forms and Fermat’s Last Theorem
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Reciprocity (Routledge Revivals)
The tendency to reciprocate – to return good for good and evil for evil – is a potent force in human life, and the concept of reciprocity is closely connected to fundamental notions of ‘justice’, ‘obligation’ or ‘duty’, ‘gratitude’ and ‘equality’. In Reciprocity, first published in 1986, Lawrence Becker presents a sustained argument about reciprocity, beginning with the strategy for developing a moral theory of the virtues. He considers the concept of reciprocity in detail, contending that it is a basic virtue that provides the basis for parental authority, obligations to future generations, and obedience to law. Throughout the first two parts of the book, Becker intersperses short pieces of his own narrative fiction to enrich reflection on the philosophical arguments. The final part is devoted to extensive bibliographical essays, ranging over anthropology, psychology, political theory and law, as well as the relevant ethics and political philosophy.
