Elliptic Tales
DOWNLOAD
Download Elliptic Tales PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Elliptic Tales book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Elliptic Tales
DOWNLOAD
Author : Avner Ash
language : en
Publisher: Princeton University Press
Release Date : 2014-10-19
Elliptic Tales written by Avner Ash and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-19 with Mathematics categories.
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profoundmay appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.
Arithmetic Tales
DOWNLOAD
Author : Olivier Bordellès
language : en
Publisher: Springer Nature
Release Date : 2020-11-26
Arithmetic Tales written by Olivier Bordellès and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Circuits And Systems For Security And Privacy
DOWNLOAD
Author : Farhana Sheikh
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Circuits And Systems For Security And Privacy written by Farhana Sheikh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Computers categories.
Circuits and Systems for Security and Privacy begins by introducing the basic theoretical concepts and arithmetic used in algorithms for security and cryptography, and by reviewing the fundamental building blocks of cryptographic systems. It then analyzes the advantages and disadvantages of real-world implementations that not only optimize power, area, and throughput but also resist side-channel attacks. Merging the perspectives of experts from industry and academia, the book provides valuable insight and necessary background for the design of security-aware circuits and systems as well as efficient accelerators used in security applications.
Elliptic Curves Modular Forms And Their L Functions
DOWNLOAD
Author : Alvaro Lozano-Robledo
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Elliptic Curves Modular Forms And Their L Functions written by Alvaro Lozano-Robledo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.
A Century Of Advancing Mathematics
DOWNLOAD
Author : Paul Zorn
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-08-23
A Century Of Advancing Mathematics written by Paul Zorn and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-23 with Mathematics categories.
The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.
Fearless Symmetry
DOWNLOAD
Author : Avner Ash
language : en
Publisher: Princeton University Press
Release Date : 2008-08-24
Fearless Symmetry written by Avner Ash and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-24 with Mathematics categories.
Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.
Abbreviated Lives Tragic Tales Of Artists Scientists And Writers
DOWNLOAD
Author : Debananda Singh Ningthoujam
language : en
Publisher: Blue Rose Publishers
Release Date : 2022-06-03
Abbreviated Lives Tragic Tales Of Artists Scientists And Writers written by Debananda Singh Ningthoujam and has been published by Blue Rose Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-03 with Art categories.
Abbreviated Lives profiles the life stories of artists, scientists & writers whose creative odysseys have been cut short by circumstances: penury, lack of recognition, mental breakdown, dictatorship and war etc. It also portrays the Matilda effect: how some women’s contributions have been ‘stolen’ by male colleagues, supervisors or husbands. However tragic the conditions in which they might have worked, all the characters in this book took passionate creative journeys till the final exit. From them, we may reaffirm that the journey matters more than the destination; one can rise to great heights in life given grit, commitment and hard work. These tragic stories also teach us that the efflorescence of artistic and scientific creativity needs democracy and freedom of thought; it may be cruelly stifled, if not completely destroyed, by unscrupulous dictators and authoritarian rulers. These tales not only can inspire the readers to carry forward their own journeys; moreover, they may ignite us to promote institutional, cultural and social factors that would help nurture the full blossoming of creative lives so that the society may fully ‘harvest’ their artistic, literary and scientific contributions. Sincere creative journeys, the lonely expeditions of pioneers would never go in vain; someday, kindred spirits would retrace the paths blazed by the forerunners.
Summing It Up
DOWNLOAD
Author : Avner Ash
language : en
Publisher: Princeton University Press
Release Date : 2018-01-30
Summing It Up written by Avner Ash and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
Computational Number Theory And Modern Cryptography
DOWNLOAD
Author : Song Y. Yan
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-29
Computational Number Theory And Modern Cryptography written by Song Y. Yan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-29 with Computers categories.
The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.
Elliptic Curves
DOWNLOAD
Author : Henry McKean
language : en
Publisher: Cambridge University Press
Release Date : 1999-08-13
Elliptic Curves written by Henry McKean and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-13 with Mathematics categories.
An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.