Elliptic Tales

Elliptic Tales Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Elliptic Tales book. This book definitely worth reading, it is an incredibly well-written.

Elliptic Tales

Avner Ash,Robert Gross
Elliptic Tales Book PDF

Author : Avner Ash,Robert Gross
Publisher : Princeton University Press
Page : 275 pages
File Size : 51,6 Mb
Release : 2014-10-19
Category : Mathematics
ISBN : 9780691163505

Get Book

Elliptic Tales by Avner Ash,Robert Gross Pdf

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.

Elliptic Tales

Avner Ash,Robert Gross
Elliptic Tales Book PDF

Author : Avner Ash,Robert Gross
Publisher : Princeton University Press
Page : 277 pages
File Size : 51,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151199

Get Book

Elliptic Tales by Avner Ash,Robert Gross Pdf

Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.

Fearless Symmetry

Avner Ash,Robert Gross
Fearless Symmetry Book PDF

Author : Avner Ash,Robert Gross
Publisher : Princeton University Press
Page : 308 pages
File Size : 41,6 Mb
Release : 2008-08-24
Category : Mathematics
ISBN : 9780691138718

Get Book

Fearless Symmetry by Avner Ash,Robert Gross Pdf

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.

Elliptic Curves, Modular Forms, and Their L-functions

Alvaro Lozano-Robledo
Elliptic Curves Modular Forms and Their L functions Book PDF

Author : Alvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 47,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852422

Get Book

Elliptic Curves, Modular Forms, and Their L-functions by Alvaro Lozano-Robledo Pdf

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.

Arithmetic Tales

Olivier Bordellès
Arithmetic Tales Book PDF

Author : Olivier Bordellès
Publisher : Springer Nature
Page : 782 pages
File Size : 47,9 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9783030549466

Get Book

Arithmetic Tales by Olivier Bordellès Pdf

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

Farhana Sheikh,Leonel Sousa
Circuits and Systems for Security and Privacy Book PDF

Author : Farhana Sheikh,Leonel Sousa
Publisher : CRC Press
Page : 382 pages
File Size : 54,9 Mb
Release : 2017-12-19
Category : Computers
ISBN : 9781315355733

Get Book

Circuits and Systems for Security and Privacy by Farhana Sheikh,Leonel Sousa Pdf

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.

A Century of Advancing Mathematics

Paul Zorn
A Century of Advancing Mathematics Book PDF

Author : Paul Zorn
Publisher : The Mathematical Association of America
Page : 436 pages
File Size : 42,7 Mb
Release : 2015-08-23
Category : Mathematics
ISBN : 9780883855881

Get Book

A Century of Advancing Mathematics by Paul Zorn Pdf

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.

Abbreviated Lives Tragic Tales of Artists Scientists and Writers

Debananda Singh Ningthoujam
Abbreviated Lives Tragic Tales of Artists Scientists and Writers Book PDF

Author : Debananda Singh Ningthoujam
Publisher : Blue Rose Publishers
Page : 232 pages
File Size : 48,8 Mb
Release : 2022-06-03
Category : Art
ISBN : 8210379456XXX

Get Book

Abbreviated Lives Tragic Tales of Artists Scientists and Writers by Debananda Singh Ningthoujam Pdf

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

Avner Ash,Robert Gross
Summing It Up Book PDF

Author : Avner Ash,Robert Gross
Publisher : Princeton University Press
Page : 248 pages
File Size : 52,8 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9780691178516

Get Book

Summing It Up by Avner Ash,Robert Gross Pdf

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.

Elliptic Curves

Henry McKean,Victor Moll
Elliptic Curves Book PDF

Author : Henry McKean,Victor Moll
Publisher : Cambridge University Press
Page : 300 pages
File Size : 41,7 Mb
Release : 1999-08-13
Category : Mathematics
ISBN : 0521658179

Get Book

Elliptic Curves by Henry McKean,Victor Moll Pdf

An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.

Computational Number Theory and Modern Cryptography

Song Y. Yan
Computational Number Theory and Modern Cryptography Book PDF

Author : Song Y. Yan
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 54,8 Mb
Release : 2013-01-29
Category : Computers
ISBN : 9781118188583

Get Book

Computational Number Theory and Modern Cryptography by Song Y. Yan Pdf

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.

Introduction to Elliptic Curves and Modular Forms

Neal I. Koblitz
Introduction to Elliptic Curves and Modular Forms Book PDF

Author : Neal I. Koblitz
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209096

Get Book

Introduction to Elliptic Curves and Modular Forms by Neal I. Koblitz Pdf

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.

Rational Points on Elliptic Curves

Joseph H. Silverman,John Tate
Rational Points on Elliptic Curves Book PDF

Author : Joseph H. Silverman,John Tate
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742527

Get Book

Rational Points on Elliptic Curves by Joseph H. Silverman,John Tate Pdf

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

Curves for the Mathematically Curious

Julian Havil
Curves for the Mathematically Curious Book PDF

Author : Julian Havil
Publisher : Princeton University Press
Page : 280 pages
File Size : 40,9 Mb
Release : 2021-11-02
Category : Art
ISBN : 9780691206134

Get Book

Curves for the Mathematically Curious by Julian Havil Pdf

Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Ancient Mathematics

Dietmar Herrmann
Ancient Mathematics Book PDF

Author : Dietmar Herrmann
Publisher : Springer Nature
Page : 462 pages
File Size : 53,7 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783662664940

Get Book

Ancient Mathematics by Dietmar Herrmann Pdf

The volume contains a comprehensive and problem-oriented presentation of ancient Greek mathematics from Thales to Proklos Diadochos. Exemplarily, a cross-section of Greek mathematics is offered, whereby also such works of scientists are appreciated in detail, of which no German translation is available. Numerous illustrations and the inclusion of the cultural, political and literary environment provide a great spectrum of the history of mathematical science and a real treasure trove for those seeking biographical and contemporary background knowledge or suggestions for lessons or lectures. The presentation is up-to-date and realizes tendencies of recent historiography. In the new edition, the central chapters on Plato, Aristotle and Alexandria have been updated. The explanations of Greek calculus, mathematical geography and mathematics of the early Middle Ages have been expanded and show new points of view. A completely new addition is a unique illustrated account of Roman mathematics. Also newly included are several color illustrations that successfully illustrate the book's subject matter. With more than 280 images, this volume represents a richly illustrated history book on ancient mathematics.