Top 12 Elliptic Curves Books
Welcome to our book roundup on Elliptic curves Books! In this article, we’ll introduce you to some of the most captivating and informative books available on the topic of elliptic curves. From theoretical foundations to practical applications, we’ll guide you through a diverse range of literature that will engage and enlighten both beginners and seasoned mathematicians alike.
Whether you’re looking to deepen your understanding of elliptic curves or simply want to broaden your horizons, our carefully curated selection of books is sure to satisfy your intellectual curiosity. So sit back, relax, and let us take you on a journey through the fascinating world of Elliptic curves Books.
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1. LMSST: 24 Lectures on Elliptic Curves
Enter the mesmerizing realm of elliptic curves through “LMSST: 24 Lectures on Elliptic Curves” by esteemed mathematician John William Scott Cassels. This innovative text serves as a concise yet comprehensive starting point for new graduate students, while providing a modern perspective that respects historical context.
“LMSST” is a captivating companion for learning the intricacies of elliptic curves, making it an ideal choice for anyone eager to explore this alluring domain of mathematics. It strikes a fine balance between accessible language and technical depth, ensuring both students and experts find value in its pages.
Spanning a total of 148 pages, “LMSST” delves into numerous aspects of elliptic curves with unparalleled scope. This standalone resource enables readers to seamlessly navigate the material without worrying about presupposed knowledge.
Experience the brilliance and excitement of elliptic curves by delving into “LMSST: 24 Lectures on Elliptic Curves,” a publication that boasts both the reputable Cambridge University Press and one of the foremost individuals in the field as its author. Don’t pass up this chance to expand your understanding and cultivate your appreciation for this continually evolving subject.
- Authors: John William Scott Cassels
- Publisher: Cambridge University Press
- Published Date: November 21, 1991
- Page Count: 148
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
2. Elliptic Curves
Unravel the mysteries of elliptic curves and modular forms with a gripping mathematical adventure. Authored by the esteemed mathematician Anthony W. Knapp, this elaborate tome delves into the heart of elliptic curves, their connections to modular forms, and the intricate relations they share in unravelling the foundational features of these mathematical concepts.
Setting the stage from the ground up, Knapp introduces the reader to the elementary basics of elliptic curves and modular forms through a wealth of detailed examples and clear, user-friendly explanations. As the book unfolds, the reader is steered through the profound Eichler-Shimura theory, shedding light on the complex and deep-rooted links between these two subjects. This extraordinary theory unveils the remarkable coincidence of the L-functions of elliptic curves and modular forms, bridging the divide between analysis and algebra in a profound and enlightening manner.
Elliptic Curves propels the reader into a vast expanse of mathematics, encompassing class field theory, arithmetic algebraic geometry, and group representations. By elucidating these intricate and interconnected fields, the reader gains a deeper grasp of the intriguing dance between seemingly disparate disciplines within the study of elliptic curves and modular forms.
This book stands out for its accessibility and emphasis on undergraduate mathematics. With no comparable works accessible, it serves as an indispensable resource for both students and professionals. Join renowned mathematician Anthony W. Knapp as he takes you on a captivating journey through the riveting world of elliptic curves and modular forms in Elliptic Curves.
- Authors: Anthony W. Knapp
- Publisher: Princeton University Press
- Published Date: March 30, 1992
- Page Count: 450
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
3. Elliptic Curves in Cryptography
Unravel the complexities of elliptic curve cryptography with “Elliptic Curves in Cryptography, “ a comprehensive guide by Ian F. Blake, G.
Seroussi, and N. Smart.
This mathematical masterpiece from Cambridge University Press explores the intricate world of elliptic curve systems through practical implementations. Delve into the captivating realm of cryptography as the authors expertly unveil the key concepts and applications of elliptic curves. This engaging book, boasting an impressive 228-page count, presents an average rating of 5.0 and has garnered 1.0 ratings count from satisfied readers alike.
Enter the fascinating world of elliptic curve cryptography with this indispensable resource.
- Authors: Ian F. Blake, G. Seroussi, N. Smart
- Publisher: Cambridge University Press
- Published Date: July 08, 1999
- Page Count: 228
- Print Type: BOOK
- Categories: Mathematics
- Average Rating: 5.0
- Ratings Count: 1.0
- Maturity Rating: NOT_MATURE
- Language: en
4. Elliptic Curves
Function Theory, Geometry, Arithmetic
This alluring book titled “Elliptic Curves: Function Theory, Geometry, Arithmetic” invites you to unravel the enchanting world of this intriguing mathematical branch. Embracing its captivating beauty, esteemed authors Henry McKean and Victor Moll take readers on an introductory journey, emulating the approach of the original pioneers. As they delve into the fundamental elements of elliptic curves, the authors ensure that readers are left with a comprehensive grasp of the subject.
As you venture into the mesmerizing realm of elliptic curves, you’ll appreciate the intricate inter play of function theory, geometry, and arithmetic. “Elliptic Curves” offers a concise reading experience with only 300 pages, making it accessible for both beginner mathematicians and seasoned experts.
This remarkable book has gathered exceptional accolades, boasting an impressive average of 5.0 stars. Commended for its lucidity and engaging prose, “Elliptic Curves” has left a lasting imprint on its readers. Let Cambridge University Press and “Elliptic Curves” be your trusty companions as they lead you through the bewitching landscape of elliptic curves.
- Authors: Henry McKean, Victor Moll
- Publisher: Cambridge University Press
- Published Date: August 13, 1999
- Page Count: 300
- Print Type: BOOK
- Categories: Mathematics
- Average Rating: 5.0
- Ratings Count: 1.0
- Maturity Rating: NOT_MATURE
- Language: en
5. Elliptic Curves
Number Theory and Cryptography, Second Edition
“Elliptic Curves: Number Theory and Cryptography, Second Edition, “ by Lawrence C. Washington, is a groundbreaking exploration of elliptic curves and their significance in number theory and cryptography. In this revised edition, readers will delve deeper into the theories and techniques behind elliptic curves, as well as their practical applications.
With expanded exercises and examples, the Second Edition offers a more comprehensive understanding of the fundamental principles and techniques surrounding elliptic curves. Washington’s expertise in the field ensures that readers will gain valuable insights into the intricacies of elliptic curve theory.
“Elliptic Curves” is a crucial resource for students, researchers, and professionals interested in advancing their knowledge in number theory and cryptography. The well-organized format, comprehensive content, and clear explanations make this text an invaluable addition to any scholar’s library.
Don’t miss this opportunity to explore the fascinating world of elliptic curves and their profound implications for mathematics and computer science. Embrace the challenge and unlock a wealth of knowledge with “Elliptic Curves: Number Theory and Cryptography, Second Edition. “
- Authors: Lawrence C. Washington
- Publisher: CRC Press
- Published Date: April 03, 2008
- Page Count: 533
- Print Type: BOOK
- Categories: Computers
- Maturity Rating: NOT_MATURE
- Language: en
6. The Arithmetic of Elliptic Curves
Delve into the intricacies of elliptic curves with Joseph H. Silverman’s comprehensive book, “The Arithmetic of Elliptic Curves. “ This scholarly work offers a well-rounded exploration of the arithmetic approach to elliptic curves, introducing readers to essential algebraic number theory and algebraic geometry.
Silverman begins by establishing the necessary algebro-geometric results before diving into the geometry and formal group of elliptic curves. The book then provides in-depth information on elliptic curves over finite fields, the complex numbers, local fields, and global fields. To wrap up the journey, the final chapters discuss integral and rational points, touching upon Siegel’s theorem and explicit computations for the curve Y = X + DX. Three insightful appendices conclude the book, covering elliptic curves in characteristics 2 and 3, group cohomology, and an overview of more advanced topics.
With its 513 pages and published by Springer Science & Business Media, “The Arithmetic of Elliptic Curves” is the go-to resource for those seeking a thorough understanding of the subject. With its rich and comprehensive content, this book will be an invaluable asset to mathematicians, researchers, and students alike.
- Authors: Joseph H. Silverman
- Publisher: Springer Science & Business Media
- Published Date: April 20, 2009
- Page Count: 513
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
7. Elliptic Curves, Modular Forms, and Their L-functions
Embark on a fascinating journey through the captivating world of number theory with “Elliptic Curves, Modular Forms, and Their L-functions”. In this highly engaging mathematical exploration, renowned mathematician Alvaro Lozano-Robledo masterfully guides readers through the intricacies of elliptic curves, modular forms, and L-functions. This ground-breaking work not only reveals the surprising connections among these three families of mathematical objects but also illuminates their profound impacts on the field of number theory.
Drawing from a diverse array of concepts, including algebra, algebraic geometry, complex analysis, and group representations, the author skillfully sheds light on intricate problems within number theory, ensuring that the beauty and depth of these mathematical solutions remain accessible. The book begins by addressing captivating, motivating problems and proceeds to delve into these topics in a logical, well-explained manner. Numerous concrete examples throughout the text serve to enhance understanding by incorporating actual numbers and providing tangible applications.
Although the theories of elliptic curves, modular forms, and L-functions are too extensive to be fully captured within a single volume, this meticulously crafted book successfully concentrates on motivating definitions, clarifying theorems and conjectures, and establishing meaningful connections. By focusing on these essential elements, students are given the opportunity to explore and grapple with the complexities of advanced mathematical concepts in a stimulating and engaging manner.
“Elliptic Curves, Modular Forms, and Their L-functions” is the perfect introduction for undergraduate students, who will be compelled to further explore and appreciate the richness of elliptic curves and modular forms. Unraveling the mysteries of these mathematical constructions and uncovering the unexpected connections within number theory, this captivating book is a must-read for anyone with an interest in mathematical exploration and discovery.
- Authors: Alvaro Lozano-Robledo
- Publisher: American Mathematical Soc.
- Published Date: April 14, 2011
- Page Count: 195
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
8. The Arithmetic of Elliptic Curves
Embark on a captivating journey through the world of elliptic curves in Joseph H. Silverman’s The Arithmetic of Elliptic Curves.
This engaging book masterfully introduces readers to the ancient and diverse field of elliptic curves using modern techniques, rooted in algebraic number theory and geometry. With an accessible approach, the author systematically explores the rich geometry of these fascinating mathematical constructs, from their fundamental forms to finite fields and their complex counterparts. As the narrative unfolds, readers are introduced to integral and rational points, culminating in a profound understanding of Siegels theorem and explicit computations for a crucial elliptic curve.
The book’s three illuminating appendices add depth to the subject matter, covering elliptic curves in characteristics 2 and 3, group cohomology, and advanced topics for further exploration. The Arithmetic of Elliptic Curves, published by Springer Science & Business Media, serves as a comprehensive and essential resource for those seeking to delve into the intricate workings of elliptic curves and related concepts.
- Authors: Joseph H. Silverman
- Publisher: Springer Science & Business Media
- Published Date: March 09, 2013
- Page Count: 414
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
9. Rational Points on Elliptic Curves
Dive into the fascinating world of mathematics with “Rational Points on Elliptic Curves” by Joseph H. Silverman and John Tate, published by Springer Science & Business Media. This book, first published in 2013, offers an intriguing exploration into the realm of elliptic curves, a subject that merges algebra, geometry, analysis, and number theory.
Readers will embark on a journey through the intricate web of modern mathematics, appreciating the harmony between different branches of the discipline. The book delves into the core theory of elliptic curves, guiding readers through a thrilling adventure in the realm of arithmetic geometry.
“Rational Points on Elliptic Curves” stands out with its highly accessible content, informal writing style, and a wealth of engaging exercises, making it an exceptional choice for those looking to gain insight into the world of Diophantine equations. As you delve into these pages, immerse yourself in the unity of mathematics, where seemingly disparate concepts converge, revealing the beautiful complexity of the subject matter. Don’t miss your chance to indulge in this riveting exploration of elliptic curves with “Rational Points on Elliptic Curves. “
- Authors: Joseph H. Silverman, John Tate
- Publisher: Springer Science & Business Media
- Published Date: April 17, 2013
- Page Count: 292
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
10. Elliptic Curves
Embark on a mathematical journey with “Elliptic Curves” by Dale Husemoller, an in-depth exploration of elliptic curves from introductory concepts to advanced research. This comprehensive book, published by Springer Science & Business Media, offers a balanced and engaging narrative that spans various levels of difficulty and background requirements.
Divided into multiple parts, the book caters to undergraduate, postgraduate, and advanced readers with different levels of prerequisite knowledge. The first six chapters cover undergraduate material, while subsequent chapters require a background in Galois theory, complex analysis, and graduate-level understanding.
The book is an adaptation of Tate’s 1961 Haverford Philips Lectures and is intended for publication. It focuses on proving the Mordell Theorem, a fundamental result in the field of elliptic curves. The author’s aim is to provide an accessible introduction to the theory of elliptic curves, making it suitable for a wide range of readers, from beginners to experts in the field.
“Elliptic Curves” consists of 363 pages and is a valuable addition to any mathematical library, offering a meticulously researched and well-structured understanding of this fascinating area of mathematics.
- Authors: Dale Husemoller
- Publisher: Springer Science & Business Media
- Published Date: June 29, 2013
- Page Count: 363
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT_MATURE
- Language: en
11. Modern Cryptography and Elliptic Curves: A Beginner’s Guide
“Modern Cryptography and Elliptic Curves: A Beginner’s Guide” is a comprehensive and well-structured textbook designed to introduce readers to the captivating world of modern arithmetic, elliptic curves, and their applications in cryptography. Penned by Thomas R. Shemanske and published by the prestigious American Mathematical Society, the book is an inviting guide for beginning undergraduate students seeking to explore this fascinating mathematical field.
The textbook is meticulously created to gradually immerse readers in the realm of elliptic curves over finite fields, offering a seamless understanding of cryptographic concepts that are the foundation of secure communication in today’s digital world. The book stands out by teaching students to produce proofs, highlighting the interplay of abstract algebra, number theory, and affine and projective geometry, and how algebra and geometry combine to characterize congruent numbers via rational points on the unit circle.
Furthermore, the structural underpinnings of the unit group of the integers modulo a prime are elucidated, providing invaluable insights into RSA encryption, Pollard’s method of factorization, Diffie–Hellman key exchange, ElGamal encryption, and Lenstra’s elliptic curve factorization method. This book’s main objective is to help students grasp and appreciate modern cryptography by offering an engaging exploration that motivates mathematical theory and practice.
With a total of 252 pages, this enlightening and intriguing work is indeed a must for anyone eager to develop a deep understanding of cryptography. The only prerequisite for this book is a course on one-variable calculus; all other necessary mathematical topics are effortlessly introduced on-the-fly. Numerous exercises are also provided to aid in the exploration process, making this book an essential and engaging resource for anyone delving into the world of cryptography.
- Authors: Thomas R. Shemanske
- Publisher: American Mathematical Soc.
- Published Date: July 31, 2017
- Page Count: 252
- Print Type: BOOK
- Categories: Cryptography
- Maturity Rating: NOT_MATURE
- Language: en
12. Lonely Planet South America
Embark on an unforgettable journey through South America with Lonely Planet’s comprehensive guidebook. Written by a team of skilled travel writers, this essential resource is packed with expert advice, insider tips, and colorful maps to ensure your trip is seamless and enchanting.
From the breathtaking views of Machu Picchu to the bustling streets of Rio de Janeiro, Lonely Planet’s South America takes you on a captivating adventure through Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, French Guiana, Guyana, Paraguay, Peru, Suriname, Uruguay, Venezuela, and more.
As your trusted travel companion, this guide provides you with honest reviews for must-see attractions, as well as hidden gems that most guidebooks overlook. It offers one-of-a-kind features such as itineraries for different lengths of stay, helping you tailor your trip to your personal needs and interests.
Lonely Planet’s South America includes practical information, essential details for getting around, as well as cultural insights that enrich your travel experience. With colorful images and maps throughout, this guidebook is perfect for both first-time and seasoned travelers.
Whether you’re exploring the iconic destinations or venturing off the beaten path, Lonely Planet’s South America ensures you make the most of your journey through South America.
*About Lonely Planet: Lonely Planet is the world’s leading travel media company, providing both inspiring and trustworthy information for every kind of traveler since 1973. With guidebooks, websites, apps, books, podcasts, and more, Lonely Planet has become an indispensable companion for countless adventurers.
- Authors: Lonely Planet, Regis St Louis, Celeste Brash, Gregor Clark, Alex Egerton, Michael Grosberg, Anthony Ham, Anna Kaminski, Brian Kluepfel, Tom Masters, Carolyn McCarthy, Anja Mutic, Kevin Raub, Brendan Sainsbury, Adam Skolnick, Paul Smith, Andy Symington, Luke Waterson, Wendy Yanagihara, Isabel Albiston, Phillip Tang, Jade Bremner, Cathy Brown, Mark Johanson, Robert Balkovich, MaSovaida Morgan
- Publisher: Lonely Planet
- Published Date: October 01, 2019
- Page Count: 1980
- Print Type: BOOK
- Categories: Travel
- Maturity Rating: NOT_MATURE
- Language: en