Top 13 Modular Arithmetic Books
Discover the world of Modular Arithmetic with our top book recommendations. In this roundup, we've compiled a list of must-reads for those curious about this fascinating branch of mathematics. From beginner-friendly guides to advanced textbooks, we've got you covered.
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1. Arithmetic Moduli of Elliptic Curves
Arithmetic Moduli of Elliptic Curves, co-authored by experts Nicholas M. Katz and Barry Mazur, delves into recent advancements in the realm of elliptic curves and their associated moduli spaces.
This captivating and comprehensive book offers a meticulous exploration of the arithmetic study, a field that started with Jacobi's "Fundamenta Nova" in 1829 and was later pioneered by Eichler-Shimura, Igusa, and Deligne-Rapoport. The authors not only delve into their own research but also incorporate the groundbreaking theories of Deligne and Drinfeld. This 513-page Princeton University Press masterpiece, published in 1985, serves as the perfect resource for anyone seeking a deep understanding of the field's modern developments.
- Authors: Nicholas M. Katz, Barry Mazur
- Publisher: Princeton University Press
- Published Date: February 21, 1985
- Page Count: 531.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
2. Algebra Interactive!
Learning Algebra in an Exciting Way
Dive into the exciting world of Algebra with "Algebra Interactive! " This innovative, interactive course offers a captivating way to master the foundational topics of first and second year Algebra, such as integers, divisions, modular arithmetic, and polynomials. The book is meticulously crafted in Java-enhanced HTML, which not only makes for smooth navigation, but also integrates engaging Java applets that illustrate the theory and even provide interactive calculators for working with integers, polynomials, and permutations.
This comprehensive guide utilizes the powerful computer algebra system, GAP, to enable users to calculate and manipulate mathematical objects effortlessly. In addition to the core content, the book provides collections of Mathematica notebooks and Maple worksheets for in-depth reviews of the algorithms presented.
Catering to both teachers and learners, "Algebra Interactive! " features multiple-choice exercises that provide instant feedback. Furthermore, the book includes advanced facilities to monitor students and access a bulletin board where users can seek assistance or participate in discussions. Experience Algebra like never before with this groundbreaking interactive course, available now!
- Authors: Arjeh M. Cohen, Hans Cuypers, Hans Sterk
- Publisher: Springer Science & Business Media
- Published Date: August 25, 1999
- Page Count: 174.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
3. The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series
Arithmetic of the Coefficients of Modular Forms and Q-series
Embark on an enthralling voyage through the universe of modular forms and q-series with Ken Ono's "The Web of Modularity". Published by the American Mathematical Society, this all-encompassing manual imparts readers with profound comprehension of the number-theoretic features of modular forms, establishing correlations between q-series and modular forms.
Not merely an expository exercise, "The Web of Modularity" is a journey of discovery into the exquisite and intricate patterns concealed within the realm of mathematics. Ken Ono's proficiency manifests itself brilliantly as he deftly leads readers through the convoluted maze of q-series and modular forms, making this book an indispensable read for anyone intrigued by advanced mathematical principles.
Spanning 226 pages, this book encapsulates decades of research and innovation into a single, compact volume, rendering it a convenient, yet comprehensive learning resource for both novices and experts alike.
Chapter 1 serves as the prologue for the reader's odyssey, introducing pivotal concepts and laying the groundwork for the thrilling adventure that ensues. "The Web of Modularity" is more than just a textbook; it's an invitation to venture into one of the most intriguing facets of mathematics, harmoniously blending intuition, logic and aesthetics.
Join Ken Ono in this exhilarating mathematical expedition and experience the intricate web of modularity in the enlightening "The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series".
- Authors: Ken Ono
- Publisher: American Mathematical Soc.
- Published Date: May 16, 2004
- Page Count: 226.0
- Print Type: BOOK
- Categories: Forms, Modular
- Maturity Rating: NOT\_MATURE
- Language: en
4. Arithmetic of p-adic Modular Forms
Unlock the mysteries of p-adic modular forms with "Arithmetic of p-adic Modular Forms" by Fernando Q. Gouvea.
Delve into the fascinating connections between these forms and p-adic Galois representations. Although the book assumes basic knowledge of modular forms, it provides a comprehensive introduction to the p-adic theory and results on the U operator and Galois representations. This well-researched monograph includes a range of new findings valuable to both beginners and specialists in the field.
With its concise page count and expert guidance, this book is a must-read for mathematicians curious about p-adic modular forms and eager to explore intriguing problems in the subject.
- Authors: Fernando Q. Gouvea
- Publisher: Springer
- Published Date: November 14, 2006
- Page Count: 129.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
5. Understanding Cryptography
A Textbook for Students and Practitioners
Unraveling the Intricacies of Cryptography: A Comprehensive Guide for Students and Professionals by Christof Paar and Jan Pelzl navigates the ever-evolving world of cryptography through clear and engaging explanations. Encompassing a vast array of applications, from secure banking systems to the advanced security of internet browsers and beyond, modern cryptography demands a robust understanding. This book offers precisely that.
The authors commence by laying the foundational groundwork of cryptography and data security, making it an excellent choice for graduate and advanced undergraduate courses as well as independent study by engineers. Following this, they delve into the core aspects of contemporary cryptography, exploring subjects such as stream ciphers, DES and 3DES, AES, RSA cryptosystems, elliptic-curve cryptography, and digital signatures, among others.
Unraveling the Intricacies of Cryptography earns praise for its user-friendly approach to intricate topics, ensuring individuals with minimal mathematics backgrounds can easily follow along. Furthermore, the book benefits from a wealth of examples, exercises, and chapter reviews, serving as an indispensable resource for both students and professionals.
The official website provides additional resources, including slides, projects, and external links to supplementary materials, enhancing the book's functionality even further. With 372 pages, an average rating of 5.0, and a count of 5.0, this book solidifies its status as a highly respected and enlightening reference on cryptography for a diverse audience.
- Authors: Christof Paar, Jan Pelzl
- Publisher: Springer Science & Business Media
- Published Date: November 27, 2009
- Page Count: 372.0
- Print Type: BOOK
- Categories: Computers
- Average Rating: 5.0
- Ratings Count: 5.0
- Maturity Rating: NOT\_MATURE
- Language: en
6. The Art of Proof
Basic Training for Deeper Mathematics
Dive into the intriguing realm of mathematics with "The Art of Proof: Fundamental Education for Greater Mathematical Insights" by Matthias Beck and Ross Geoghegan. This meticulously developed textbook serves as a perfect match for a one-semester or two-quarter course, tailored for students who have prior knowledge in calculus.
"The Art of Proof" seamlessly combines a laid-back conversational tone with enthralling examples, ensuring that students build a robust understanding of mathematics on a steady intellectual base. The book spans a wide range of crucial topics, encompassing integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets.
What sets "The Art of Proof" apart from other textbooks is its integration of essential mathematical techniques such as axioms, theorems, and proofs into the content, thereby emphasizing their practical applications.
To wrap up, the book features fascinating essays on advanced topics suited for seminar-style presentations by small groups of students. These thought-provoking essays explore various captivating subjects, including continuity, cryptography, groups, complex numbers, ordinal numbers, and generating functions.
"The Art of Proof: Fundamental Education for Greater Mathematical Insights" is a must-have addition to any mathematics curriculum, offering both in-depth knowledge and accessibility that will undoubtedly spark a keen interest in mathematics among budding mathematicians.
- Authors: Matthias Beck, Ross Geoghegan
- Publisher: Springer Science & Business Media
- Published Date: August 17, 2010
- Page Count: 182.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
7. Modern Computer Arithmetic
Dive into the world of efficient high-precision arithmetic operations with "Modern Computer Arithmetic" by authors Sir Richard P. Brent and Paul Zimmermann. This comprehensive guide covers algorithms for performing addition, multiplication, and division, as well as their connections to modular arithmetic, greatest common divisors, and the Fast Fourier Transform (FFT). Moreover, it explores the computation of elementary and special functions. The book, published by Cambridge University Press, offers ready-to-implement algorithms in favorable languages along with a high-level approach, ensuring a clear understanding.
Designed for individuals in design and implementation of efficient numerical algorithms, the book also serves as an essential resource in a graduate-level mathematics or computer science course. It comes equipped with a variety of exercises catering to different levels of difficulty, ranging from easy to small research projects, all expanding on the topics discussed within the text. Selected exercise solutions are available from the authors, making this book a valuable tool for anyone seeking to deepen their understanding of modern computer arithmetic.
- Authors: Richard P. Brent, Paul Zimmermann
- Publisher: Cambridge University Press
- Published Date: November 25, 2010
- Print Type: BOOK
- Categories: Computers
- Maturity Rating: NOT\_MATURE
- Language: en
8. Finite Fields: Theory and Computation
The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Embark on a fascinating journey into the intersection of number theory, computer science, coding theory, and cryptography with Igor Shparlinski's seminal work "Finite Fields: Theory and Computation. " This comprehensive guide delves into computational and algorithmic problems in finite fields, offering novel insights into polynomial factorization, irreducible and primitive polynomials, primitive points on elliptic curves, and more.
With new applications of finite fields to other mathematical realms, this book offers a unique perspective on the subject matter. Furthermore, it serves as a valuable reference for professionals in computer science, coding theory, cryptography, and beyond. With a balanced blend of cutting-edge theories and widely scattered results from Russian and other sources, you'll discover the power of finite fields and their vast array of applications. Experience the meeting point of disciplines, as Shparlinski illuminates these essential concepts and connects the worlds of number theory, computer science, and beyond.
- Authors: Igor Shparlinski
- Publisher: Springer Science & Business Media
- Published Date: March 09, 2013
- Page Count: 532.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
9. Elementary Number Theory with Programming
Elementary Number Theory with Programming is a groundbreaking textbook that presents the fundamental concepts of number theory and computer programming in a unique and accessible way. Written by top-notch experts in the fields of computer science and mathematics, this book successfully bridges the existing gap between these two disciplines. Ideal for undergraduate and graduate-level students majoring in mathematics or computer science as well as a valuable learning resource for professionals and researchers, the book comprehensively covers the methodology and applications of the key concepts in number theory, while also introducing programming concepts without relying on prerequisite knowledge.
The textbook features engaging content that combines theory with practical application, including chapter exercises, solutions, and sample computer programs that aid in reader comprehension. Additionally, it provides a well-structured website with links to select exercises and an Instructor’s Solutions Manual on a companion website. With a concise pace of 232 pages, this book is a must-read for anyone looking for a comprehensive yet approachable introduction to the fascinating world of elementary number theory and computer programming.
- Authors: Marty Lewinter, Jeanine Meyer
- Publisher: John Wiley & Sons
- Published Date: May 06, 2015
- Page Count: 232.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
10. Number Theory - Modular Arithmetic
Math for Gifted Students
"Number Theory - Modular Arithmetic: Math for Gifted Students" by Xing Zhou offers a comprehensive guide to mastering remaining arithmetic and excelling in competitive math. Suitable for middle and high school students, this enlightening book delves into the complexities of modular arithmetic, a branch of mathematics that studies remainders and tackles related problems. Many math competitions incorporate these kinds of challenging problems, yet they are rarely taught in schools.
As a result, students often rely on their intuition, leading to inconsistent performance. This book fills that gap by providing a complete coverage of modular arithmetic at an appropriate level. Packed with both theoretical knowledge and practical techniques, the book is designed to equip students with a solid skill base to tackle such problems.
Get your copy today and experience the thrill of competitive math like never before!
- Authors: Xing Zhou
- Publisher: Createspace Independent Publishing Platform
- Published Date: March 16, 2017
- Page Count: 128.0
- Print Type: BOOK
- Maturity Rating: NOT\_MATURE
- Language: en
11. Elementary Abstract Algebra, Examples and Applications Volume 1: Foundations
"Elementary Abstract Algebra, Examples and Applications Volume 1: Foundations" by Justin Hill and Christopher Thron is a must-read for anyone looking to delve into the world of abstract algebra. This comprehensive textbook takes an engaging, practical approach to teaching group theory by providing a thorough treatment of key concepts through illuminating examples.
Beginning with the fundamental notions of modular arithmetic and complex numbers, the authors guide readers through the intricacies of symmetries and permutations. With a strong emphasis on practical applications, they include illuminating examples that extend to modern-day subject matters such as cryptography and coding theory.
Published in 2018 by Lulu. com, this highly-regarded textbook is perfect for students, educators, and professionals seeking a solid foundation in abstract algebra. Whether you're new to the subject or a seasoned expert, "Elementary Abstract Algebra, Examples and Applications Volume 1: Foundations" offers a wealth of knowledge presented in an easily digestible format, making it an essential resource in the field of education.
- Authors: Justin Hill, Christopher Thron
- Publisher: Lulu.com
- Published Date: August 22, 2018
- Page Count: 402.0
- Print Type: BOOK
- Categories: Education
- Maturity Rating: NOT\_MATURE
- Language: en
12. Programming Bitcoin
Learn How to Program Bitcoin from Scratch
Embark on a captivating journey into the heart of Bitcoin technology with "Programming Bitcoin" by renowned teacher and expert, Jimmy Song. This comprehensive guide caters to Python programmers and developers seeking to engage with the groundbreaking cryptocurrency and its intricate blockchain payment system.
Through engaging exercises and step-by-step instructions, you'll explore the fundamentals of Bitcoin, including the core mathematical concepts, transaction verification, block mining, and the intricate network that sustains it. Discover the power of script, the smart contract language driving Bitcoin, and learn how to create transactions, retrieve valuable data, and send them across the network.
With an emphasis on simplicity, the book guides you through the process of parsing, validating, and constructing Bitcoin transactions. Delve into the concept of proof-of-work as the cornerstone of blockchain security and unveil the underpinnings of simplified payment verification and light wallets.
Furthermore, you'll gain insight into public-key cryptography and the essential cryptographic primitives, which form the basis of Bitcoin security protocols. As you progress, the book will help you program Bitcoin using Python 3, ensuring a solid foundation for future endeavors in this exciting field.
"Programming Bitcoin" offers a practical approach to understanding the cryptocurrency revolution and is the perfect starting point for developers and enthusiasts eager to make their mark in this transformative industry.
- Authors: Jimmy Song
- Publisher: O'Reilly Media
- Published Date: February 08, 2019
- Page Count: 322.0
- Print Type: BOOK
- Categories: Computers
- Average Rating: 5.0
- Ratings Count: 3.0
- Maturity Rating: NOT\_MATURE
- Language: en
13. Modular Arithmetic
Unlock the mysteries of modular arithmetic with "Modular Arithmetic" by N. B. Singh. This concise and accessible guide is perfect for students and enthusiasts seeking to delve into the foundational concepts of this essential mathematical framework.
Discover the properties and operations within modular systems, exploring topics such as addition, subtraction, multiplication, and exponentiation. With clear explanations and illustrative examples, this handbook equips readers with the knowledge to tackle problems in cryptography, computer science, and other mathematical disciplines. At just 145 pages, "Modular Arithmetic" is the ideal companion for those looking to grasp and apply this vital mathematical concept.
- Authors: N.B. Singh
- Publisher: N.B. Singh
- Page Count: 145.0
- Print Type: BOOK
- Categories: Mathematics
- Maturity Rating: NOT\_MATURE
- Language: en
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