Download or read book A Handbook of Modular Arithmetic written by N.B. Singh and published by N.B. Singh. This book was released on with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A Handbook of Modular Arithmetic" is a beginner-friendly guide that introduces readers to the fascinating realm of modular arithmetic, offering clear explanations, practical examples, and engaging exercises. Designed for those with no mathematical background, the book gently introduces the concepts of modular arithmetic, exploring its applications in computer science, cryptography, and number theory. From understanding basic concepts to unraveling the mysteries of modular arithmetic, this handbook serves as a comprehensive resource for anyone eager to delve into the world of numbers and problem-solving.
Download or read book The Web of Modularity Arithmetic of the Coefficients of Modular Forms and q series written by Ken Ono and published by American Mathematical Soc.. This book was released on 2004 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1.
Download or read book Number Theory Modular Arithmetic written by Xing Zhou and published by Createspace Independent Publishing Platform. This book was released on 2017-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Remainder does not seem to be a big topic in school math. However, in competition math, it is. Almost every contest at middle school and high school level has remainder related problems. For example, in 2017 AMC 10B, out of total 25 problems, at least 3 are related to this topic: the 14th, 23rd, and 25th. Modular arithmetic is a branch in mathematics which studies remainders and tackles related problems. However, this important subject is not taught in schools. Consequently, many students rely on their intuition when attempting to solve such problems. This is clearly not the best situation. This book aims to provide a complete coverage of this topic at the level which is suitable for middle school and high school students. Contents will include both theoretical knowledge and practical techniques. Therefore, upon completion, students will have a solid skill base to solve related problems in math competitions. More information, including table of contents, pre-assessment etc, can be found at http: //www.mathallstar.org/
Download or read book Arithmetic of p adic Modular Forms written by Fernando Q. Gouvea and published by Springer. This book was released on 2006-11-14 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.
Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Download or read book A First Course in Modular Forms written by Fred Diamond and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Download or read book A Beginner s Guide to Discrete Mathematics written by W. D. Wallis and published by Springer Science & Business Media. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Included are discussions of scientific notation and the representation of numbers in computers. Lists are presented as an example of data structures. An introduction to counting includes the Binomial Theorem and mathematical induction, which serves as a starting point for a brief study of recursion. The basics of probability theory are then covered.Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined. The book concludes with an introduction to cryptography, including the RSA cryptosystem, together with the necessary elementary number theory, e.g., Euclidean algorithm, Fermat's Little Theorem.Good examples occur throughout. At the end of every section there are two problem sets of equal difficulty. However, solutions are only given to the first set. References and index conclude the work.A math course at the college level is required to handle this text. College algebra would be the most helpful.
Download or read book Understanding Cryptography written by Christof Paar and published by Springer Science & Business Media. This book was released on 2009-11-27 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography is now ubiquitous – moving beyond the traditional environments, such as government communications and banking systems, we see cryptographic techniques realized in Web browsers, e-mail programs, cell phones, manufacturing systems, embedded software, smart buildings, cars, and even medical implants. Today's designers need a comprehensive understanding of applied cryptography. After an introduction to cryptography and data security, the authors explain the main techniques in modern cryptography, with chapters addressing stream ciphers, the Data Encryption Standard (DES) and 3DES, the Advanced Encryption Standard (AES), block ciphers, the RSA cryptosystem, public-key cryptosystems based on the discrete logarithm problem, elliptic-curve cryptography (ECC), digital signatures, hash functions, Message Authentication Codes (MACs), and methods for key establishment, including certificates and public-key infrastructure (PKI). Throughout the book, the authors focus on communicating the essentials and keeping the mathematics to a minimum, and they move quickly from explaining the foundations to describing practical implementations, including recent topics such as lightweight ciphers for RFIDs and mobile devices, and current key-length recommendations. The authors have considerable experience teaching applied cryptography to engineering and computer science students and to professionals, and they make extensive use of examples, problems, and chapter reviews, while the book’s website offers slides, projects and links to further resources. This is a suitable textbook for graduate and advanced undergraduate courses and also for self-study by engineers.
Download or read book Programming Bitcoin written by Jimmy Song and published by O'Reilly Media. This book was released on 2019-02-08 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dive into Bitcoin technology with this hands-on guide from one of the leading teachers on Bitcoin and Bitcoin programming. Author Jimmy Song shows Python programmers and developers how to program a Bitcoin library from scratch. You’ll learn how to work with the basics, including the math, blocks, network, and transactions behind this popular cryptocurrency and its blockchain payment system. By the end of the book, you'll understand how this cryptocurrency works under the hood by coding all the components necessary for a Bitcoin library. Learn how to create transactions, get the data you need from peers, and send transactions over the network. Whether you’re exploring Bitcoin applications for your company or considering a new career path, this practical book will get you started. Parse, validate, and create bitcoin transactions Learn Script, the smart contract language behind Bitcoin Do exercises in each chapter to build a Bitcoin library from scratch Understand how proof-of-work secures the blockchain Program Bitcoin using Python 3 Understand how simplified payment verification and light wallets work Work with public-key cryptography and cryptographic primitives
Download or read book Modular Functions and Dirichlet Series in Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
Download or read book Modular Forms a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Download or read book Numbers Sequences and Series written by Keith Hirst and published by Butterworth-Heinemann. This book was released on 1994-12-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerned with the logical foundations of number systems from integers to complex numbers.
Download or read book Modular Forms and Hecke Operators written by A. N. Andrianov and published by American Mathematical Soc.. This book was released on 2016-01-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Download or read book Maple and Mathematica written by Inna K. Shingareva and published by Springer Science & Business Media. This book was released on 2010-04-29 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.
Download or read book Modular Forms written by Henri Cohen and published by American Mathematical Soc.. This book was released on 2017-08-02 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.
Download or read book High School Mathematics Extensions written by and published by Delta 4G Company. This book was released on with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebra Interactive written by Arjeh M. Cohen and published by Springer Science & Business Media. This book was released on 1999-08-25 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first interactive course covering first and second year algebra. Starting from such fundamental topics as integers and divisions, modular arithmetic and polynomials the content extends to rings, fields and permutation groups. The hypertext is written in Java-enhanced HTML, and Java applets illustrate the theory while also contributing interactive calculators for computing with integers, polynomials and permutations. The computer algebra system GAP is integrated throughout, allowing the calculation and manipulation of mathematical objects. In addition, collections for Mathematica notebooks and Maple worksheets review the algorithms presented. Multiple choice exercises provide users with instant feedback, while facilities for monitoring students and a bulletin board complete this digital course.
