The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series PDF Download
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Author: Ken Ono
Publisher: American Mathematical Soc.
ISBN: 0821833685
Category : Mathematics
Languages : en
Pages : 226
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Book Description
Chapter 1.
Author: Ken Ono
Publisher: American Mathematical Soc.
ISBN: 0821833685
Category : Mathematics
Languages : en
Pages : 226
Get Book Here
Book Description
Chapter 1.
Author: N.B. Singh
Publisher: N.B. Singh
ISBN:
Category : Mathematics
Languages : en
Pages : 149
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Book Description
"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.
Author: Xing Zhou
Publisher: Createspace Independent Publishing Platform
ISBN: 9781544876085
Category :
Languages : en
Pages : 128
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Book Description
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/
Author: Fernando Q. Gouvea
Publisher: Springer
ISBN: 3540388540
Category : Mathematics
Languages : en
Pages : 129
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Book Description
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.
Author: Jimmy Song
Publisher: O'Reilly Media
ISBN: 1492031461
Category : Computers
Languages : en
Pages : 322
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Book Description
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
Author: Fred Diamond
Publisher: Springer Science & Business Media
ISBN: 0387272267
Category : Mathematics
Languages : en
Pages : 462
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Book Description
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.
Author: Carl Friedrich Gauss
Publisher: Springer
ISBN: 1493975609
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Author: William A. Stein
Publisher: American Mathematical Soc.
ISBN: 0821839608
Category : Mathematics
Languages : en
Pages : 290
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Book Description
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.
Author: W. D. Wallis
Publisher: Springer Science & Business Media
ISBN: 0817642692
Category : Combinatorics
Languages : en
Pages : 386
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Book Description
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.
Author: Tom M. Apostol
Publisher: Springer Science & Business Media
ISBN: 1461209994
Category : Mathematics
Languages : en
Pages : 218
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Book Description
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.
