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Author: Yuan Wang
Publisher: American Mathematical Soc.
ISBN: 0821850849
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.
Author: Yuan Wang
Publisher: American Mathematical Soc.
ISBN: 0821850849
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.
Author: Kenneth H. Rosen
Publisher:
ISBN: 9780071244749
Category : Computer science
Languages : en
Pages : 109
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Book Description
The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation
Author: Istvan Mezo
Publisher: CRC Press
ISBN: 1351346385
Category : Computers
Languages : en
Pages : 499
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Book Description
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.
Author: Fuhuo Li
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814425636
Category : Mathematics
Languages : en
Pages : 194
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Book Description
This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon - the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the Euler function is treated in several different places, as the number of generators of a finite cyclic group, as one counting the order of the multiplicative group of reduced residue classes modulo q, and as the order and degree of the Galois group of the cyclotomic field, respectively. One of the important principles of learning is to work with the material many times. This book presents many worked-out examples and exercises to enhance the reader's comprehension on the topics covered in an in-depth manner. This is done in a differ-ent setting each time such that the reader will always be challenged. For the keen reader, even browsing the text alone, without solving the exercises, will yield some knowledge and enjoyment.
Author: Jianqiang Zhao
Publisher: World Scientific
ISBN: 9814689416
Category : Mathematics
Languages : en
Pages : 618
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Book Description
This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter.
Author: Masayoshi Hata
Publisher: World Scientific Publishing Company
ISBN: 9813142847
Category : Mathematics
Languages : en
Pages : 376
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Book Description
This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.
Author: Yuan Wang
Publisher: World Scientific
ISBN: 9812561978
Category : Mathematics
Languages : en
Pages : 512
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Book Description
This volume presents a comprehensive collection of Wang Yuan's original important papers which are not available elsewhere, since the majority of the papers were published in China.Covering both pure number theory and applied mathematics, this book is important for understanding Wang Yuan's academic career and also the development of Chinese mathematics in recent years, since Wang Yuan's work has a wide-ranging influence in China.Wang Yuan is a professor and academician of the Chinese Academy of Sciences. He received his honorable Doctorship from Hong Kong Baptist University. He has published 70 papers and ten books.
Author: Song Y. Yan
Publisher: Springer
ISBN: 3319258230
Category : Computers
Languages : en
Pages : 259
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Book Description
This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification. The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems. Chapters also cover various other quantum algorithms for Pell's equation, principal ideal, unit group, class group, Gauss sums, prime counting function, Riemann's hypothesis and the BSD conjecture. Quantum Computational Number Theory is self-contained and intended to be used either as a graduate text in computing, communications and mathematics, or as a basic reference in the related fields. Number theorists, cryptographers and professionals working in quantum computing, cryptography and network security will find this book a valuable asset.
Author: Lianghuo Fan
Publisher: World Scientific
ISBN: 9789812562241
Category : Mathematics
Languages : en
Pages : 594
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Book Description
The book has been written by an international group of very activeresearchers and scholars who have a passion for the study of Chinesemathematics education. It aims to provide readers with a comprehensiveand updated picture of the teaching and learning of mathematicsinvolving Chinese students from various perspectives, including theways in which Chinese students learn mathematics in classrooms, schools and homes, the influence of the cultural and socialenvironment on Chinese students'' mathematics learning, and thestrengths and weaknesses of the ways in which Chinese learnmathematics
Author: Shigeru Kanemitsu
Publisher: World Scientific
ISBN: 9814452467
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series.
