Number Theory And Its Applications

Author by : Fuhuo Li
Languange : en
Publisher by : World Scientific Publishing Company
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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 different 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.


Elementary Number Theory And Its Applications

Author by : Kenneth H. Rosen
Languange : en
Publisher by : Pearson College Division
Format Available : PDF, ePub, Mobi
Total Read : 85
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Description : This text blends classical theory with modern applications and is notable for its comprehensive exercise sets.


Number Theory And Its Applications

Author by : Cheon Seoung Ryoo
Languange : en
Publisher by : BoD – Books on Demand
Format Available : PDF, ePub, Mobi
Total Read : 77
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Description : Number theory and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on number theory and its applications has been done in mathematics, applied mathematics, and the sciences. In particular, number theory plays a fundamental and important role in mathematics and applied mathematics. This book is based on recent results in all areas related to number theory and its applications.


Number Theory And Its Applications Ii

Author by : Hailong Li
Languange : en
Publisher by : World Scientific Publishing Company
Format Available : PDF, ePub, Mobi
Total Read : 99
Total Download : 658
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Description : The aim of the book is to give a smooth analytic continuation from basic subjects including linear algebra, group theory, Hilbert space theory, etc. to number theory. With plenty of practical examples and worked-out exercises, and the scope ranging from these basic subjects made applicable to number-theoretic settings to advanced number theory, this book can then be read without tears. It will be of immense help to the reader to acquire basic sound skills in number theory and its applications. Number theory used to be described as the queen of mathematics, that is, there is no practical use. However, with the development of computers and the security of internet communications, the importance of number theory has been exponentially increasing daily. The raison d'être of the present book in this situation is that it is extremely reader-friendly while keeping the rigor of serious mathematics and in-depth analysis of practical applications to various subjects including control theory and pseudo-random number generation. The use of operators is prevailing rather abundantly in anticipation of applications to electrical engineering, allowing the reader to master these skills without much difficulty. It also delivers a very smooth bridging between elementary subjects including linear algebra and group theory (and algebraic number theory) for the reader to be well-versed in an efficient and effortless way. One of the main features of the book is that it gives several different approaches to the same topic, helping the reader to gain deeper insight and comprehension. Even just browsing through the materials would be beneficial to the reader.


Group Theory And Its Applications

Author by : Ernest M. Loebl
Languange : en
Publisher by : Academic Press
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Total Read : 67
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Description : Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger’s and Dirac’s for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.


Number Theory And Its Applications

Author by : Cem Y. Yildrim
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 36
Total Download : 954
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Description : This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.


Number Theory And Its Applications

Author by : Satyabrota Kundu
Languange : en
Publisher by : CRC Press
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Total Read : 21
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Description : Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.


Number Theory And Its Applications In China

Author by : Yuan Wang
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 11
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Description : Of all modern mathematical forms, number theory is one of the earliest to be explored in China and is the one to which the Chinese have made their greatest contributions. Yan Wu-zhi first introduced number theory into China in the 1920s. Particularly influential in the field was Hua Loo-keng, who studied with G. H. Hardy and made significant contributions in the areas estimating complete exponential sums, Waring's problems, Tarry's problems, and Vinogradov's method. Interest in number theory continued to flourish following the founding of the People's Republic of China. The most noted accomplishments by Chinese mathematicians were focused on the solution of Goldbach's Conjecture and on the sieve method. Although the Cultural Revolution interrupted research in number theory for more than 10 years, the field is now growing in China.A number of universities now have advanced programs in the subject and a wide variety of topics, including the applications of number theory. This volume contains nine survey articles and three articles on current research. The collection emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. The collection is intended not only to survey the significant contributions of Chinese mathematicians, but also to reflect the latest developments and current state of research in number theory in China.


Group Theory And Its Application To Physical Problems

Author by : Morton Hamermesh
Languange : en
Publisher by : Courier Corporation
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Total Read : 12
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Description : "A remarkably intelligible survey . . . well organized, well written and very clear throughout." — Mathematical Reviews This excellent text, long considered one of the best-written, most skillful expositions of group theory and its physical applications, is directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. No knowledge of group theory is assumed, but the reader is expected to be familiar with quantum mechanics. And while much of the book concerns theory, readers will nevertheless find a large number of physical applications in the fields of crystallography, molecular theory, and atomic and nuclear physics. The first seven chapters of the book are concerned with finite groups, focusing on the central role of the symmetric group. This section concludes with a chapter dealing with the problem of determining group characters, as it discusses Young tableaux, Yamanouchi symbols, and the method of Hund. The remaining five chapters discuss continuous groups, particularly Lie groups, with the final chapter devoted to the ray representation of Lie groups. The author, Professor Emeritus of Physics at the University of Minnesota, has included a generous selection of problems. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. 77 illustrations. "A very welcome addition to [the] literature. . . . I would warmly recommend the book to all serious students of Group Theory as applied to Physics." — Contemporary Physics. Index. Bibliography. Problems. Tables.


Fundamental Number Theory With Applications

Author by : Richard A. Mollin
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 9
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Description : Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to cryptography factoring primality testing complexity analysis computer arithmetic computational number theory Fundamental Number Theory with Applications also covers: Carmichael numbers Dirichlet products Jacobsthal sums Mersenne primes perfect numbers powerful numbers self-contained numbers Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material. Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.


Unusual Applications Of Number Theory

Author by : Melvyn Bernard Nathanson
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 25
Total Download : 132
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Description : This volume contains the proceedings of the workshop held at the DIMACS Center of Rutgers University (Piscataway, NJ) on Unusual Applications of Number Theory. Standard applications of number theory are to computer science and cryptology. In this volume, well-known number theorist, Melvyn B. Nathanson, gathers articles from the workshop on other, less standard applications in number theory, as well as topics in number theory with potential applications in science and engineering. The material is suitable for graduate students and researchers interested in number theory and its applications.


Group Theory And Its Application To Physical Problems

Author by : Morton Hamermesh
Languange : en
Publisher by : Courier Corporation
Format Available : PDF, ePub, Mobi
Total Read : 79
Total Download : 805
File Size : 51,6 Mb
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Description : One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.


Number Theory And Its Applications Ii

Author by : Hailong Li
Languange : en
Publisher by : World Scientific Publishing Company
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 947
File Size : 42,9 Mb
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Description : Preface -- Linear algebraic approach to algebraic number theory -- Group-theoretic aspects of algebraic number theory -- Arithmetic functions and stieltjes integrals -- Number theory in the unit disc -- Hilbert space and number theory -- Control systems and number theory


Fuzzy Set Theory And Its Applications

Author by : Hans-Jürgen Zimmermann
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 522
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Description :


Group Theory And Its Applications In Chemistry Second Edition

Author by : KUNJU, A. SALAHUDDIN
Languange : en
Publisher by : PHI Learning Pvt. Ltd.
Format Available : PDF, ePub, Mobi
Total Read : 18
Total Download : 913
File Size : 49,9 Mb
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Description : This book, divided into two parts, now in its second edition, presents the basic principles of group theory and their applications in chemical theories. While retaining the thorough coverage of the previous edition, the book in Part I, discusses the symmetry elements, point groups and construction of character tables for different point groups. In Part II, it describes the concept of hybridization to explain the shapes of molecules and analyzes the character tables to predict infrared and Raman active vibrational modes of molecules. It also brings into fore the molecular orbital theory and the techniques of group theory to interpret bonding in transition metal complexes and their electronic spectra. Finally, the book describes the crystal symmetry in detail as well as the Woodward–Hoffmann rules to determine the pathways of electrocyclic and cycloaddition reactions. NEW TO THE SECOND EDITION • New sections on Direct Product, Group–sub-group Relationships, Effect of Descent in Octahedral Symmetry on Degeneracy, Jahn–Teller Distortion, Group–sub-group Relationships and Electronic Spectra of Complexes and Influence of Coordination on the Infrared Spectra of Oxoanionic Ligands, Space Groups • Revised sections on Projection Operator, SALC Molecular Orbitals of Benzene and π-Molecular Orbitals of 1, 3-Butadiene KEY FEATURES • Provides mathematical foundations to understand group theory. • Includes several examples to illustrate applications of group theory. • Presents chapter-end exercises to help the students check their understanding of the subject matter. The book is designed for the senior undergraduate students and postgraduate students of Chemistry. It will also be of immense use to the researchers in the fields where group theory is applied.


Set Theory And Its Applications

Author by : Liljana Babinkostova
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 342
File Size : 46,5 Mb
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Description : This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.


Elementary Number Theory With Applications

Author by : Thomas Koshy
Languange : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 42
Total Download : 735
File Size : 55,6 Mb
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Description : This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East


Number Theory And Applications

Author by : S.D. Adhikari
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 83
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Description : This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.


Axiomatic Fuzzy Set Theory And Its Applications

Author by : Xiaodong Liu
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 322
File Size : 44,8 Mb
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Description : It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.


Vague Valued Possibility Neutrosophic Vague Soft Expert Set Theory And Its Applications

Author by : Anjan Mukherjee
Languange : en
Publisher by : Infinite Study
Format Available : PDF, ePub, Mobi
Total Read : 20
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Description : In this paper, we first propose the concept of Vague-valued possibility Neutrosophic vague soft expert sets (VPNVSEsets in short). It is a combination of vague-valued possibility neutrosophic vague sets and soft expert sets. We also define its basic operations and study some related properties. Lastly an algorithm is proposed applied to the concept of vague-valued possibility Neutrosophic vague soft expert sets in hypothetical decision making problem. Here we associate the degree of belongingness degree of indeterminacy and non-belongingness of the elements of universe set with the vague –valued possibility set.


Fuzzy Set Theory And Its Applications

Author by : Hans-Jürgen Zimmermann
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 50
Total Download : 302
File Size : 42,5 Mb
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Description : This introduction to fuzzy set theory and its multitude of applications seeks to balance the character of the book with the dynamic nature of the research. This edition includes new chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. Existing material has been updated, and extended exercises are included.


Algebraic Number Theory

Author by : Anonim
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 37
Total Download : 131
File Size : 43,9 Mb
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Description : Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and


Elementary Number Theory With Applications

Author by : Thomas Koshy
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 175
File Size : 49,7 Mb
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Description : In revising his undergraduate text, Koshy incorporates new sections and exercises dealing with the latest discoveries and reinvigorates the standards in number theory, as well. Elementary Number Theory is the only number theory text that shows the student how modular systems can be employed to create beautiful designs, tying the theory to both geometry and art. This text is ideal for undergraduate mathematics and computer science students, and any instructor teaching a course in number theory will find the content to be ideally suited for their current curricula. The second edition of Elementary Number Theory features real-world applications of number theory, used in computer security and is the only text that covers barcodes, ZIP codes, ISBNs, EAN, and VIN. It is loaded with pedagogical features including many fully worked examples, graded exercises, chapter summaries, and computer exercises. This is a well-organized, non-intimidating book written with students in mind. Koshy also keeps the instructor in mind, allowing maximum flexibility in chapter selection based on the course length and students' needs.


Fundamental Number Theory With Applications Second Edition

Author by : Richard A. Mollin
Languange : en
Publisher by : Chapman and Hall/CRC
Format Available : PDF, ePub, Mobi
Total Read : 16
Total Download : 789
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Description : An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.


Number Theory And Its History

Author by : Oystein Ore
Languange : en
Publisher by : Courier Corporation
Format Available : PDF, ePub, Mobi
Total Read : 88
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Description : Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.


Elementary Number Theory And Its Applications

Author by : Kenneth H. Rosen
Languange : en
Publisher by : Addison-Wesley
Format Available : PDF, ePub, Mobi
Total Read : 23
Total Download : 334
File Size : 48,5 Mb
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Description : New edition of a standard text. Integrates classical material with applications to cryptography and computer science. The author is with AT&T Bell Labs. Annotation copyright Book News, Inc. Portland, Or.


Number Theory And Its Applications

Author by : Cem Y Yildirim
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 53
Total Download : 568
File Size : 49,7 Mb
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Description : This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey. With nearly 1500 references, equations, drawings, and tables, Number Theory and Its Applications especially benefits number theorists, coding theorists, algebraists, algebraic geometers, applied mathematicians, information theorists, and upper-level undergraduate and graduate students in these fields.