Number Theory and Combinatorics: A Collection in Honor of the Mathematics of Ronald Graham, Aaron Robertson, Bruce M. Landman, Florian Luca, Jaroslav Nesetril, Melvyn B. Nathanson
Автор: Graham Ronald L. Название: Concrete Mathematics ISBN: 0201558025 ISBN-13(EAN): 9780201558029 Издательство: Pearson Education Рейтинг: Цена: 103450.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Introduces the mathematics that supports advanced computer programming and the analysis of algorithms. This book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems. It is useful for computer scientists and also for users of mathematics in various disciplines.
Автор: Kevin Broughan Название: Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents ISBN: 1107197120 ISBN-13(EAN): 9781107197121 Издательство: Cambridge Academ Рейтинг: Цена: 155230.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This two-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 2 covers equivalents with a strong analytic orientation and is supported by an extensive set of appendices.
Автор: Yufei Zhao Название: Graph Theory and Additive Combinatorics: Exploring Structure and Randomness ISBN: 1009310941 ISBN-13(EAN): 9781009310949 Издательство: Cambridge Academ Рейтинг: Цена: 58070.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemeredi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turan problem, Szemeredi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.
Автор: Wang Название: Mathematical Foundations of Public Key Cryptography ISBN: 1498702236 ISBN-13(EAN): 9781498702232 Издательство: Taylor&Francis Рейтинг: Цена: 80630.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.
Rather than simply combining number theory and modern algebra, this textbook features the interdisciplinary characteristics of cryptography--revealing the integrations of mathematical theories and public-key cryptographic applications. Incorporating the complexity theory of algorithms throughout, it introduces the basic number theoretic and algebraic algorithms and their complexities to provide a preliminary understanding of the applications of mathematical theories in cryptographic algorithms. Supplying a seamless integration of cryptography and mathematics, the book includes coverage of elementary number theory; algebraic structure and attributes of group, ring, and field; cryptography-related computing complexity and basic algorithms, as well as lattice and fundamental methods of lattice cryptanalysis. The text consists of 11 chapters. Basic theory and tools of elementary number theory, such as congruences, primitive roots, residue classes, and continued fractions, are covered in Chapters 1-6. The basic concepts of abstract algebra are introduced in Chapters 7-9, where three basic algebraic structures of groups, rings, and fields and their properties are explained. Chapter 10 is about computational complexities of several related mathematical algorithms, and hard problems such as integer factorization and discrete logarithm. Chapter 11 presents the basics of lattice theory and the lattice basis reduction algorithm--the LLL algorithm and its application in the cryptanalysis of the RSA algorithm. Containing a number of exercises on key algorithms, the book is suitable for use as a textbook for undergraduate students and first-year graduate students in information security programs. It is also an ideal reference book for cryptography professionals looking to master public-key cryptography.
Название: Connections in discrete mathematics ISBN: 1316607887 ISBN-13(EAN): 9781316607886 Издательство: Cambridge Academ Рейтинг: Цена: 57030.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: For over fifty years, Ron Graham has been able to illuminate the common threads connecting different areas in discrete mathematics. Inspired by Graham, this collection of papers written by top researchers in discrete mathematics encompasses a broad range of topics from numbers and geometry to juggling and probability.
Автор: Cai, Tianxin (zhejiang Univ, China) Название: Perfect numbers and fibonacci sequences ISBN: 9811244073 ISBN-13(EAN): 9789811244070 Издательство: World Scientific Publishing Рейтинг: Цена: 79200.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this book, we first review the history and current situation of the perfect number problem, including the origin story of the Mersenne primes, and then consider the history and current situation of the Fibonacci sequence. Both topics include results from our own research. In the later sections, we define the square sum perfect numbers, and describe for the first time the secret relationships connecting the square sum perfect numbers, the Fibonacci sequence, the Lucas sequence, the twin prime conjecture, and the Fermat primes. Throughout, we raise various interesting questions and conjectures.
Автор: Vazzana Название: Introduction to Number Theory, 2nd Edition ISBN: 1498717497 ISBN-13(EAN): 9781498717496 Издательство: Taylor&Francis Рейтинг: Цена: 107190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler's theorem in RSA encryption, and quadratic residues in the construction of tournaments.
Ideal for a one- or two-semester undergraduate-level course, this Second Edition:
Features a more flexible structure that offers a greater range of options for course design
Adds new sections on the representations of integers and the Chinese remainder theorem
Expands exercise sets to encompass a wider variety of problems, many of which relate number theory to fields outside of mathematics (e.g., music)
Provides calculations for computational experimentation using SageMath, a free open-source mathematics software system, as well as Mathematica(R) and Maple(TM), online via a robust, author-maintained website
Includes a solutions manual with qualifying course adoption
By tackling both fundamental and advanced subjects--and using worked examples, numerous exercises, and popular software packages to ensure a practical understanding--Introduction to Number Theory, Second Edition instills a solid foundation of number theory knowledge.
Автор: Behrends, Ehrhard Название: Math behind the magic ISBN: 1470448661 ISBN-13(EAN): 9781470448660 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 29260.00 T Наличие на складе: Нет в наличии. Описание: A magician appears able to banish chaos at will: a deck of cards arranged in order is shuffled--apparently randomly--by a member of the audience. Then, hey presto! The deck is suddenly put back in its original order! Magic tricks like this are easy to perform and have an interesting mathematical foundation. In this rich, colorfully illustrated volume, Ehrhard Behrends presents around 30 card tricks and number games that are easy to learn, with no prior knowledge required. This is math as you've never experienced it before: entertaining and fun!
Автор: Michael A Radin Название: Analyzing Mathematical Patterns - Detection & Formulation: Inductive Approach To Recognition, Analysis And Formulations Of Patterns ISBN: 9811262101 ISBN-13(EAN): 9789811262104 Издательство: World Scientific Publishing Рейтинг: Цена: 58080.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community.
This volume is dedicated to the life and memory of Ron Graham, and includes 20-articles by leading scientists across a broad range of subjects that refl ect some of the many areas in which Ron worked.
Elwyn Berlekamp, John Conway, and Richard Guy wrote ‘Winning Ways for your Mathematical Plays’ and turned a recreational mathematics topic into a full mathematical fi eld. They combined set theory, combinatorics, codes, algorithms, and a smattering of other fi elds, leavened with a liberal dose of humor and wit. Their legacy is a lively fi eld of study that still produces many surprises. Despite being experts in other areas of mathematics, in the 50 years since its publication, they also mentored, talked, and played games, giving their time, expertise, and guidance to several generations of mathematicians.
This volume is dedicated to Elwyn Berlekamp, John Conway, and Richard Guy. It includes 20 contributions from colleagues that refl ect on their work in combinatorial game theory.
Elwyn Berlekamp, John Conway, and Richard Guy wrote ‘Winning Ways for your Mathematical Plays’ and turned a recreational mathematics topic into a full mathematical fi eld. They combined set theory, combinatorics, codes, algorithms, and a smattering of other fi elds, leavened with a liberal dose of humor and wit. Their legacy is a lively fi eld of study that still produces many surprises. Despite being experts in other areas of mathematics, in the 50 years since its publication, they also mentored, talked, and played games, giving their time, expertise, and guidance to several generations of mathematicians.
This volume is dedicated to Elwyn Berlekamp, John Conway, and Richard Guy. It includes 20 contributions from colleagues that refl ect on their work in combinatorial game theory.
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