Number Theory: Structures, Examples & Problems, Nik Pachis
Автор: Jin-Yi Cai, Xi Chen Название: Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain ISBN: 1107062373 ISBN-13(EAN): 9781107062375 Издательство: Cambridge Academ Рейтинг: Цена: 155230.00 T Наличие на складе: Невозможна поставка. Описание: Complexity theory aims to understand and classify computational problems according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems on the Boolean domain and is broadly accessible to researchers and graduate students.
Автор: Shanks, Daniel Название: Solved and unsolved problems in number theory ISBN: 082182824X ISBN-13(EAN): 9780821828243 Издательство: Mare Nostrum (Eurospan) Цена: 36790.00 T Наличие на складе: Невозможна поставка. Описание: The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. This book shows how each result leads to further results and conjectures.
Автор: Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf Название: Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups ISBN: 3110413329 ISBN-13(EAN): 9783110413328 Издательство: Walter de Gruyter Цена: 43330.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
Автор: Martin Hanke Название: A Taste of Inverse Problems: Basic Theory and Examples ISBN: 1611974933 ISBN-13(EAN): 9781611974935 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 53090.00 T Наличие на складе: Невозможна поставка. Описание: Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data.This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles.A Taste of Inverse Problems: Basic Theory and Examplesrigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;presents diverse real-world applications, important test cases, and possible pitfalls; andtreats these applications with the same rigor and depth as the theory.
Автор: Murty M. Ram Название: Problems in Algebraic Number Theory ISBN: 1441919678 ISBN-13(EAN): 9781441919670 Издательство: Springer Рейтинг: Цена: 65210.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Автор: Ribenboim Paulo Название: Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo ISBN: 9814725811 ISBN-13(EAN): 9789814725811 Издательство: World Scientific Publishing Рейтинг: Цена: 33790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
"This is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book."
Mathematical Association of America
Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience.
Автор: Ribenboim Paulo Название: Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo ISBN: 9814725803 ISBN-13(EAN): 9789814725804 Издательство: World Scientific Publishing Рейтинг: Цена: 65470.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
"This is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book."
Mathematical Association of America
Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience.
Автор: Duverney Daniel Название: Number Theory: An Elementary Introduction Through Diophantine Problems ISBN: 9814307459 ISBN-13(EAN): 9789814307451 Издательство: World Scientific Publishing Рейтинг: Цена: 68640.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.
Автор: Grigorieva Ellina Название: Methods of Solving Number Theory Problems ISBN: 3030081303 ISBN-13(EAN): 9783030081300 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking.
The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores the representations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day.
Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
Автор: Titu Andreescu, Gabriel Dospinescu, Oleg Mushkarov Название: Number Theory: Concepts and Problems ISBN: 0988562200 ISBN-13(EAN): 9780988562202 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 82230.00 T Наличие на складе: Невозможна поставка. Описание: Challenge your problem-solving aptitude in number theory with powerful problems that have concrete examples which reflect the potential and impact of theoretical results. Each chapter focuses on a fundamental concept or result, reinforced by each of the subsections, with scores of challenging problems that allow you to comprehend number theory like never before.
Автор: Danyal Sadik Название: Problems in Analytic Number Theory ISBN: 1681175657 ISBN-13(EAN): 9781681175652 Издательство: Gazelle Book Services Рейтинг: Цена: 217350.00 T Наличие на складе: Невозможна поставка. Описание: "One might have thought that number theory was simply the study of numbers, but that is too broad a definition, since numbers are almost ubiquitous in mathematics. Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor function, Riemann zeta function, and totient function. Analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking problems in other fields. Recent advances in analytic number theory have had repercussions in various mathematical subjects, such as harmonic analysis, ergodic theory and dynamics, additive and multiplicative combinatorics and theoretical computer science. The biggest technical change after 1950 has been the development of sieve methods, particularly in multiplicative problems. These are combinatorial in nature, and quite varied. The extremal branch of combinatorial theory has in return been greatly influenced by the value placed in analytic number theory on quantitative upper and lower bounds. Another recent development is probabilistic number theory, which uses methods from probability theory to estimate the distribution of number theoretic functions, such as how many prime divisors a number has. Problems in Analytic Number Theory present a problem-solving approach to the difficult subject of analytic number theory. This book is focused at researchers, teachers, and graduate students interested in number theory and its links with other branches of science."
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