This book provides a detailed description of a most important unsolved mathematical problem — the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.

Although higher mathematics is beautiful, natural and interconnected, to the uninitiated it can feel like an arbitrary mass of disconnected technical definitions, symbols, theorems and methods. An intellectual gulf needs to be crossed before a true, deep appreciation of mathematics can develop. This book bridges this mathematical gap. It focuses on the process of discovery as much as the content, leading the reader to a clear, intuitive understanding of how and why mathematics exists in the way it does.The narrative does not evolve along traditional subject lines: each topic develops from its simplest, intuitive starting point; complexity develops naturally via questions and extensions. Throughout, the book includes levels of explanation, discussion and passion rarely seen in traditional textbooks. The choice of material is similarly rich, ranging from number theory and the nature of mathematical thought to quantum mechanics and the history of mathematics. It rounds off with a selection of thought-provoking and stimulating exercises for the reader.

This book is designed to meet the needs of the first course in Number Theory for the undergraduate students of various Indian and foreign universities. The students who are appearing at various competitive examinations where mathematics is on for testing shall also find it useful.

This book provides a detailed description of a most important unsolved mathematical problem ? the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.

The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.

Natural numbers are the oldest human inventions. This volume describes their nature, laws, history and current status. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. For the first time in history, the Chinese Remainder Theorem is renamed the Qin Jiushao Theorem to give him the full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.In this volume, there is supplementary material after each section to broaden the reader's knowledge and imagination. It either discusses the rudiments of some aspects or introduces new topics, such as the perfect number problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Waring's problem, Catalan's conjecture, Euler's conjecture, Fermat's Last Theorem, etc.Originally published in Chinese as in 2014, The Book of Numbers is written for anyone who loves natural numbers. The author is not only a mathematician, but also a literary and science writer, with more than 20 books published, many of which were translated into 20 languages.

Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Laudau's problem and etc.This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.

This volume presents a comprehensive collection of Wang YuanOCOs 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 YuanOCOs academic career and also the development of Chinese mathematics in recent years, since Wang YuanOCOs 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."

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.

Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.