An Adventurer S Guide To Number Theory

This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises, many of which are small research problems requiring substantial study or outside reading. Some problems call for new proofs for theorems already covered or for inductive explorations and proofs of theorems found in later chapters.

Edited by acclaimed science writer and physicist James Trefil, the Encyclopedia's 1000 entries combine in-depth coverage with a vivid graphic format to bring every facet of science, technology, and medicine into stunning focus. From absolute zero to the Mesozoic era to semiconductors to the twin paradox, Trefil and his co-authors have an uncanny ability to convey how the universe works and to show readers how to apply that knowledge to everyday problems.

An introductory guide to elementary number theory for advanced undergraduates and graduates.

This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Unlock the mysteries of integers and their properties with "Introduction to Number Theory," your comprehensive guide to the fascinating world of number theory. From the basic principles of divisibility and primes to the intricate realms of elliptic curves and Fermat's Last Theorem, this book offers a meticulous exploration of the core concepts and advanced topics within number theory. Delve into the historical and practical applications, including its pivotal role in cryptography and digital security, and discover the beauty and utility of numbers through clear explanations, detailed examples, and engaging exercises. Designed for students, educators, and professionals, "Introduction to Number Theory" simplifies complex theories and techniques, making them accessible to readers with a basic understanding of algebra. Each chapter is carefully structured to build on prior knowledge, guiding you through the landscape of number theory with a direct and informative style. Whether you aim to solidify your understanding of number theory, seek to apply its principles in related fields, or simply are fascinated by the mathematical underpinnings of the digital world, this book is an invaluable resource. Embrace the opportunity to expand your mathematical horizons and uncover the secrets of number theory with "Introduction to Number Theory."