Theory of Numbers
Sacred Number And the Origins of Civilization
The Unfolding of History Through the Mystery of Number
Paperback ISBN: 1594771316
An exploration of the origins and influences of number from prehistory to modern time • Reveals the deeper meaning of the symbols and esoteric knowledge of secret societies • Explains the numerical sophistication of ancient monuments • Shows how the Templar design for Washington, D.C., represents the New Jerusalem The ubiquitous use of certain sacred numbers and ratios can be found throughout history, influencing everything from art and architecture to the development of religion and secret societies. In Sacred Number and the Origins of Civilization, Richard Heath reveals the origins, widespread influences, and deeper meaning of these synchronous numerical occurrences and how they were left within our planetary environment during the creation of the earth, the moon, and our solar system. Exploring astronomy, harmony, geomancy, sacred centers, and myth, Heath reveals the secret use of sacred number knowledge in the building of Gothic cathedrals and the important influence of sacred numbers in the founding of modern Western culture. He explains the role secret societies play as a repository for this numerical information and how those who attempt to decode its meaning without understanding the planetary origins of this knowledge are left with contradictory, cryptic, and often deceptive information. By examining prehistoric and monumental cultures through the Dark Ages and later recorded history, Sacred Number and the Origins of Civilization provides a key to understanding the true role and meaning of number.
A Mathematician's Odyssey to Uncover the Origins of Numbers
Hardcover ISBN: 1137279842
"The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero--the keystone of our entire system of numbers--on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves--who finally reveal where our numbers come from. "--
Additive Number Theory
Density Theorems and the Growth of Sumsets
Hardcover ISBN: 0387709983
Advanced Number Theory
Paperback ISBN: 048664023x
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, theories have evolved during last 2 centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.
The Arithmetic of Fundamental Groups
Hardcover ISBN: 3642239048
In the more than 100 years since the fundamental group was first introduced by Henri PoincarÃ© it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, â„“-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the â„“-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and TamÃ¡s Szamuely, respectively.
A Comprehensive Treatment of q-Calculus
Hardcover ISBN: 303480430x
Addressing the persistently divergent views on notation that have hampered the development of q-calculus theory, this potent new notation method is based on logarithms. The book covers a multitude of q-notation topics and outlines its uses in modern physics.
Computational Number Theory
Hardcover ISBN: 0521452481
Curves, Counting, and Number Theory
Paperback ISBN: 0691163502
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.