Primes Of The Form X2 Ny2

Author: David A. Cox
Publisher: Wiley
ISBN: 9781118390184
Size: 53.13 MB
Format: PDF
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Primes Of The Form X2 Ny2 from the Author: David A. Cox. An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.

Basic Atonal Theory

Author: John Rahn
Publisher: MacMillan Publishing Company
ISBN:
Size: 66.12 MB
Format: PDF, ePub
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Basic Atonal Theory from the Author: John Rahn.

Harmony Book

Author: Elliott Carter
Publisher: Carl Fischer, L.L.C.
ISBN: 9780825845949
Size: 18.90 MB
Format: PDF, Mobi
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Harmony Book from the Author: Elliott Carter. This comprehensive resource features more than 400 projections and colour illustrations augmented by MRI images for added detail to enhance the anatomy and positioning presentations.

Euclid S Elements

Author: Euclid
Publisher: Green Lion Pr
ISBN:
Size: 78.99 MB
Format: PDF
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Euclid S Elements from the Author: Euclid. The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.

Schaum S Outline Of Discrete Mathematics Revised Third Edition

Author: Seymour Lipschutz
Publisher: McGraw Hill Professional
ISBN: 0071615873
Size: 44.15 MB
Format: PDF
View: 6974
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Schaum S Outline Of Discrete Mathematics Revised Third Edition from the Author: Seymour Lipschutz. Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you: Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

Analyzing Atonal Music

Author: Michiel Schuijer
Publisher: University Rochester Press
ISBN: 9781580462709
Size: 29.34 MB
Format: PDF, Mobi
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Analyzing Atonal Music from the Author: Michiel Schuijer. An engaging study -- the first ever -- of the principles used by noted scholars to unravel the masterpieces of Schoenberg, Stravinsky, and other modernists.

Prime Obsession

Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309512573
Size: 14.19 MB
Format: PDF, ePub
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Prime Obsession from the Author: John Derbyshire. In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark — a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic — defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark — the Riemann Hypothesis — that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows — subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many — the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof — and those who have been consumed by it.

Introduction To Post Tonal Theory

Author: Joseph N. Straus
Publisher: W. W. Norton & Company
ISBN: 0393938832
Size: 66.13 MB
Format: PDF, Docs
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Introduction To Post Tonal Theory from the Author: Joseph N. Straus. Now published by Norton, Introduction to Post-Tonal Theory has been thoroughly updated to reflect the latest developments in the field, with additional coverage of transformational theory and voice leading. The Fourth Edition helps students identify key theoretical points and guides them through the process of analysis, while also offering new recently composed musical examples—all at an exceptional value.

Fibonacci And Lucas Numbers With Applications

Author: Thomas Koshy
Publisher: John Wiley & Sons
ISBN: 1118031318
Size: 27.42 MB
Format: PDF, ePub, Docs
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Fibonacci And Lucas Numbers With Applications from the Author: Thomas Koshy. The first comprehensive survey of mathematics' most fascinating number sequences Fibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation. The author has assembled a myriad of fascinating properties of both Fibonacci and Lucas numbers-as developed by a wide range of sources-and catalogued their applications in a multitude of widely varied disciplines such as art, stock market investing, engineering, and neurophysiology. Most of the engaging and delightful material here is easily accessible to college and even high school students, though advanced material is included to challenge more sophisticated Fibonacci enthusiasts. A historical survey of the development of Fibonacci and Lucas numbers, biographical sketches of intriguing personalities involved in developing the subject, and illustrative examples round out this thorough and amusing survey. Most chapters conclude with numeric and theoretical exercises that do not rely on long and tedious proofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports and projects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richer perspective to the topic * Reference sections providing important symbols, problem solutions, and fundamental properties from the theory of numbers and matrices Fibonacci and Lucas Numbers with Applications provides mathematicians with a wealth of reference material in one convenient volume and presents an in-depth and entertaining resource for enthusiasts at every level and from any background.