## The Higher Arithmetic

*An Introduction to the Theory of Numbers*

**Author**: H. Davenport

**Publisher:**Cambridge University Press

**ISBN:**9780521634465

**Category:**Mathematics

**Page:**241

**View:**4225

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Seventh edition of a classic elementary number theory book.

## Higher Arithmetic

*Or, The Science and Application of Numbers; Combining the Analytic and Synthetic Modes of Instruction ...*

**Author**: James Bates Thomson

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**422

**View:**4427

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## Higher Arithmetic, Or, The Science and Application of Numbers

*Combining the Analytic and Synthetic Modes of Instruction : Designed for Advanced Classes in Schools and Academies*

**Author**: James Bates Thomson

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**422

**View:**5382

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## Ray's New Higher Arithmetic

*A Revised Edition of the Higher Arithmetic*

**Author**: Joseph Ray

**Publisher:**Franklin Classics Trade Press

**ISBN:**9780343791384

**Category:**

**Page:**416

**View:**4726

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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

## The Progressive Higher Arithmetic

*For Schools, Academies, and Mercantile Colleges. Combining the Analytic and Synthetic Methods; and Forming a Complete Treatise on Arithmetical Science, and Its Commercial and Business Applications*

**Author**: Horatio Nelson Robinson

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**456

**View:**2562

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## Higher Arithmetic

*Designed for the Use of High Schools, Academies, and Colleges ... with an Appendix*

**Author**: George Roberts Perkins

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**342

**View:**1532

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## Higher Arithmetic

*An Algorithmic Introduction to Number Theory*

**Author**: Harold M. Edwards

**Publisher:**American Mathematical Soc.

**ISBN:**9780821844397

**Category:**Mathematics

**Page:**210

**View:**1417

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Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.

## The Nature and Growth of Modern Mathematics

**Author**: Edna Ernestine Kramer

**Publisher:**Princeton University Press

**ISBN:**9780691023724

**Category:**Mathematics

**Page:**758

**View:**999

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Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

## Higher Arithmetic

**Author**: Virgil Sampson Mallory,Kenneth C. Skeen

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**418

**View:**1163

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## Higher Arithmetic

**Author**: George Wentworth,David Eugene Smith

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**250

**View:**6538

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## Combinatory Analysis

**Author**: Percy A. MacMahon

**Publisher:**American Mathematical Soc.

**ISBN:**0821828320

**Category:**Mathematics

**Page:**642

**View:**1516

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By ``combinatory analysis'', the author understands the part of combinatorics now known as ``algebraic combinatorics''. In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness. From the Introduction (1915): ``The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject ... ``In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond.''

## The Development of Mathematics

**Author**: E. T. Bell

**Publisher:**Courier Corporation

**ISBN:**0486152286

**Category:**Mathematics

**Page:**656

**View:**5146

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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

## A Complete Treatise on Arithmetic, Rational and Practical

*Wherein the Properties of Numbers are Clearly Pointed Out: the Theory and Practice of the Science are Deduced from First Principles and Demonstrated in a Familiar Manner; with a Great Variety of Proper Examples in All the Rules, Perfectly Suited to the Man of Business, Academies, Schools, and Students of Every Denomination, Desirousof Becoming Proficients in Accounts ...*

**Author**: Paul Deighan

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**N.A

**View:**6899

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## A Day in Old Rome

*A Picture of Roman Life*

**Author**: William Stearns Davis

**Publisher:**Biblo & Tannen Publishers

**ISBN:**9780819601063

**Category:**History

**Page:**482

**View:**4580

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Descriptions of daily Roman life including details about marriage, homes, food, costume, slaves, physicians, and libraries

## Mathematik

*Probleme — Themen — Fragen*

**Author**: STEWART

**Publisher:**Springer-Verlag

**ISBN:**3034861176

**Category:**Science

**Page:**313

**View:**1765

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## Prime Obsession

*Bernhard Riemann and the Greatest Unsolved Problem in Mathematics*

**Author**: John Derbyshire

**Publisher:**Joseph Henry Press

**ISBN:**0309085497

**Category:**Science

**Page:**446

**View:**7382

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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 â€" 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 â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" 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 â€" 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 â€" 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 â€" and those who have been consumed by it.

## The North American Arithmetic

*For Advanced Scholars. part third*

**Author**: Frederick Emerson

**Publisher:**N.A

**ISBN:**N.A

**Category:**Arithmetic

**Page:**288

**View:**6058

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## A Classical Introduction to Modern Number Theory

**Author**: Kenneth Ireland,Michael Rosen,Michael Ira Rosen

**Publisher:**Springer Science & Business Media

**ISBN:**9780387973296

**Category:**Mathematics

**Page:**389

**View:**6581

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Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.