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The Higher Arithmetic

The Higher Arithmetic Author H. Davenport
ISBN-10 0521634466
Release 1999-12-09
Pages 241
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Seventh edition of a classic elementary number theory book.



The Higher Arithmetic

The Higher Arithmetic Author H. Davenport
ISBN-10 9781139643528
Release 2008-10-23
Pages
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The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers and number theory, and primality testing. Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.



The Higher Arithmetic

The Higher Arithmetic Author H. Davenport
ISBN-10 9780521722360
Release 2008-10-23
Pages 239
Download Link Click Here

The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers and number theory, and primality testing. Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.



Higher Arithmetic

Higher Arithmetic Author J. H. Davenport
ISBN-10 OCLC:59915551
Release 1992
Pages 189
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Higher Arithmetic has been writing in one form or another for most of life. You can find so many inspiration from Higher Arithmetic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Higher Arithmetic book for free.



Higher Arithmetic

Higher Arithmetic Author J. H. Davenport
ISBN-10 OCLC:59915551
Release 1992
Pages 189
Download Link Click Here

Higher Arithmetic has been writing in one form or another for most of life. You can find so many inspiration from Higher Arithmetic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Higher Arithmetic book for free.



The Higher Arithmetic

The Higher Arithmetic Author Harold Davenport
ISBN-10 OCLC:299876350
Release 1952
Pages 172
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The Higher Arithmetic has been writing in one form or another for most of life. You can find so many inspiration from The Higher Arithmetic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Higher Arithmetic book for free.



An Introduction to the Theory of Numbers

An Introduction to the Theory of Numbers Author Godfrey Harold Hardy
ISBN-10 0199219869
Release 2008-07-31
Pages 621
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An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter on one of the mostimportant developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader and the clarityof exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.



The Higher Arithmetic

The Higher Arithmetic Author Horace W. Davenport
ISBN-10 OCLC:318168435
Release 1952
Pages 172
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The Higher Arithmetic has been writing in one form or another for most of life. You can find so many inspiration from The Higher Arithmetic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Higher Arithmetic book for free.



Elementary Number Theory Primes Congruences and Secrets

Elementary Number Theory  Primes  Congruences  and Secrets Author William Stein
ISBN-10 9780387855257
Release 2008-10-28
Pages 168
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This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.



Introduction to the Theory of Numbers

Introduction to the Theory of Numbers Author Harold N. Shapiro
ISBN-10 9780486466699
Release 1983
Pages 459
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Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate for undergraduate courses. The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters.



Higher Arithmetic

Higher Arithmetic Author Harold M. Edwards
ISBN-10 0821844393
Release 2008
Pages 210
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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.



An Adventurer s Guide to Number Theory

An Adventurer s Guide to Number Theory Author Richard Friedberg
ISBN-10 9780486152691
Release 2012-07-06
Pages 240
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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.



Elementary Theory of Numbers

Elementary Theory of Numbers Author William J. LeVeque
ISBN-10 9780486150765
Release 2014-01-15
Pages 160
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Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.



An Experimental Introduction to Number Theory

An Experimental Introduction to Number Theory Author Benjamin Hutz
ISBN-10 9781470430979
Release 2018-04-17
Pages 376
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This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.



Elementary Number Theory

Elementary Number Theory Author Gareth A. Jones
ISBN-10 9781447106135
Release 2012-12-06
Pages 302
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An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.



Number Theory

Number Theory Author Helmut Koch
ISBN-10 0821820540
Release 2000
Pages 368
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Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem.There are a detailed exposition of the theory of Hecke L-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory.



Numbers and Functions

Numbers and Functions Author Victor H. Moll
ISBN-10 9780821887950
Release 2012
Pages 504
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New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to discover and prove interesting properties of these functions. The book provides a transition between elementary mathematics and more advanced topics, trying to make this transition as smooth as possible. Many topics occur in the book, but they are all part of a bigger picture of mathematics. By delving into a variety of them, the reader will develop this broad view. The large collection of problems is an essential part of the book. The problems vary from routine verifications of facts used in the text to the exploration of open questions.