number theory and its history

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Number Theory And Its History

Author : Oystein Ore
ISBN : 9780486136431
Genre : Mathematics
File Size : 34. 8 MB
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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Number Theory

Author : André Weil
ISBN : 9780817645717
Genre : Mathematics
File Size : 38. 19 MB
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This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Mathematics And Its History

Author : John Stillwell
ISBN : 9781468492811
Genre : Mathematics
File Size : 66. 57 MB
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This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added as well as commentary that helps place the exercises in context.

Lectures On Number Theory

Author : Peter Gustav Lejeune Dirichlet
ISBN : 9780821820179
Genre : Mathematics
File Size : 41. 79 MB
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Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.

Labyrinth Of Thought

Author : Jose Ferreiros
ISBN : 3764357495
Genre : Mathematics
File Size : 85. 30 MB
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"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Algebraic Number Theory

Author : Richard A. Mollin
ISBN : 0849339898
Genre : Mathematics
File Size : 27. 11 MB
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From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.

Number Theory

Author : Benjamin Fine
ISBN : 9780817645410
Genre : Mathematics
File Size : 37. 54 MB
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This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.

Fundamentals Of Number Theory

Author : William J. LeVeque
ISBN : 9780486141503
Genre : Mathematics
File Size : 37. 71 MB
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DIVBasic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition. /div

Elements Of Number Theory

Author : John Stillwell
ISBN : 0387955879
Genre : Mathematics
File Size : 44. 6 MB
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Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Old And New Unsolved Problems In Plane Geometry And Number Theory

Author : Victor Klee
ISBN : 0883853159
Genre : Mathematics
File Size : 30. 76 MB
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This book discusses 24 unsolved problems in number theory and geometry.

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