Author: Daniel Shanks
Publisher: American Mathematical Soc.
ISBN: 082182824X
Category : Number theory
Languages : en
Pages : 322
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Book Description
The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.
Author: Daniel Shanks
Publisher: American Mathematical Society
ISBN: 1470476452
Category : Mathematics
Languages : en
Pages : 321
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Book Description
The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.
Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 1475717385
Category : Mathematics
Languages : en
Pages : 176
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Book Description
Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.
Author: Victor Klee
Publisher: American Mathematical Soc.
ISBN: 1470454610
Category : Education
Languages : en
Pages : 333
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Book Description
Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.
Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 1489935851
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Category : Science
Languages : en
Pages : 446
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Book Description
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.
Author: George Polya
Publisher: Courier Corporation
ISBN: 048631832X
Category : Mathematics
Languages : en
Pages : 80
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Book Description
Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.
Author: Waclaw Sierpinski
Publisher: Elsevier
ISBN: 1483151468
Category : Mathematics
Languages : en
Pages : 127
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Book Description
A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.
Author: Heinrich Tietze
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 410
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Book Description
Topics include prime numbers and prime twins, traveling on surfaces; geodesics-surface curvature, trisection of an angle, on neighboring domains, squaring a circle, three dimensions-higher dimensions, more on prime numbers-their distribution, counting and calculating, the regular polygon of 17 sides, solving algebraic equations by means of root extraction, the four color problem, infinity in mathematics, Ferment's last problem, space curvature.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 38
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Book Description
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and geometric progressions are exposed.
