Perfect Amicable and Sociable Numbers

Author: Song Y. Yan
Publisher: World Scientific
ISBN: 9810228473
Release Date: 1996
Genre: Mathematics

This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and sociable numbers and reviews the long history of the search for these numbers. It examines various methods, both numerical and algebraic, of generating these numbers, and also includes a set of important and interesting open problems in the area. The book is self-contained, and accessible to researchers, students, and even amateurs in mathematics and computing science. The only prerequisites are some familiarity with high-school algebra and basic computing techniques.

Nice Numbers

Author: John Barnes
Publisher: Birkhäuser
ISBN: 9783319468310
Release Date: 2016-12-25
Genre: Mathematics

In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author informs and intrigues his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal's triangle, the Rubik cube, Mersenne's curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty style and requiring only basic school mathematical knowledge, this book will appeal to both young and mature readers fascinated by the curiosities of numbers.

A Number for your Thoughts

Author: Lines M E
Publisher: CRC Press
ISBN: 0852744951
Release Date: 1986-01-01
Genre: Mathematics

Why do we count the way we do? What is a prime number or a friendly, perfect, or weird one? How many are there and who has found the largest yet known? What is the Baffling Law of Benford and can you really believe it? Do most numbers you meet in every day life really begin with a 1, 2, or 3? What is so special about 6174? Can cubes, as well as squares, be magic? What secrets lie hidden in decimals? How do we count the infinite, and is one infinity really larger than another? These and many other fascinating questions about the familiar 1, 2, and 3 are collected in this adventure into the world of numbers. Both entertaining and informative, A Number for Your Thoughts: Facts and Speculations about Numbers from Euclid to the Latest Computers contains a collection of the most interesting facts and speculations about numbers from the time of Euclid to the most recent computer research. Requiring little or no prior knowledge of mathematics, the book takes the reader from the origins of counting to number problems that have baffled the world's greatest experts for centuries, and from the simplest notions of elementary number properties all the way to counting the infinite.

Divisor Function

Author: LLC Books
ISBN: 1155873335
Release Date: 2010-05

Chapters: Perfect Number, Amicable Number, Table of Divisors, Hyperperfect Number, Harmonic Divisor Number, Friendly Number, Aliquot Sequence, Abundant Number, Superabundant Number, Highly Abundant Number, Weird Number, Sociable Number, Superperfect Number, Deficient Number, Untouchable Number, Colossally Abundant Number, Almost Perfect Number, Quasiperfect Number, Sublime Number. Source: Wikipedia. Pages: 95. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, say, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/3 = 7 (and 7 is also a divisor of 21). If m is a divisor of n then so is m. The tables below only list positive divisors. ...More: http: //

Number Theory for Computing

Author: Song Y. Yan
Publisher: Springer Science & Business Media
ISBN: 9783662047736
Release Date: 2013-11-11
Genre: Computers

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

Unsolved Problems in Number Theory

Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 9781489935854
Release Date: 2013-11-11
Genre: Mathematics

Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

History of the Theory of Numbers

Author: Leonard Eugene Dickson
Publisher: American Mathematical Soc.
ISBN: 0821819364
Release Date: 1999
Genre: Mathematics

The last volume of Dickson's History is the most modern, covering quadratic and higher forms. The treatment here is more general than in Volume II, which, in a sense, is more concerned with special cases. Indeed, this volume chiefly presents methods of attacking whole classes of problems. Again, Dickson is exhaustive with references and citations.

Handbook of Number Theory I

Author: József Sándor
Publisher: Springer Science & Business Media
ISBN: 9781402042157
Release Date: 2005-11-17
Genre: Mathematics

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

The Story Of Numbers

Author: Mallik Asok Kumar
Publisher: #N/A
ISBN: 9789813222946
Release Date: 2017-07-27
Genre: Juvenile Nonfiction

This book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers. Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of "Chaos". Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail. The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level. The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.

An Introduction to Formal Languages and Machine Computation

Author: Song Y. Yan
Publisher: World Scientific
ISBN: 9810234228
Release Date: 1998-01
Genre: Computers

This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.

I Capture the Castle

Author: Dodie Smith
Publisher: Macmillan
ISBN: 031231616X
Release Date: 2003-04-01
Genre: Fiction

The 1934 journal of seventeen-year-old Cassandra Mortmain reveals her perspective on six stormy months in the eccentric and poverty-stricken life of her family in a ruined Suffolk castle, ending with the revelation that Cassandra is deeply in love. Reissue. (A Samuel Goldwyn Films production, directed by Tim Fywell, starring Henry Thomas) (General Fiction)

Prime Numbers

Author: David Wells
Publisher: John Wiley & Sons
ISBN: 1118045718
Release Date: 2011-01-13
Genre: Mathematics

A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

Fermat s Last Theorem

Author: Simon Singh
Publisher: HarperCollins UK
ISBN: 9780007381999
Release Date: 2012-11-22
Genre: Science

‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’