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Prime Numbers Friends Who Give Problems
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Book Synopsis Prime Numbers, Friends Who Give Problems by : Paulo Ribenboim
Download or read book Prime Numbers, Friends Who Give Problems written by Paulo Ribenboim and published by World Scientific. This book was released on 2016-10-27 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: '" Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience. Contents:What are Prime Numbers?Division is Harder than MultiplicationAnother Paulo! Is a Dialogue of Three Possible?How Natural Numbers are Made Out of PrimesTell Me Which is the Largest Prime?Trying Hard to Find PrimesA Formula, A Formula, PleasePaulo Came with a LassoBeautiful Old Elementary ArithmeticThe Old Man Still KnowsCan You Tell Me All About Congruences?Homework CheckedTesting for Primality and FactorizationFermat Numbers are Friendly. Are They Primes?This World is PerfectUnfriendly Numbers from a Friend of Fermat''sPaying My DebtMoney and PrimesSecret MessagesNew Numbers and FunctionsPrinceps GaussGathering ForcesThe After "Math" of GaussPrimes After Dinner: Bad Dreams?Primes in Arithmetic ProgressionSelling PrimesThe Great Prime MysteriesMysteries in Sequences: More But Not AllThe End and the Beginning Readership: College students, high school teachers and beginners interested in number theory and important facts about prime numbers. "'
Book Synopsis Advances In Number Theory And Applied Analysis by : Pradip Debnath
Download or read book Advances In Number Theory And Applied Analysis written by Pradip Debnath and published by World Scientific. This book was released on 2023-05-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.
Book Synopsis Secrets of Creation by : Matthew Watkins
Download or read book Secrets of Creation written by Matthew Watkins and published by John Hunt Publishing. This book was released on 2015-03-27 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mystery of the Prime Numbers uses an innovative visual approach to communicate some surprisingly advanced mathematical ideas without any need for formulas or equations. The issue of prime numbers acts as a gateway into some truly strange philosophical territory whose relevance extends well beyond mathematics. The series Secrets of Creation is in three volumes: Secrets of Creation Volume 1 The Mystery of the Prime Numbers Secrets of Creation, Volume 2 The Enigma of the Spiral Waves Secrets of Creation, Volume 3 Prime Numbers, Quantum Physics and a Journey to the Centre of Your Mind
Book Synopsis The Solitude of Prime Numbers by : Paolo Giordano
Download or read book The Solitude of Prime Numbers written by Paolo Giordano and published by Penguin. This book was released on 2010-03-18 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the author of Heaven and Earth, a sensational novel about whether a "prime number" can ever truly connect with someone else A prime number is inherently a solitary thing: it can only be divided by itself, or by one: it never truly fits with another. Alice and Mattia, too, move on their own axis, alone with their personal tragedies. As a child, Alice’s overbearing father drove her first to a terrible skiing accident, and then to anorexia. When she meets Mattia she recognizes a kindred, tortured spirit, and Mattia reveals to Alice his terrible secret: that as a boy he abandoned his mentally-disabled twin sister in a park to go to a party, and when he returned, she was nowhere to be found. These two irreversible episodes mark Alice and Mattia’s lives for ever, and as they grow into adulthood their destinies seem intertwined: they are divisible only by themselves and each other. But the shadow of the lost twin haunts their relationship, until a chance sighting by Alice of a woman who could be Mattia’s sister forces a lifetime of secret emotion to the surface. A meditation on loneliness and love, The Solitude of Prime Numbers asks, can we ever truly be whole when we’re in love with another? And when Mattia is asked to choose between human love and his professional love — of mathematics — which will make him more complete?
Book Synopsis My Numbers, My Friends by : Paulo Ribenboim
Download or read book My Numbers, My Friends written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2006-05-10 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.
Book Synopsis Subcritical Brain, The: A Synergy Of Segregated Neural Circuits In Memory, Cognition And Sensorimotor Control by : Yoram Baram
Download or read book Subcritical Brain, The: A Synergy Of Segregated Neural Circuits In Memory, Cognition And Sensorimotor Control written by Yoram Baram and published by World Scientific. This book was released on 2021-05-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have over a hundred years of brain research revealed all its secrets? This book is motivated by a realization that cortical structure and behavior can be explained by a synergy of seemingly different mathematical notions: global attractors, which define non-invertible neural firing rate dynamics, random graphs, which define connectivity of neural circuit, and prime numbers, which define the dimension and category of cortical operation. Quantum computation is shown to ratify the main conclusion of the book: loosely connected small neural circuits facilitate higher information storage and processing capacities than highly connected large circuits. While these essentially separate mathematical notions have not been commonly involved in the evolution of neuroscience, they are shown in this book to be strongly inter-related in the cortical arena. Furthermore, neurophysiological experiments, as well as observations of natural behavior and evidence found in medical testing of neurologically impaired patients, are shown to support, and to be supported by the mathematical findings.Related Link(s)
Book Synopsis You Can Count on Monsters by : Richard Evan Schwartz
Download or read book You Can Count on Monsters written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2015-03-19 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique teaching tool that takes math lovers on a journey designed to motivate kids (and kids at heart) to learn the fun of factoring and prime numbers. This volume visually explores the concepts of factoring and the role of prime and composite numbers. The playful and colorful monsters are designed to give children (and even older audiences) an intuitive understanding of the building blocks of numbers and the basics of multiplication. The introduction and appendices can also help adult readers answer questions about factoring from their young audience. The artwork is crisp and creative and the colors are bright and engaging, making this volume a welcome deviation from standard math texts. Any person, regardless of age, can profit from reading this book. Readers will find themselves returning to its pages for a very long time, continually learning from and getting to know the monsters as their knowledge expands. You Can Count on Monsters is a magnificent addition for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the visually fascinating world of the numbers 1 through 100.
Download or read book Prime Numbers written by David Wells and published by Turner Publishing Company. This book was released on 2011-01-13 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematica®: A Problem-Centered Approach by : Roozbeh Hazrat
Download or read book Mathematica®: A Problem-Centered Approach written by Roozbeh Hazrat and published by Springer. This book was released on 2016-01-04 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked-out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool. This new edition has been extensively revised and updated, and includes new chapters with problems and worked examples.
Book Synopsis The Fundamental Theorem of Arithmetic by : Demetrios P Kanoussis Ph D
Download or read book The Fundamental Theorem of Arithmetic written by Demetrios P Kanoussis Ph D and published by Independently Published. This book was released on 2023-12-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A prime number is a natural number greater than 1, which cannot be expressed as a product of two smaller natural numbers. Stated differently, a prime number is a number divided only by 1 and by itself. No other natural number can divide a prime number. For example, the numbers: 2, 3, 5, 7, 11, 13, 17, 19, etc, are prime numbers. All the other numbers are called composite numbers. For example, the numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc, are composite numbers. The prime number 7 is divided by 1 and 7 only, while the composite number 12 is divided by 1, by 12, but also, by 2, and by 3, and by 4, and by 6. Prime numbers, despite their simple definition, still hide many secrets, and their intensive study has been the subject of many eminent mathematicians, for more than 25 centuries. Prime numbers and their properties were studied, for the first time, by the ancient Greeks. Euclid defined a prime number as "a number measured by a unit alone" and also gave the first proof that there are infinitely many prime numbers, (around 300 BC). Eratosthenes of Cyrene, around 200 BC, devised a procedure, (an algorithm), to find all the prime numbers less than a given natural number, (the sieve of Eratosthenes). The main problem with prime numbers is that the way they appear is highly irregular. There is no known formula, or method, to predict the next prime number from the preceding one. Great mathematicians, Gauss, Euler and Riemann among others, have made important contributions to the prime numbers, but, the main problem of finding a pattern as how the prime numbers are distributed, still, remains unsolved. There are also, many other unsolved problems concerning the prime numbers. One of them is the Goldbach's conjecture, that every even number greater than 2 can be expressed as the sum of two primes. Another famous unsolved problem is the twin prime conjecture, that there are infinitely many pairs of primes that differ by 2, (like 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc). Other unsolved problems concerning prime numbers and some historical remarks, like, Euclid's theorem, the sieve of Eratosthenes of Cyrene, Fermat numbers, etc, are discussed in section 3-4. Primes are of fundamental importance in number theory, because of the fundamental theorem of arithmetic: every natural number greater than 1, can be expressed as a product of prime numbers, and this product representation is unique. In this little book we provide a rigorous proof of this theorem and present some of its applications, (like for instance, to find the number of divisors and the sum of the divisors of any natural number, the perfect numbers and the amicable numbers). The material covered in the book is shown analytically in the table of contents. A comprehensive introduction to the prime numbers and some of its more important properties are presented, which are essential for the proof of the fundamental theorem. Solving problems with prime numbers is not an easy task. Most of the times, the solution requires ingenuity and imagination. Some other times, when a direct method of approach does not lead to the solution of the problem, we may proceed by contradiction, which is a popular and powerful method when working with prime numbers. The careful reader will find that many of the solved exercises have been solved by contradiction. The book contains 60 illustrative, solved exercises and 115 problems for solution.
Book Synopsis Prime Obsession by : John Derbyshire
Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Math Problems Notebook by : Valentin Boju
Download or read book The Math Problems Notebook written by Valentin Boju and published by Springer Science & Business Media. This book was released on 2007-08-15 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a collection of non-trivial, unconventional problems that require deep insight and imagination to solve. They cover many topics, including number theory, algebra, combinatorics, geometry and analysis. The problems start as simple exercises and become more difficult as the reader progresses through the book to become challenging enough even for the experienced problem solver. The introductory problems focus on the basic methods and tools while the advanced problems aim to develop problem solving techniques and intuition as well as promote further research in the area. Solutions are included for each problem.
Book Synopsis How Not to Be Wrong by : Jordan Ellenberg
Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Download or read book Friends' Review written by Enoch Lewis and published by . This book was released on 1869 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Closing the Gap written by Vicky Neale and published by Oxford University Press. This book was released on 2017-09-29 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career. Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers. Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.
Book Synopsis The Little Book of Bigger Primes by : Paulo Ribenboim
Download or read book The Little Book of Bigger Primes written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could have been called "Selections from the Book of Prime Number Records." However, I prefered the title which propelled you on the first place to open it, and perhaps (so I hope) to buy it! Richard K. Guy, with his winning ways, suggested the title to me, and I am grateful. But the book isn't very different from its parent. Like a bonsai, which has all the main characteristics of the full-sized tree, this little paperback should exert the same fatal attraction. I wish it to be as dangerous as the other one, in the saying of John Brillhart. I wish that you, young student, teacher or retired mathematician, engineer, computer buff, all of you who are friends of numbers, to be driven into thinking about the beautiful theory of prime numbers, with its inherent mystery. I wish you to exercise your brain and fingers-not vice-versa. But I do not wish you, specialist in number theory to look at this little book-most likely you have been eliminated from this shorter version-what a terrible feeling. But do not cry, you had your book already. This one is for those who will be taking over and should put their steps forward, mostly little, occasionally giant, to develop the science of numbers. Paulo Ribenboim Contents Preface vii Guiding the Reader xii Index of Notations xiii Introduction 1 1 How Many Prime Numbers Are There? 3 I. Euclid's Proof .. 3 11. Kummer's Proof 4 II. P6lya's Proof . .
Book Synopsis Puzzles, Paradoxes, and Problem Solving by : Marilyn A. Reba
Download or read book Puzzles, Paradoxes, and Problem Solving written by Marilyn A. Reba and published by CRC Press. This book was released on 2014-12-15 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text’s five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design. The text uses a core set of common representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches. Requiring no mathematical prerequisites, this book helps students explore creative mathematical thinking and enhance their own critical-thinking skills. Students will acquire quantitative literacy and appreciation of mathematics through the text’s unified approach and wide range of interesting applications.
