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Number Theory with Computations (Springer Undergraduate Mathematics Series)
by Peter ShiuThis introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of 𝜁(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.
Number Words and Number Symbols: A Cultural History of Numbers
by Karl MenningerThis book is not only a fascinating introduction to the concept of number and to numbers themselves, hut a multifaceted linguistic and historical analysis of how numbers have developed and evolved in many different cultures. Drawing on evidence from history, literature, philosophy and ethnology, noted German scholar Karl Menninger. recounts the development of numbers both as they are spoken (and written as words) and as symbolic abstract numerals that can he readily manipulated and combined.Despite the immense erudition the author brings to the topic, he maintains a light tone throughout, presenting much of the information in anecdotal form. Moreover, almost 300 illustrations (photographs and drawings) and many comparative language tables serve to enhance the text. The author begins with a lucid treatment of number sequence and number language, including the formation of number words in both Indo-European and non-IndoEuropean languages, hidden number words and the evolution of the number sequence. He then turns to written numerals and computations: finger counting, folk symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and more. The final section concerns the development of our modem decimal system, with its place notation and zero, based on the Indian number system, and its introduction to the West through the work of the Italian mathematician Fibonacci. The author concludes with a review of spoken numbers and number symbols in China and Japan.
Numbers: Their History and Meaning
by Graham FleggExtremely readable, jargon-free book for general readers traces the evolution of counting systems, from the primitive techniques of antiquity to computers. Text examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." -- Choice.
Numbers: Arithmetic and Computation
by Asok Kumar Mallik Amit Kumar DasThis book contains a number of elementary ideas on numbers, their representations, interesting arithmetical problems and their analytical solutions, fundamentals of computers and programming plus programming solutions as an alternative to the analytical solutions and much more.Spanning seven chapters, this book, while keeping its lucid storytelling verve, describes integers, real numbers and numerous interesting properties and historical references; followed by a good collection of arithmetic problems and their analytical solutions. Please note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Numbers (Picture This)
by Judith NouvionNumbers are everywhere in nature. From one tiny red-eyed frog to ten sweet and scruffy dogs, children will practice counting to ten all while finding out some fun facts about animals in our natural world. Vibrant photography and simple, fun read-aloud text make this board book a perfect first look at nonfiction for very new and curious learners! The Picture This series pairs learning concepts with extraordinary photographs of animals in their habitats. Check out all four books in the Picture This series: Colors, Homes, Numbers, and Shapes!
Numbers (Math Counts: Updated Editions)
by Henry PluckroseAn introduction to capacity for the youngest readers!Math Counts series introduces young readers (grades K-3) to early math concepts. Real-world examples and corresponding photos make math concepts easy to grasp.Numbers help us in many ways by giving us all types of information-from a person's addresses to the size of a dress and more.
Numbers: Their Tales, Types, and Treasures
by Alfred S. Posamentier Bernd ThallerDid you grow up thinking math is boring? It's time to reconsider. This book will teach you everything you ever wondered about numbers--and more.How and why did human beings first start using numbers at the dawn of history? Would numbers exist if we Homo sapiens weren't around to discover them? What's so special about weird numbers like pi and the Fibonacci sequence? What about rational, irrational, real, and imaginary numbers? Why do we need them?Two veteran math educators explain it all in ways even the most math phobic will find appealing and understandable. You'll never look at those squiggles on your calculator the same again.From the Trade Paperback edition.
Numbers: 10 Things You Should Know
by Colin StuartUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.Our world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut cake the wrong way? How can there be different sizes of infinity?All these questions and more are answered in this engaging romp through the history of numbers by acclaimed science writer, Colin Stuart. From the mathematicians who have (and haven't) shouted 'Eureka!' to the theories that affect and inform our everyday lives; Numbers shows us that maths was never boring - we were just being taught it in the wrong way.Consisting of ten bite-sized essays, there's no better guide to this fundamental science.
Numbers: 10 Things You Should Know
by Colin StuartUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.Our world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut cake the wrong way? How can there be different sizes of infinity?All these questions and more are answered in this engaging romp through the history of numbers by acclaimed science writer, Colin Stuart. From the mathematicians who have (and haven't) shouted 'Eureka!' to the theories that affect and inform our everyday lives; Numbers shows us that maths was never boring - we were just being taught it in the wrong way.Consisting of ten bite-sized essays, there's no better guide to this fundamental science.
Numbers
by Paul ThurlbyAn incredibly stylish numbers book - perfect for children and adults alike.Have fun with numbers with an award-winning illustrator. Paul creates an amazing world where each number becomes its word. From '3 for 3D' and '5 for high five' to '10 for a perfect 10', each number is familiar, yet unique. Praise for Alphabet: 'Skilfully constructed and cleverley composed, it's an awesome alphabet book that adults will also appreciate.' Kirkus Reviews'Paul Thurlby's prints are so ludicrously beautiful that I am seriously tempted to blow the budget, order the whole lot and paper a wall with them.' India Knight, journalist and author
Numbers: Histories, Mysteries, Theories (Aurora: Dover Modern Math Originals)
by John J. Watkins Albrecht Beutelspacher Andrea Bruder Andrea EasterdayPosing the question "What exactly is a number?" a distinguished German mathematician presents this intriguing and accessible survey. Albrecht Beutelspacher ― founder of the renowned interactive mathematics museum, Mathematikum ― characterizes the wealth of experiences that numbers have to offer. In addition, he considers the many things that can be described by numbers and discusses which numbers possess special fascinations and pose lasting mysteries. Starting with natural numbers, the book examines representations of numbers, rational and irrational numbers, transcendental numbers, and imaginary and complex numbers. Readers will explore the history of numbers from Pythagoras to Fermat and discover such practical applications as cryptography and barcodes. A thoughtful and enlightening introduction to the past, present, and future of numbers, this volume will captivate mathematicians and nonmathematicians alike.
Numbers and Computers
by Ronald T. KneuselThis is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, floating point numbers, big integers and rational arithmetic. This book is for anyone who develops software including software engineerings, scientists, computer science students, engineering students and anyone who programs for fun.
Numbers and Computers
by Ronald T. KneuselThis is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second examines several other number representations. Details are explained thoroughly, with clarity and specificity. Each chapter ends with a summary, recommendations, carefully selected references, and exercises to review the key points. Topics covered include interval arithmetic, fixed-point numbers, big integers and rational arithmetic. This new edition has three new chapters: Pitfalls of Floating-Point Numbers (and How to Avoid Them), Arbitrary Precision Floating Point, and Other Number Systems. This book is for anyone who develops software including software engineers, scientists, computer science students, engineering students and anyone who programs for fun.
Numbers and Functions
by R. P. BurnThe transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this new edition of Numbers and Functions, Dr Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.
Numbers and Other Math Ideas Come Alive
by Theoni PappasMost people don't think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive. Pappas explores mathematical ideas by looking behind the scenes of what numbers, points, lines, and other concepts are saying and thinking. In each story, properties and characteristics of math ideas are entertainingly uncovered and explained through the dialogues and actions of its math characters. In fact, you forget that you are actually learning mathematics as you get caught up in the characters' private lives, secrets and how they interact with one another. You may even forget that these math actors come from the imaginary worlds of mathematics. They seem so real! This is the crux of Numbers and Other Math Ideas Come Alive -- number and math ideas tell their own stories in their own words. As you read these stories you will be amazed at how math ideas come to life and develop their own personalities. We learn about their foibles and strengths, and see why mathematicians had to develop new concepts when the old ones were not sufficient for the problems at hand. You'll see how mathematics is constantly evolving. How new numbers appeared, and old ones were reticent to accept the newcomers. How certain math ideas lay hidden for centuries, until they were resurrected or discovered by a mathematician. Love, hate, jealousy, excitement--all emotions we associate with human behavior are taken on by these math characters. You will come away learning how indispensable these math ideas and their roles are in our world today.
Numbers and Stories: Using Children's Literature to Teach Young Children Number Sense
by Ms Rita C. Janes Ms Elizabeth L. StrongCount on children’s books to build number sense! Math and reading go hand in hand, especially among children who are new to both. If you’re looking for a surefire way to build number sense and reading skills at the very same time, rely on this indispensable K-2 resource. Using children’s books as a springboard for learning, it provides 22 ready-to-use lessons—all aligned to the Common Core Standards for Math and ELA. Inside you’ll find 22 interactive, research-based mathematics investigations High-quality children’s book selections Reflection and discussion questions and prompts for both teachers and students Children’s work pages and formative assessment tools An online facilitator’s guide
Numbers and Symmetry: An Introduction to Algebra
by Bernard L. JohnstonThis textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism.Designed for a typical one-semester undergraduate course in modern algebra, it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples, rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures, such as the Gaussian integers and the various rings of integers modulo n, and is encouraged to take the time to explore and become familiar with those structures.In terms of classical algebraic structures, the text divides roughly into three parts:
Numbers Are Forever
by Liz StrachanThis book is only about numbers - that is, whole numbers and nothing but the whole numbers, which start from from 0, 1, 2, 3, 4... and go on forever. Here you can meet perfect numbers, happy numbers, lucky, untouchable, weird, narcissistic, evil and deficient numbers, not to mention nice Friedmans and multi-legged repunits, as well as primes and their cousins, the sexy primes. It is also full of fascinating facts and curios, prime number conjectures, the sieve of Eratosthenes, the Fibonacci series, and much more besides. This is an accessible, clearly explained approach which will appeal to recreational maths enthusiasts, puzzle solvers, and mathematicians of all ages.
Numbers Are Forever
by Liz StrachanThis book is only about numbers - that is, whole numbers and nothing but the whole numbers, which start from from 0, 1, 2, 3, 4... and go on forever. Here you can meet perfect numbers, happy numbers, lucky, untouchable, weird, narcissistic, evil and deficient numbers, not to mention nice Friedmans and multi-legged repunits, as well as primes and their cousins, the sexy primes. It is also full of fascinating facts and curios, prime number conjectures, the sieve of Eratosthenes, the Fibonacci series, and much more besides. This is an accessible, clearly explained approach which will appeal to recreational maths enthusiasts, puzzle solvers, and mathematicians of all ages.
Numbers at Work: A Cultural Perspective
by Rudolf TaschnerDrawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, pol
The Numbers Behind NUMB3RS
by Keith Devlin Gary LordenThe companion to the hit CBS crime series Numb3rs presents the fascinating way mathematics is used to fight real-life crime Using the popular CBS prime-time TV crime series Numb3rs as a springboard, Keith Devlin (known to millions of NPR listeners as ?the Math Guy? on NPR?s Weekend Edition with Scott Simon) and Gary Lorden (the principal math advisor to Numb3rs) explain real-life mathematical techniques used by the FBI and other law enforcement agencies to catch and convict criminals. From forensics to counterterrorism, the Riemann hypothesis to image enhancement, solving murders to beating casinos, Devlin and Lorden present compelling cases that illustrate how advanced mathematics can be used in state-of-the-art criminal investigations.
The Numbers Behind Numb3rs
by Keith Devlin Gary LordenThe companion to the hit CBS crime series Numb3rs presents the fascinating way mathematics is used to fight real-life crime Using the popular CBS prime-time TV crime series Numb3rs as a springboard, Keith Devlin (known to millions of NPR listeners as ?the Math Guy? on NPR?s Weekend Edition with Scott Simon) and Gary Lorden (the principal math advisor to Numb3rs) explain real-life mathematical techniques used by the FBI and other law enforcement agencies to catch and convict criminals. From forensics to counterterrorism, the Riemann hypothesis to image enhancement, solving murders to beating casinos, Devlin and Lorden present compelling cases that illustrate how advanced mathematics can be used in state-of-the-art criminal investigations. .
Numbers Don't Lie: 71 Stories to Help Us Understand the Modern World
by Vaclav Smil"There is no author whose books I look forward to more than Vaclav Smil."--Bill GatesAn essential guide to understanding how numbers reveal the true state of our world--exploring a wide range of topics including energy, the environment, technology, transportation, and food production.Vaclav Smil's mission is to make facts matter. An environmental scientist, policy analyst, and a hugely prolific author, he is Bill Gates' go-to guy for making sense of our world. In Numbers Don't Lie, Smil answers questions such as: What's worse for the environment--your car or your phone? How much do the world's cows weigh (and what does it matter)? And what makes people happy? From data about our societies and populations, through measures of the fuels and foods that energize them, to the impact of transportation and inventions of our modern world--and how all of this affects the planet itself--in Numbers Don't Lie, Vaclav Smil takes us on a fact-finding adventure, using surprising statistics and illuminating graphs to challenge conventional thinking. Packed with fascinating information and memorable examples, Numbers Don't Lie reveals how the US is leading a rising worldwide trend in chicken consumption, that vaccination yields the best return on investment, and why electric cars aren't as great as we think (yet). Urgent and essential, with a mix of science, history, and wit--all in bite-sized chapters on a broad range of topics--Numbers Don't Lie inspires readers to interrogate what they take to be true.
The Numbers Game
by Michael Blastland Andrew DilnotThe Strunk and White of statistics team up to help the average person navigate the numbers in the news Drawing on their hugely popular BBC Radio 4 show More or Less, journalist Michael Blastland and internationally known economist Andrew Dilnot delight, amuse, and convert American mathphobes by showing how our everyday experiences make sense of numbers. The radical premise of The Numbers Game is to show how much we already know and give practical ways to use our knowledge to become cannier consumers of the media. If you've ever wondered what "average" really means, whether the scare stories about cancer risk should convince you to change your behavior, or whether a story you read in the paper is biased (and how), you need this book. Blastland and Dilnot show how to survive and thrive on the torrent of numbers that pours through everyday life.
The Numbers Game: Baseball's Lifelong Fascination with Statistics
by Alan SchwarzThe Numbers Game is the first-ever history of baseball statistics - the keeping of them, the study of them, the people who devised them, the cultural phenomenon of them, from 1845 until today.Most baseball fans, players and even team executives assume that the National Pastime's infatuation with statistics is simply a byproduct of the information age, a phenomenon that blossomed only after the arrival of Bill James and computers in the 1980s. They couldn't be more wrong.In this unprecedented new book, Alan Schwarz - whom bestselling Moneyball author Michael Lewis calls "one of today's best baseball journalists" - provides the first-ever history of baseball statistics, showing how baseball and its numbers have been inseparable ever since the pastime's birth in 1845. He tells the history of this obsession through the lives of the people who felt it most: Henry Chadwick, the 19th-century writer who invented the first box score and harped endlessly about which statistics mattered and which did not; Allan Roth, Branch Rickey's right-hand numbers man with the late-1940s Brooklyn Dodgers; Earnshaw Cook, a scientist and Manhattan Project veteran who retired to pursue inventing the perfect baseball statistic; John Dewan, a former Strat-O-Matic maven who built STATS Inc. into a multimillion-dollar powerhouse for statistics over the Internet; and dozens more.Almost every baseball fan for 150 years has been drawn to the game by its statistics, whether through newspaper box scores, the backs of Topps baseball cards, The Baseball Encyclopedia, or fantasy leagues. Today's most ardent stat scientists, known as "sabermetricians," spend hundreds of hours coming up with new ways to capture the game in numbers, and engage in holy wars over which statistics are best. Some of these men--and women --are even being hired by major league teams to bring an understanding of statistics to a sport that for so long shunned it.Taken together, Schwarz paints a history not just of baseball statistics, but of the soul of the sport itself. The Numbers Game will be an invaluable part of any fan's library and go down as one of the sport's classic books.