Mathematical Curiosities
An innovative and appealing way for the layperson to develop math skills--while actually enjoying itMost people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill.The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum. The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions.If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.
No Bullshit Guide to Math and Physics
Often calculus and mechanics are taught as separate subjects. It shouldn't be like that. Learning calculus without mechanics is incredibly boring. Learning mechanics without calculus is missing the point. This textbook integrates both subjects and highlights the profound connections between them. This is the deal. Give me 350 pages of your attention, and I'll teach you everything you need to know about functions, limits, derivatives, integrals, vectors, forces, and accelerations. This book is the only math book you'll need for the first semester of undergraduate studies in science. With concise, jargon-free lessons on topics in math and physics, each section covers one concept at the level required for a first-year university course. Anyone can pick up this book and become proficient in calculus and mechanics, regardless of their mathematical background.
The Siddhantasundara of J鎙naraja
The first English translation of this major work of classical Indian astronomy and mathematics.A treasure for anyone interested in early modern India and the history of mathematics, this first English translation of the Siddhantasundara reveals the fascinating work of the scholar-astronomer J簽anaraja (circa 1500 C.E.). Toke Lindegaard Knudsen begins with an introduction to the traditions of ancient Hindu astronomy and describes what is known of J簽anaraja's life and family. He translates the Sanskrit verses into English and offers expert commentary on the style and substance of J簽anaraja's treatise.The Siddhantasundara contains a comprehensive exposition of the system of Indian astronomy, including how to compute planetary positions and eclipses. It also explores deep, probing questions about the workings of the universe and sacred Hindu traditions. In a philosophical discussion, the treatise seeks a synthesis between the cosmological model used by the Indian astronomical tradition and the cosmology of a class of texts sacred in Hinduism. In his discourse, which includes a discussion of the direction of down and adhesive antipodeans, J簽anaraja rejects certain principles from the astronomical tradition and reinterprets principles from the sacred texts. He also constructs a complex poem on the seasons, many verses of which have two layers of meaning, one describing a season, the other a god's activities in that season. The Siddhantasundara is the last major treatise of Indian astronomy and cosmology to receive serious scholarly attention, Knudsen's careful effort unveils the 500-year-old Sanskrit verses and shows the clever quirkiness of J簽anaraja's writing style, his keen use of mathematics, and his subtle philosophical arguments.
A Beginner's Guide to Mathematical Logic
Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems.Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.
Slide Rules
In the hopes of "preserving these delightful devices for future generations," this collector of slide rules covers everything one could possibly want to know about this crude form of analog computer: from its invention in the 17th century to manufacturers- retailers, 1850-1998, and the Oughtred Society for collectors. Includes a glossary with biographies, patent data, component specs, dating and valuing, care, historical milestones, and illustrations
Why Is There Philosophy of Mathematics at All?
This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Mathematics Activities for Elementary Teachers
This resource provides hands-on, manipulative-based activities keyed to the text that involve future elementary school teachers discovering concepts, solving problems, and exploring mathematical ideas. These activities can be adapted for use with elementary students at a later time. Colorful, perforated paper manipulatives are provided in a convenient pouch at the back of the manual.
The Rainbow of Mathematics
He charts the growth of mathematics through its refinement by ancient Greeks and then medieval Arabs, to its systematic development by Europeans from the Middle Ages to the early twentieth century. This book describes the evolution of arithmetic and geometry, trigonometry and algebra; the interplay between mathematics, physics, and mathematical astronomy; and "new" branches such as probability and statistics. Authoritative and comprehensive, The Rainbow of Mathematics is a unique account of the development of the science that is at the heart of so many other sciences. Originally published under the title The Norton History of the Mathematical Sciences.
The Joy of X
"Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!"--Scientific AmericanMany people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how real-world math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the accessible math teacher you wish you'd had. Whether you aced integral calculus or aren't sure what an integer is, you'll find profound wisdom and persistent delight in The Joy of x.This witty and insightful guide to the big ideas in mathematics reveals: Math in Everyday Life: From how often you should flip your mattress to the surprising principles behind how Google searches the internet.Big Ideas Made Simple: Clear, unforgettable explanations of major concepts like calculus and the Pythagorean theorem, illuminated with brilliant examples.Accessible for Everyone: Whether you aced integral calculus or aren't sure what an integer is, Steven Strogatz is the brilliant and patient teacher you wish you'd had.Unexpected Connections: Discover how mathematical principles connect to pop culture, medicine, law, philosophy, and even the art of settling down.
Operational Calculus and Generalized Functions
This brief monograph by a distinguished professor is based on a mathematics course offered at the California Institute of Technology. The majority of students taking this course were advanced undergraduates and graduate students of engineering. A solid background in advanced calculus is a prerequisite.Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, and exponential functions of operators. Tools developed in the preceding chapters are then applied to problems in partial differential equations. Solutions to selected problems appear at the end of the book.
An Introduction to Phase-Integral Methods
The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.
Math for Real Life for Dummies
The easy way to brush up on the math skills you need in real life Not everyone retains the math they learned in school. Like any skill, your ability to speak "math" can deteriorate if left unused. From adding and subtracting money in a bank account to figuring out the number of shingles to put on a roof, math in all of its forms factors into daily life. Math For Real Life For Dummies provides you with the simple formulas and theorems that you're likely to encounter in the workplace, the kitchen, and even when playing games. You can turn to Math For Real Life For Dummies to brush up on your math skills or to handle everyday encounters, like calculating restaurant tips, understanding interest rates, and figuring out percentages and odds. Packed with real-world examples that make sense, Math For Real Life For Dummies takes the stress out of your daily calculation encounters. Provides tips for understanding and using basic mathematical concepts Shows you how math helps the mind to reason and organize complicated situations or problems into clear, simple, and logical steps Covers all of the math skills you're likely to need in everyday situations If you're looking for a practical, plain-English guide to mastering everyday math skills, Math For Real Life For Dummies has you covered.
Trigonometric Delights
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights. ? Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.
An Introduction to Mathematical Logic
Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy. An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of G繹del, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.
Games and Mathematics
The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.
The Best Writing on Mathematics 2012
The year's finest writing on mathematics from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The Geometer's Sketchpad, Exploring Geometry
Dynamic Geometry(R) software enriches the study of high school geometry, and its use is recommended in the Common Core State Standards. This collection of Sketchpad activities is aligned to the High School Geometry Common Core State Standards, and covers virtually every concept studied in high school geometry. The activities will help your students visualize geometry concepts, make and test conjectures and justify their conclusions, and deeply explore content related to: - constructing geometric figures- transformations and tessellations- areas of polygons and circles- introductory trigonometry- modeling with mathematics
Exploring Plane and Solid Geometry in Grades 6-8 With the Geometer's Sketchpad Version 5
Ancient and Modern Mathematics
Discover modern solutions to ancient mathematical problems with this engaging guide, written by a mathematics enthusiast originally from South Vietnam. Author Dat Phung To provides a theory that defines the compositions of partial permutations. To help you apply it, he looks back at the ancient mathematicians who solved challenging problems. Unlike people today, the scholars who lived in the ancient world didn't have calculators and computers to help answer complicated questions. Even so, they still achieved great works, and their methods continue to hold relevance. In this textbook, you'll find fourteen ancient problems along with their solutions. The problems are arranged from easiest to toughest, so you can focus on building your knowledge as you progress through the text. Fourteen Ancient Problems also explores partial permutations theory, a mathematical discovery that has many applications. It provides a specific and unique method to write down the whole expansion of nPn = n! into single permutations with n being a finite number. Take a thrilling journey throughout the ancient world, discover an important theory, and build upon your knowledge of mathematics with Fourteen Ancient Problems.
Ancient and Modern Mathematics
Discover modern solutions to ancient mathematical problems with this engaging guide, written by a mathematics enthusiast originally from South Vietnam. Author Dat Phung To provides a theory that defines the compositions of partial permutations. To help you apply it, he looks back at the ancient mathematicians who solved challenging problems. Unlike people today, the scholars who lived in the ancient world didn't have calculators and computers to help answer complicated questions. Even so, they still achieved great works, and their methods continue to hold relevance. In this textbook, you'll find fourteen ancient problems along with their solutions. The problems are arranged from easiest to toughest, so you can focus on building your knowledge as you progress through the text. Fourteen Ancient Problems also explores partial permutations theory, a mathematical discovery that has many applications. It provides a specific and unique method to write down the whole expansion of nPn = n! into single permutations with n being a finite number. Take a thrilling journey throughout the ancient world, discover an important theory, and build upon your knowledge of mathematics with Fourteen Ancient Problems.
The Music of the Primes
Inthe tradition of Fermat's Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics--the formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes "an amazing book. . . . I could not put it down once Ihad started." Simon Winchester, author of The Professor and the Madman, writes, "this fascinating account, decoding the inscrutable language of themathematical priesthood, is written like the purest poetry. Marcus du Sautoy's enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe."
Everyday Math DeMystified
Solve your math troubles with DeMYSTiFieD If you cannot tell the difference between your Roman and Arabic numerals, or if when someone asks 'what is pi' you say "delicious," you need Everyday Math DeMYSTiFieD, Second Edition, to unravel these fundamental concepts and theories at your own pace. This practical guide eases you into basic math, starting with counting and simple operations. As you progress, you will master essential concepts such as division, converting decimals into fractions, determining volume, and more. You will learn to measure capital gains and losses as well as apply percentages in the real world. Detailed examples make it easy to understand the material, and end-of- chapter quizzes and a final exam help reinforce key ideas. It's a no-brainer! You'll learn about: Decimals Proportions Prime numbers Surface area Powers of 10 Graphs English vs. metric units Simple enough for a beginner but challenging enough for an advanced student, Everyday Math DeMYSTiFieD, Second Edition, helps you master this essential subject.
Philosophical Papers: Volume 1, Mathematics, Matter and Method
Professor Hilary Putnam has been one of the most influential and sharply original of recent American philosophers in a whole range of fields. His most important published work is collected here, together with several new and substantial studies, in two volumes. The first deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry; the second deals with the philosophy of language and mind. Volume one is now issued in a new edition, including an essay on the philosophy of logic first published in 1971.
Show Me the Numbers
Addressing the prevalent issue of poorly designed quantitative information presentations, this accessible, practical, and comprehensive guide teaches how to properly create tables and graphs for effective and efficient communication. The critical numbers that measure the health, identify the opportunities, and forecast the future of organizations are often misrepresented because few people are trained to design accurate, informative materials, but this manual helps put an end to misinformation. This revised edition of the highly successful book includes updated figures and 91 additional pages of content, including new chapters about quantitative narrative and current misuses of graphs--such as donut, circle, unit, and funnel charts--and new appendices that cover constructing table lens displays and box plots in Excel and useful color palettes for presentation materials.
Trigonometry Demystified 2/E
DeMYSTiFieD is your solution for tricky subjects like trigonometry If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extreme exaggeration, you need Trigonometry DeMYSTiFieD, Second Edition, to unravel this topic's fundamental concepts and theories at your own pace. This practical guide eases you into "trig," starting with angles and triangles. As you progress, you will master essential concepts such as mapping, functions, vectors, and more. You will learn to transform polar coordinates as well as apply trigonometry in the real world. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas. It's a no-brainer! You'll learn about: Right triangles Circular functions Hyperbolic functions Inverse functions Geometrical optics Infinite-series expansions Trigonometry on a sphere Simple enough for a beginner, but challenging enough for an advanced student, Trigonometry DeMYSTiFieD, Second Edition, helps you master this essential subject.
Alan M. Turing
'In a short life he accomplished much, and to the roll of great names in the history of his particular studies added his own.' So is described one of the greatest figures of the twentieth century, yet Alan Turing's name was not widely recognised until his contribution to the breaking of the German Enigma code became public in the 1970s. The story of Turing's life fascinates and in the years since his suicide, Turing's reputation has only grown, as his contributions to logic, mathematics, computing, artificial intelligence and computational biology have become better appreciated. To commemorate the centenary of Turing's birth, this republication of his mother's biography is enriched by a new foreword by Martin Davis and a never-before-published memoir by Alan's older brother. The contrast between this memoir and the original biography reveals tensions and sheds new light on Turing's relationship with his family, and on the man himself.
The History of Mathematics: A Very Short Introduction
This Very Short Introduction explores the rich historical and cultural diversity of mathematical practice, ranging from the distant past to the present. Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.
The Cartoon Guide to Calculus
"In Gonick's work, clever design and illustration make complicated ideas or insights strikingly clear."--New York Times Book ReviewLarry Gonick, master cartoonist, former Harvard instructor, and creator of the New York Times bestselling, Harvey Award-winning Cartoon Guide series now does for calculus what he previously did for science and history: making a complex subject comprehensible, fascinating, and fun through witty text and light-hearted graphics. Gonick's The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.
Math for the Frightened
There's something about a language of symbols and equations that most people find intimidating. Mathematician Colin Pask gently introduces you to the main ideas of mathematics and painlessly demonstrates how they are expressed in terms of symbols. He teaches the reader not onlywhy symbols are used, and how and why equations are constructed, but also exactly what is achieved by doing that. Through simple yet intriguing examples in number theory, Pask generates confidence in thinking mathematically and reveals the pleasure of seeing how mathematical patterns evolve and are explored.
Practice Makes Perfect Precalculus
Don't be perplexed by precalculus. Master this math with practice, practice, practice! Practice Makes Perfect: Precalculus is a comprehensive guide and workbook that covers all the basics of precalculus that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples, so you can learn at your own pace and really absorb the information. You get to apply your knowledge and practice what you've learned through a variety of exercises, with an answer key for instant feedback. Offering a winning solution for getting a handle on math right away, Practice Makes Perfect: Precalculus is your ultimate resource for building a solid understanding of precalculus fundamentals.
Die Keplersche Vermutung
Sir Walter Raleigh wollte wissen, wie Kanonenkugeln in einem Schiff am dichtesten gestapelt werden k繹nnen. Der Astronom Johannes Kepler lieferte im Jahr 1611 die Antwort: genau so, wie Gem羹seh瓣ndler ihre Orangen und Tomaten aufstapeln. Noch war dies lediglich eine Vermutung - erst 1998 gelang dem amerikanischen Mathematiker Thomas Hales mit Hilfe von Computern der mathematische Beweis. Einer der besten Autoren f羹r popul瓣rwissenschaftliche Mathematik beschreibt auf faszinierende Art und Weise ein ber羹hmtes mathematisches Problem und dessen L繹sung.
Die Verflixte Mathematik Der Demokratie
Die verflixte Mathematik der Demokratie ist eine Erl瓣uterung und historische Einf羹hrung in die Probleme, die in einer Demokratie entstehen k繹nnen. Die Mehrheitswahl und die Zuteilung von Sitzen in einem Parlament werfen mathematische Fragen auf, zu deren Beschreibung zwar nicht mehr als Arithmetik ben繹tigt wird, deren L繹sung aber 羹berraschend schwierig oder sogar unm繹glich ist. Das sogenannte Condorcet Paradoxon zeigt zum Beispiel, dass eine Mehrheitswahl zu scheinbar widersinnigen Resultaten f羹hren kann. Und wie viele Sitze sollen zum Beispiel einer Partei im Parlament zugeteilt werden, die 23,6 Prozent der Stimmen erhielt? Die Erz瓣hlung beginnt mit den alten Griechen und R繹mern und f羹hrt 羹ber mittelalterliche Kirchenherren, Pers繹nlichkeiten der franz繹sischen Revolution und die amerikanischen Gr羹ndungsv瓣ter bis zu heutigen Nobelpreistr瓣gern. Sowohl f羹r allgemein interessierte Leser als auch Studierende der politischen Wissenschaften und der Wirtschaftswissenschaften wird das Buch von gro?em Interesse sein.
Here's Looking at Euclid
Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place." Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games. Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here's Looking at Euclid is a rare gem that brings the beauty of math to life.
The Calculus of Friendship
The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.
The Triumph of Numbers
The great historian of science I. B. Cohen explores how numbers have come to assume a leading role in science, in the operations and structure of government, in marketing, and in many other aspects of daily life. Consulting and collecting numbers has been a feature of human affairs since antiquity--taxes, head counts for military service--but not until the Scientific Revolution in the twelfth century did social numbers such as births, deaths, and marriages begin to be analyzed. Cohen shines a new light on familiar figures such as Thomas Jefferson, Benjamin Franklin, and Charles Dickens; and he reveals Florence Nightingale to be a passionate statistician. Cohen has left us with an engaging and accessible history of numbers, an appreciation of the essential nature of statistics.
A History of Mathematics
The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincar矇 Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincar矇 and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
The Laplace Transform
The theory of integral operators constitutes a major branch of analysis, and transforms represent an important subdivision. This volume focuses on the Laplace and Stieltjes transforms. Highly theoretical in its emphasis, this classic treatment was derived from a series of lectures by a prominent Harvard mathematician.Suitable for graduate-level mathematics majors, this introductory text explores fundamental formulas, the moment problem, monotonic functions, and Tauberian theorems. The Bulletin of the American Mathematical Society praised it as "extremely satisfactory," noting that "it will have a most valuable effect both on research and graduate study."
The Best Writing on Mathematics
The year's most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else-and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us-and where it's headed.
Scattered Matherticles
The volume comprises author's mathematical writings through the year, 2006. Though nearly 80 % of Mathematical Reflections were written since 2003, a few, modified from certain articles, go back to the 1980's. However, the subjects are time independent. The kernels of the Reflections are drawn from everyday classrooms to mathematical conventions attended. The style is compact wrapping a couple of strands around a central theme. Some of the Reflections, like Calculus Defines Civilization, have been widely circulated. A few have been published in the Focus, the newsletter of the Mathematical Association of America. They are all fine-tuned after getting feedback from 100-strong readers on my e-mailing list. The Rise of Bernoullis and Hopitals has a predictive element in it, as it is very common today in the academe where research, over teaching, carries all the marbles. A few Reflections are centered on individuals including my colleagues, students, and teachers. Perhaps, one or two may be mathematically x-rated. There is a unique blend of mathematics as a language with English of which the author has his own stamp. The book is an easy reading for its small bites. However, it is the chewing part of a Reflection that uncovers its soul.
Instructor's Manual to Euclidean Geometry
This book is a companion to the textbook Euclidean Geometry: a First Course by Mark Solomonovich. The main part of the manual contains 70 additional detailed solutions that can be used for tests and home assignments. Also included are some comments and tests with solutions to the first two chapters, which may facilitate the reading and getting accustomed to the language of the subject. Lastly, it contains lists of all the axioms, on which the discussion is based, as well as all the theorems derived in the textbook and other major results, such as basic constructions.
The Square Root of 2
Using no more than the most basic algebra and geometry, Flannery (Cork Institute of Technology, Ireland) manages to convey not only why irrational numbers are fascinating, but how the whole enterprise of mathematical thinking is imaginative, intriguing, and engaging. A startlingly original and informative dialog, this book is a one-of-a-kind introduction to the pleasure and playful beauty of mathematical thinking.
A Mathematical Tapestry
This easy-to-read book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.
