Download or read book Imagining Numbers written by Barry Mazur and published by Penguin UK. This book was released on 2004-03-25 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.
Download or read book Imagining Numbers written by Barry Mazur and published by Macmillan + ORM. This book was released on 2004-02-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: How the elusive imaginary number was first imagined, and how to imagine it yourself Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.
Download or read book The Book of Numbers written by John H. Conway and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL
Download or read book Mathematical Imagining written by Christof Weber and published by Taylor & Francis. This book was released on 2023-10-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imagine a plastic cup lying on the floor. Give the cup a nudge so that it begins to roll. What does the path it takes look like? So begins the journey that Christof Weber takes you on in Mathematical Imagining: A Routine for Secondary Classrooms . Along the way, he makes the case that the ability to imagine, manipulate, and explain mathematical images and situations is fundamental to all mathematics and particularly important to higher level study. Most importantly, drawing on years of experiments in his own classroom, Weber shows that mathematical imagining is a skill that can be taught efficiently and effectively. Mathematical Imagining describes an original routine that gives students space and time to imagine a mathematical situation and then revise, discuss, and act upon the mental images they create. You can use this creative routine to glimpse into your students' thinking and discover teaching opportunities, while empowering them to create their own mathematics.Inside you’ll find the following: An introduction to the routine including the rationale behind it, facilitation guidance, and classroom examples Modifications to implement the routine in your classroom, even with varying time constraints 37 exercises broken into four categories: constructions, problem-solving, reasoning, and paradoxes Discussions of the mathematics involved in each exercise, including possible follow-up questions Instructions on how to create your own exercises beyond the book This one-of-a-kind resource is for secondary teachers looking to inspire student creativity and curiosity, deepen their own subject matter knowledge and pedagogical content knowledge, and invite all students to access the power of their own mathematical imaginations.
Download or read book Making Numbers Count written by Chip Heath and published by Simon and Schuster. This book was released on 2022-01-11 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, practical, first-of-its-kind guide to communicating and understanding numbers and data—from bestselling business author Chip Heath. How much bigger is a billion than a million? Well, a million seconds is twelve days. A billion seconds is…thirty-two years. Understanding numbers is essential—but humans aren’t built to understand them. Until very recently, most languages had no words for numbers greater than five—anything from six to infinity was known as “lots.” While the numbers in our world have gotten increasingly complex, our brains are stuck in the past. How can we translate millions and billions and milliseconds and nanometers into things we can comprehend and use? Author Chip Heath has excelled at teaching others about making ideas stick and here, in Making Numbers Count, he outlines specific principles that reveal how to translate a number into our brain’s language. This book is filled with examples of extreme number makeovers, vivid before-and-after examples that take a dry number and present it in a way that people click in and say “Wow, now I get it!” You will learn principles such as: -SIMPLE PERSPECTIVE CUES: researchers at Microsoft found that adding one simple comparison sentence doubled how accurately users estimated statistics like population and area of countries. -VIVIDNESS: get perspective on the size of a nucleus by imagining a bee in a cathedral, or a pea in a racetrack, which are easier to envision than “1/100,000th of the size of an atom.” -CONVERT TO A PROCESS: capitalize on our intuitive sense of time (5 gigabytes of music storage turns into “2 months of commutes, without repeating a song”). -EMOTIONAL MEASURING STICKS: frame the number in a way that people already care about (“that medical protocol would save twice as many women as curing breast cancer”). Whether you’re interested in global problems like climate change, running a tech firm or a farm, or just explaining how many Cokes you’d have to drink if you burned calories like a hummingbird, this book will help math-lovers and math-haters alike translate the numbers that animate our world—allowing us to bring more data, more naturally, into decisions in our schools, our workplaces, and our society.
Download or read book Thinking In Numbers written by Daniel Tammet and published by Little, Brown Spark. This book was released on 2013-07-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The irresistibly engaging book that "enlarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers" (Oliver Sacks, MD). Thinking in Numbers is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired variously by the complexity of snowflakes, Anne Boleyn's eleven fingers, and his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. His provocative and inspiring new book will change the way you think about math and fire your imagination to view the world with fresh eyes.
Download or read book Really Big Numbers written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2014-06-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.
Download or read book Mathematics as Sign written by Brian Rotman and published by Stanford University Press. This book was released on 2000 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Rotman argues that mathematics is a vast and unique man-made imagination machine controlled by writing. It addresses both aspects—mental and linguistic—of this machine. The essays in this volume offer an insight into Rotman's project, one that has been called "one of the most original and important recent contributions to the philosophy of mathematics."
Download or read book The Story Of Numbers written by Asok Kumar Mallik and published by #N/A. This book was released on 2017-07-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: '… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
Download or read book Imagining the Creator God written by Georges De Schrijver and published by Wipf and Stock Publishers. This book was released on 2016-09-30 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since it was demonstrated in the 1920s that the universe, with its trillions of galaxies, is caught up in a process of steady expansion, it became evident that it must have originated from an "initial singularity," a "Big Bang," which gave rise to the formation of subatomic parts, atoms, molecules, clouds of gas, and finally, stars and galaxies. Running this expansion back in time, scientists began to reckon with the miracle of an evolving universe of which we are the outcome: the iron in our blood has been formed in the stars. This book gives an overview of the cosmologies that were in vogue in antiquity--the Jewish and Christian concepts of Creation, and the classical thinkers in Greek cosmology: Plato, Aristotle, and Ptolemy--and in modern times, Copernicus, Galileo, Kepler, and Newton. The book brings us right down to the present day with a careful and readable treatment of the scientific innovations inaugurated by Einstein and the specialists in quantum physics, and to recent developments in astrophysics. This path of exploration opens the avenue for imagining a Creator God who is so generous that he invites creation to share in his own creativity.
Download or read book Imagining Human Rights written by Susanne Kaul and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-09-25 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why is it that human rights are considered inviolable norms of justice at local and global scales although the number of their violations has steadily increased in modern history? On the surface, this paradox seems to be reducible to a straightforward discrepancy between idealism and reality in humanitarian affairs, but Imagining Human Rights complicates the picture by offering interdisciplinary perspectives on the imaginary status of human rights. By that the contributors mean not merely subject to imagination, open to interpretation or far too abstract, but also formative of a social imaginary with emphatic identifications and shared values. From a variety of disciplinary perspectives, they explore critical ways of engaging in rigorous interdisciplinary conversations about the origin and language of human rights, personal dignity, redistributive justice, and international solidarity. Together, they show how and why a careful examination of the intersection between disciplinary investigations is essential for imagining human rights at large. Examples range from the legitimacy of land ownership rights and the inadequacy of human faculty to make sense of mass violence in visual representation to the stewardship of human rights promoters and the genealogy of human rights.
Download or read book Symbols and Things written by Kevin Lambert and published by University of Pittsburgh Press. This book was released on 2021-10-12 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the steam-powered mechanical age of the eighteenth and nineteenth centuries, the work of late Georgian and early Victorian mathematicians depended on far more than the properties of number. British mathematicians came to rely on industrialized paper and pen manufacture, railways and mail, and the print industries of the book, disciplinary journal, magazine, and newspaper. Though not always physically present with one another, the characters central to this book—from George Green to William Rowan Hamilton—relied heavily on communication technologies as they developed their theories in consort with colleagues. The letters they exchanged, together with the equations, diagrams, tables, or pictures that filled their manuscripts and publications, were all tangible traces of abstract ideas that extended mathematicians into their social and material environment. Each chapter of this book explores a thing, or assembling of things, mathematicians needed to do their work—whether a textbook, museum, journal, library, diagram, notebook, or letter—all characteristic of the mid-nineteenth-century British taskscape, but also representative of great change to a discipline brought about by an industrialized world in motion.
Download or read book Divine Imagining written by Edward Douglas Fawcett and published by . This book was released on 1921 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Negative Math written by Alberto A. Martínez and published by Princeton University Press. This book was released on 2006 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores controversies in the history of numbers, especially the so-called negative and ''impossible'' numbers. This book uses history, puzzles, and lively debates to demonstrate how it is possible to devise new artificial systems of mathematical rules. It contends that departures from traditional rules can even be the basis for new applications.
Download or read book Analyzing Neural Time Series Data written by Mike X Cohen and published by MIT Press. This book was released on 2014-01-17 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the conceptual, mathematical, and implementational aspects of analyzing electrical brain signals, including data from MEG, EEG, and LFP recordings. This book offers a comprehensive guide to the theory and practice of analyzing electrical brain signals. It explains the conceptual, mathematical, and implementational (via Matlab programming) aspects of time-, time-frequency- and synchronization-based analyses of magnetoencephalography (MEG), electroencephalography (EEG), and local field potential (LFP) recordings from humans and nonhuman animals. It is the only book on the topic that covers both the theoretical background and the implementation in language that can be understood by readers without extensive formal training in mathematics, including cognitive scientists, neuroscientists, and psychologists. Readers who go through the book chapter by chapter and implement the examples in Matlab will develop an understanding of why and how analyses are performed, how to interpret results, what the methodological issues are, and how to perform single-subject-level and group-level analyses. Researchers who are familiar with using automated programs to perform advanced analyses will learn what happens when they click the “analyze now” button. The book provides sample data and downloadable Matlab code. Each of the 38 chapters covers one analysis topic, and these topics progress from simple to advanced. Most chapters conclude with exercises that further develop the material covered in the chapter. Many of the methods presented (including convolution, the Fourier transform, and Euler's formula) are fundamental and form the groundwork for other advanced data analysis methods. Readers who master the methods in the book will be well prepared to learn other approaches.
Download or read book Imagining the Internet written by Janna Quitney Anderson and published by Rowman & Littlefield Publishers. This book was released on 2005-07-21 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1990s, people predicted the death of privacy, an end to the current concept of 'property,' a paperless society, 500 channels of high-definition interactive television, world peace, and the extinction of the human race after a takeover engineered by intelligent machines. Imagining the Internet zeroes in on predictions about the Internet's future and revisits past predictions—and how they turned out. It gives the history of communications in a nutshell, illustrating the serious impact of pervasive networks and how they will change our lives over the next century.
Download or read book New Foundations for Classical Mechanics written by D. Hestenes and published by Springer Science & Business Media. This book was released on 2005-12-17 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: (revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
