Imagining Numbers
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Imagining Numbers
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Author : Barry Mazur
language : en
Publisher: Penguin UK
Release Date : 2004-03-25
Imagining Numbers written by Barry Mazur and has been published by Penguin UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-25 with Mathematics categories.
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.
Imagining Numbers
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Author : Barry Mazur
language : en
Publisher: Macmillan + ORM
Release Date : 2004-02-01
Imagining Numbers written by Barry Mazur and has been published by Macmillan + ORM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-01 with Mathematics categories.
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.
Mathematical Imagining
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Author : Christof Weber
language : en
Publisher: Taylor & Francis
Release Date : 2023-10-10
Mathematical Imagining written by Christof Weber and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Education categories.
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.
The Story Of Numbers
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Author : Asok Kumar Mallik
language : en
Publisher: #N/A
Release Date : 2017-07-27
The Story Of Numbers written by Asok Kumar Mallik and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-27 with Mathematics categories.
'… 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.
The Book Of Numbers
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Author : John H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Book Of Numbers written by John H. Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"...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
Complex Numbers And Vectors
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Author : Les Evans
language : en
Publisher: Aust Council for Ed Research
Release Date : 2006
Complex Numbers And Vectors written by Les Evans and has been published by Aust Council for Ed Research this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Electronic books categories.
Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries of complex numbers. The text includes historical and background material, discussion of key concepts, skills and processes, commentary on teaching and learning approaches, comprehensive illustrative examples with related tables, graphs and diagrams throughout, references for each chapter (text and web-based), student activities and sample solution notes, and an extensive bibliography.
Analyzing Neural Time Series Data
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Author : Mike X Cohen
language : en
Publisher: MIT Press
Release Date : 2014-01-17
Analyzing Neural Time Series Data written by Mike X Cohen and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-17 with Psychology categories.
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.
Algebra I All In One For Dummies
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Author : Mary Jane Sterling
language : en
Publisher: John Wiley & Sons
Release Date : 2021-11-18
Algebra I All In One For Dummies written by Mary Jane Sterling and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Mathematics categories.
Solve for ‘X’ with this practical and easy guide to everything algebra A solid understanding of algebra is the key to unlocking other areas of math and science that rely on the concepts and skills that happen in a foundational Algebra class. Algebra I All-In-One For Dummies is the key! With it, you’ll get everything you need to solve the mystery of Algebra I. This book proves that algebra is for everyone with straightforward, unit-based instruction, hundreds of examples and practice problems, and two quizzes for every chapter – one in the book and another (totally different!) online. From graph and word problems to the FOIL method and common algebra terminology, Algebra I All-In-One For Dummies walks you step-by-step through ALL the concepts you need to know to slay your Algebra I class. In this handy guide, you’ll also: Receive instruction and tips on how to handle basic and intermediate algebraic tasks such as factoring and equation simplification Banish math anxiety forever by developing an intuitive understanding of how algebra works Get a handle on graphing problems and functions, as well as inequalities and word problems Algebra I All-In-One For Dummies is a must-read for Algebra students looking for an everything-in-one-book supplement to their coursework, as well as anyone hoping to brush up on their math before tackling a related subject, such as physics, chemistry, or a more advanced math topic.
Symbols And Things
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Author : Kevin Lambert
language : en
Publisher: University of Pittsburgh Press
Release Date : 2021-10-12
Symbols And Things written by Kevin Lambert and has been published by University of Pittsburgh Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-12 with Mathematics categories.
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.
A Brief History Of Numbers
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Author : Leo Corry
language : en
Publisher: OUP Oxford
Release Date : 2015-08-27
A Brief History Of Numbers written by Leo Corry and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.