Students, researchers, historians, specialists — in short, everyone with an interest in mathematics — will find it engrossing and stimulating.Beginning with the ancient Near East, the author traces the ideas and techniques developed in Egypt, Babylonia, China, and Arabia, looking into such manuscripts as the Egyptian Papyrus Rhind, the Ten Classics of China, and the Siddhantas of India. He considers Greek and Roman developments from their beginnings in Ionian rationalism to the fall of Constantinople; covers medieval European ideas and Renaissance trends; analyzes 17th- and 18th-century contributions; and offers an illuminating exposition of 19th century concepts. Every important figure in mathematical history is dealt with — Euclid, Archimedes, Diophantus, Omar Khayyam, Boethius, Fermat, Pascal, Newton, Leibniz, Fourier, Gauss, Riemann, Cantor, and many others.For this latest edition, Dr. Struik has both revised and updated the existing text, and also added a new chapter on the mathematics of the first half of the 20th century. Concise coverage is given to set theory, the influence of relativity and quantum theory, tensor calculus, the Lebesgue integral, the calculus of variations, and other important ideas and concepts. The book concludes with the beginnings of the computer era and the seminal work of von Neumann, Turing, Wiener, and others."The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature Magazine.

    Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard).With this volume Descartes founded modern analytical geometry. Reducing geometry to algebra and analysis and, conversely, showing that analysis may be translated into geometry, it opened the way for modern mathematics. Descartes was the first to classify curves systematically and to demonstrate algebraic solution of geometric curves. His geometric interpretation of negative quantities led to later concepts of continuity and the theory of function. The third book contains important contributions to the theory of equations.This edition contains the entire definitive Smith-Latham translation of Descartes' three books: Problems the Construction of which Requires Only Straight Lines and Circles; On the Nature of Curved Lines; and On the Construction of Solid and Supersolid Problems. Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography.

    The book encourages a critical discussion of the different approaches and looks at some of the most important thinkers and their influence.

    Worked examples and exercises support the text. An ELBS/LPBB edition is available.

    Escher, I am absolutely crazy about your work. In your print Reptiles you have given such a striking illustration of reincarnation.' I replied, 'Madame, if that's the way you see it, so be it, '" An engagingly sly comment by the renowned Dutch graphic artist Maurits Cornelis Escher (1898-1972)--the complex ambiguities of whose work leave hasty or single-minded interpretations far behind. Long before the first computer-generated 3-D images were thrilling the public, Escher was a master of the third dimension. His lithograph "Magic Mirror" dates as far back as 1946. In taking that title for this book, mathematician Bruno Ernst is stressing the magic spell Escher's work invariably casts on those who see it. Ernst visited Escher every week for a year, systematically talking through his entire oeuvre with him. Their discussions resulted in a friendship that gave Ernst intimate access to the life and conceptual world of Escher. Ernst's account was meticulously scrutinized and made accurate by the artist himself. Escher's work refuses to be pigeonholed. Scientific, psychological, or aesthetic criteria alone cannot do it justice. The questions remain. Why did he create the pictures? How did he construct them? What preliminary studies were necessary before he could arrive at the final version? And how are the various images Escher created interrelated? This book, complete with biographical data, 250 illustrations, and explications of mathematical problems, offers answers to these and many other questions, and is an authentic source text of the first order.

    The book begins with an introduction to the language of statistics and then covers descriptive statistics and inferential statistics. Throughout, the author offers readers:- Difficulty Rating Index for each chapter′s material- Tips for doing and thinking about a statistical technique- Top tens for everything from the best ways to create a graph to the most effective techniques for data collection- Steps that break techniques down into a clear sequence of procedures- SPSS tips for executing each major statistical technique- Practice exercises at the end of each chapter, followed by worked out solutions.The book concludes with a statistical software sampler and a description of the best Internet sites for statistical information and data resources. Readers also have access to a website for downloading data that they can use to practice additional exercises from the book. Students and researchers will appreciate the book′s unhurried pace and thorough, friendly presentation.

    Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

    The author believes that there are such things as "The Mathematics of Life" and "The Mathematics of Art," and that the two coincide. Using simple mathematical formulas, most as basic as Pythagoras' theorem and requiring only a very limited knowledge of mathematics, Professor Ghyka shows the fascinating relationships between geometry, aesthetics, nature, and the human body.Beginning with ideas from Plato, Pythagoras, Archimedes, Ockham, Kepler, and others, the author explores the outlines of an abstract science of space, which includes a theory of proportions, an examination of "the golden section," a study of regular and semi-regular polyhedral, and the interlinking of these various shapes and forms. He then traces the transmission of this spatial science through the Pythagorean tradition and neo-Pythagorism, Greek, and Gothic canons of proportion, the Kabbala, Masonic traditions and symbols, and modern applications in architecture, painting, and decorative art. When we judge a work of art, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures both in art and nature that forms the core of Professor Ghyka's book. He also shows this geometry at work in living organisms. The ample illustrations and figures give concrete examples of the author's analysis: the Great Pyramid and tomb of Rameses IV, the Parthenon, Renaissance paintings and architecture, the work of Seurat, Le Corbusier, and flowers, shells, marine life, the human face, and much more.For the philosopher, scientist, archaeologist, art historian, biologist, poet, and artist as well as the general reader who wants to understand more about the fascinating properties of numbers and geometry, and their relationship to art and life, this is a thought-provoking book.

    A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.

    The late Soviet physicist, activist, and Nobel laureate describes his upbringing, scientific work, rejection of Soviet repression, peace and human rights concerns, marriage and family, and persecution by the KGB.

    He draws on interviews with some of the world’s highest performing researchers, the literature and his own experience to identify a small number of important insights that can transform how researchers work. The book is based on an unparalleled breadth of interdisciplinary evidence that speaks directly to researchers of all disciplines and career stages. The lessons in this book will make you more productive, more satisfied with what you produce, and enable you to be happy working less, and being more. The hardback edition has the title and design imprinted on a fabric cover, hand crafted by a book maker in Yorkshire. It contains spectacular colour photography throughout. Chapters are accompanied by close-up images of trees that build up to the forest metaphor that concludes the book. These are bookended by wide perspective canopy images that accompany the front matter (from which the cover design is derived) and concluding chapter. The overall effect is a touch and feel that makes this a book to savour. Mark Reed is Professor of Socio-Technical Innovation at Newcastle University and Visiting Professor at Birmingham City University and the University of Leeds. He has over 140 publications that have been cited more than 10,000 times. He is author of The Research Impact Handbook, which he has used to train over 4000 researchers from more than 200 institutions in 55 countries.

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.

    Just read this till the end You don’t have to buy this book. Just read this till end & you will learn something that will change the way you do math forever. Warning: I am revealing this secret only to the first set of readers who will buy this book & plan to put this secret back inside the book once I have enough sales. So read this until the very end while you still can.School taught you the wrong way to do mathThe way you were taught to do math, uses a lot of working memory. Working memory is the short term memory used to complete a mental task. You struggle because trying to do mental math the way you were taught in school, overloads your working memory. Let me show you what I mean with an example:Try to multiply the 73201 x 3. To do this you multiply the following:1 x 3 =0 x 3 =2 x 3 =3 x 3 =7 x 3 =This wasn’t hard, & it might have taken you just seconds to multiply the individual numbers. However, to get the final answer, you need to remember every single digit you calculated to put them back together. It takes effort to get the answer because you spend time trying to recall the numbers you already calculated. Math would be easier to do in your head if you didn’t have to remember so many numbers. Imagine when you tried to multiply 73201 x 3, if you could have come up with the answer, in the time it took you to multiply the individual numbers. Wouldn’t you have solved the problem faster than the time it would have taken you to punch in the numbers inside a calculator? Do the opposite of what you were taught in schoolThe secret of doing mental math is to calculate from left to right instead of from right to left. This is the opposite of what you were taught in school. This works so well because it frees your working memory almost completely. It is called the LR Method where LR stands for Left to Right.Lets try to do the earlier example where we multiplied 73201 x 3. This time multiply from left to right, so we get:7 x 3 = 213 x 3 = 93 x 2 = 60 x 3 = 03 x 1 = 3Notice that you started to call out the answer before you even finished the whole multiplication problem. You don’t have to remember a thing to recall & use later. So you end up doing math a lot faster. The Smart ChoiceYou could use what you learnt & apply it to solve math in the future. This might not be easy, because we just scratched the surface. I've already done the work for you. Why try to reinvent the wheel, when there is already a proven & tested system you can immediately apply. This book was first available in video format & has helped 10,000+ students from 132 countries. It is available at ofpad.com/mathcourse to enroll. This book was written to reach students who consume the information in text format. You can use the simple techniques in this book to do math faster than a calculator effortlessly in your head, even if you have no aptitude for math to begin with.Imagine waking up tomorrow being able to do lightning fast math in your head. Your family & friends will look at you like you are some kind of a genius. Since calculations are done in your head, you will acquire better mental habits in the process. So you will not just look like a genius. You will actually be one. Limited Time BonusWeekly training delivered through email for $97 is available for free as a bonus at the end of this book for the first set of readers. Once we have enough readers, this bonus will be charged $97. Why Price Is So LowThis book is priced at a ridiculous discount only to get our first set of readers. When we have enough readers the price will go up.

    Robert Lawlor sets out the system that determines the dimension and the form of both man-made and natural structures, from Gothic cathedrals to flowers, from music to the human body. By also involving the reader in practical experiments, he leads with ease from simple principles to a grasp of the logarithmic spiral, the Golden Proportion, the squaring of the circle and other ubiquitous ratios and proportions.Art and Imagination: These large-format, gloriously-illustrated paperbacks cover Eastern and Western religion and philosophy, including myth and magic, alchemy and astrology. The distinguished authors bring a wealth of knowledge, visionary thinking and accessible writing to each intriguing subject.