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| nature of mathematics book: Mathematics in Nature John Adam, 2011-10-02 From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure. |
| nature of mathematics book: The Nature of Mathematics Philip E. B. Jourdain, 2013-01-09 Anyone interested in mathematics will appreciate this survey, which explores the distinction between the body of knowledge known as mathematics and the methods used in its discovery. 1913 edition. |
| nature of mathematics book: 18 Unconventional Essays on the Nature of Mathematics Reuben Hersh, 2006-01-16 Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines |
| nature of mathematics book: Patterns in Nature Tony Hyland, 2008-10-10 If you go camping, you may see patterns in animals' fur or as part of birds' feathers. Certain fish move in a zigzag pattern, while some birds fly in a V-shaped pattern. Certain patterns help different animals camouflage themselves. Even pinecones have spiral patterns. |
| nature of mathematics book: The Nature and Power of Mathematics Donald M. Davis, 2013-03-19 This captivating book explains some of the most fascinating ideas of mathematics to nonspecialists, focusing on non-Euclidean geometry, number theory, and fractals. Numerous illustrations. 1993 edition. |
| nature of mathematics book: Nature of Mathematics Karl J. Smith, 2016-01-01 Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya’s problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have experienced mathematics rather than just do problems--and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday lives. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| nature of mathematics book: Manual of Mathematics and Mechanics Guy Roger Clements, Levi Thomas Winson, 2008-05-01 This manual contains facts and formulas that are useful in courses in mathematics and mechanics in colleges and engineering schools, arranged and printed in a form that makes them readily available for rapid work with minimum eye strain. |
| nature of mathematics book: The Nature of Mathematical Knowledge Philip Kitcher, 1984 This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified. |
| nature of mathematics book: The Mathematics of Patterns, Symmetries, and Beauties in Nature Bourama Toni, 2023-02-25 This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations, statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature’s beauty in its various manifestations. This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books. |
| nature of mathematics book: Mind and Nature Hermann Weyl, 2015-09-30 A new study of the mathematical-physical mode of cognition. |
| nature of mathematics book: Our Mathematical Universe Max Tegmark, 2015-02-03 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| nature of mathematics book: Mathematics, Nature, Art Maria Mannone, 2019 This book presents images from nature investigated in light of mathematics (category theory), and their possible musical rendition. |
| nature of mathematics book: The Nature of Mathematics Max Black, 2000 First Published in 2000. Routledge is an imprint of Taylor & Francis, an informa company. |
| nature of mathematics book: Nature's Numbers Ian Stewart, 2008-08-04 It appears to us that the universe is structured in a deeply mathematical way. Falling bodies fall with predictable accelerations. Eclipses can be accurately forecast centuries in advance. Nuclear power plants generate electricity according to well-known formulas. But those examples are the tip of the iceberg. In Nature's Numbers, Ian Stewart presents many more, each charming in its own way.. Stewart admirably captures compelling and accessible mathematical ideas along with the pleasure of thinking of them. He writes with clarity and precision. Those who enjoy this sort of thing will love this book.—Los Angeles Times |
| nature of mathematics book: Mathematics Elsewhere Marcia Ascher, 2018-06-05 Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical. Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies. The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia. This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader. |
| nature of mathematics book: The Nature of Mathematical Modeling Neil Gershenfeld, 2011-06-23 This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications. |
| nature of mathematics book: The Nature of Mathematics Philip Edward Bertrand Jourdain, 1919 |
| nature of mathematics book: A Mathematical Nature Walk John A. Adam, 2011-09-12 How heavy is that cloud? Why can you see farther in rain than in fog? Why are the droplets on that spider web spaced apart so evenly? If you have ever asked questions like these while outdoors, and wondered how you might figure out the answers, this is a book for you. An entertaining and informative collection of fascinating puzzles from the natural world around us, A Mathematical Nature Walk will delight anyone who loves nature or math or both. John Adam presents ninety-six questions about many common natural phenomena--and a few uncommon ones--and then shows how to answer them using mostly basic mathematics. Can you weigh a pumpkin just by carefully looking at it? Why can you see farther in rain than in fog? What causes the variations in the colors of butterfly wings, bird feathers, and oil slicks? And why are large haystacks prone to spontaneous combustion? These are just a few of the questions you'll find inside. Many of the problems are illustrated with photos and drawings, and the book also has answers, a glossary of terms, and a list of some of the patterns found in nature. About a quarter of the questions can be answered with arithmetic, and many of the rest require only precalculus. But regardless of math background, readers will learn from the informal descriptions of the problems and gain a new appreciation of the beauty of nature and the mathematics that lies behind it. |
| nature of mathematics book: Nature of Mathematics Karl J. Smith, 2011-01-01 Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya's problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have experienced mathematics rather than just do problems--and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday lives. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. |
| nature of mathematics book: The Beauty of Numbers in Nature Ian Stewart, 2017-03-29 Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature. |
| nature of mathematics book: Higher Mathematics for Students of Chemistry and Physics Joseph William Mellor, 1902 |
| nature of mathematics book: Mathematics in Nature, Space and Time John Blackwood, 2011 Here is a Waldorf teachers' book for math. Its contents include: Mathematics in Nature Pythagoras and Numbers Platonic Solids Rhythm and Cycles Full-color illustrations and diagrams throughout Mathematics in Nature, Space, and Time is a Waldorf teacher resource for math in class 7 (ages 12-13) and class 8 (ages 13-14). This new edition combines two previously published handbooks: Mathematics around Us and Mathematics in Space and Time. |
| nature of mathematics book: The Nature of Mathematical Thinking Robert J. Sternberg, Talia Ben-Zeev, 2012-10-12 Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat. |
| nature of mathematics book: The Language of Mathematics Bill Barton, 2007-12-24 The book emerges from several contemporary concerns in mathematics, language, and mathematics education. However, the book takes a different stance with respect to language by combining discussion of linguistics and mathematics using examples from each to illustrate the other. The picture that emerges is of a subject that is much more contingent, much more relative, much more subject to human experience than is usually accepted. Another way of expressing this, is that the thesis of the book takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than most writers allow. |
| nature of mathematics book: The Mathematics of Life Ian Stewart, 2011-06-07 Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself. |
| nature of mathematics book: That's Maths Peter Lynch, 2016-10-14 From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn't just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his Irish Times newspaper column and blog, That's Maths.Here, he shows how maths is all around us, with chapters on the beautiful equations behind designing a good concert venue, predicting the stock market and modelling the atom bomb, as well as playful meditations on everything from coin-stacking to cartography. If you left school thinking maths was boring, think again! |
| nature of mathematics book: Undiluted Hocus-Pocus Martin Gardner, 2015-11-03 The autobiography of the beloved writer who inspired a generation to study math and science Martin Gardner wrote the Mathematical Games column for Scientific American for twenty-five years and published more than seventy books on topics as diverse as magic, religion, and Alice in Wonderland. Gardner's illuminating autobiography is a candid self-portrait by the man evolutionary theorist Stephen Jay Gould called our single brightest beacon for the defense of rationality and good science against mysticism and anti-intellectualism. Gardner takes readers from his childhood in Oklahoma to his varied and wide-ranging professional pursuits. He shares colorful anecdotes about the many fascinating people he met and mentored, and voices strong opinions on the subjects that matter to him most, from his love of mathematics to his uncompromising stance against pseudoscience. For Gardner, our mathematically structured universe is undiluted hocus-pocus—a marvelous enigma, in other words. Undiluted Hocus-Pocus offers a rare, intimate look at Gardner’s life and work, and the experiences that shaped both. |
| nature of mathematics book: An Introduction to the Mathematics of Map Projections R. K. Melluish, 2014-10-09 Originally published in 1931 as a guide for mathematically-minded geography students, this book addresses the mathematical theories underlying the construction of maps. Melluish reviews the problems inherent in depicting a sphere on a flat plane and the various ways in which these problems can be solved by varying projections. This book will be of value to anyone with an interest in the mathematical underpinnings of maps. |
| nature of mathematics book: Men of Mathematics E.T. Bell, 2014-03-31 From one of the greatest minds in contemporary mathematics, Professor E.T. Bell, comes a witty, accessible, and fascinating look at the beautiful craft and enthralling history of mathematics. Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possible—and who also led intriguing, complicated, and often surprisingly entertaining lives. Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary. |
| nature of mathematics book: Elements of Mathematics John Stillwell, 2017-11-07 An exciting look at the world of elementary mathematics Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become elementary. Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of reverse mathematics confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries. |
| nature of mathematics book: The Language of Nature Geoffrey Gorham, 2016 Galileo's dictum that the book of nature is written in the language of mathematics is emblematic of the accepted view that the scientific revolution hinged on the conceptual and methodological integration of mathematics and natural philosophy. Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated, and that philosophical controversies about the implications of mathematization cannot be understood in isolation from broader social developments related to the status and practice of mathematics in various commercial, political, and academic institutions. Contributors: Roger Ariew, U of South Florida; Richard T. W. Arthur, McMaster U; Lesley B. Cormack, U of Alberta; Daniel Garber, Princeton U; Ursula Goldenbaum, Emory U; Dana Jalobeanu, U of Bucharest; Douglas Jesseph, U of South Florida; Carla Rita Palmerino, Radboud U, Nijmegen and Open U of the Netherlands; Eileen Reeves, Princeton U; Christopher Smeenk, Western U; Justin E. H. Smith, U of Paris 7; Kurt Smith, Bloomsburg U of Pennsylvania. |
| nature of mathematics book: An Introduction to the Language of Mathematics Frédéric Mynard, 2018-11-24 This is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study. |
| nature of mathematics book: The Argument of Mathematics Andrew Aberdein, Ian J Dove, 2013-07-01 Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. |
| nature of mathematics book: Mathematical Concepts Jürgen Jost, 2015-09-10 The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning. |
| nature of mathematics book: Quantum Riemannian Geometry Edwin J. Beggs, Shahn Majid, 2020-01-31 This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute. This requires a reinvention of differential geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than to actual points. Such a theory is needed for the geometry of Hopf algebras or quantum groups, which provide key examples, as well as in physics to model quantum gravity effects in the form of quantum spacetime. The mathematical formalism can be applied to any algebra and includes graph geometry and a Lie theory of finite groups. Even the algebra of 2 x 2 matrices turns out to admit a rich moduli of quantum Riemannian geometries. The approach taken is a `bottom up’ one in which the different layers of geometry are built up in succession, starting from differential forms and proceeding up to the notion of a quantum `Levi-Civita’ bimodule connection, geometric Laplacians and, in some cases, Dirac operators. The book also covers elements of Connes’ approach to the subject coming from cyclic cohomology and spectral triples. Other topics include various other cohomology theories, holomorphic structures and noncommutative D-modules. A unique feature of the book is its constructive approach and its wealth of examples drawn from a large body of literature in mathematical physics, now put on a firm algebraic footing. Including exercises with solutions, it can be used as a textbook for advanced courses as well as a reference for researchers. |
| nature of mathematics book: Mathematics and Physical Science in Classical Antiquity Johan Ludvig Heiberg, 1922 |
| nature of mathematics book: The Nature of Mathematics Karl J. Smith, 1987 Karl Smith's loyal customers adopt his book for its clear writing, its coverage of historical topics, selection of topics, level, exercise sets (featuring great applications problems), and emphasis on problem solving. Since the First Edition of Smith's text was published, thousands of liberal arts students have experienced mathematics rather than just doing problems. Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. The emphasis on problem solving and estimation, along with numerous in-text study aids, encourages students to understand the concepts while mastering techniques. |
| nature of mathematics book: The Nature and Growth of Modern Mathematics Edna E. Kramer, 1981 Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful ideals of Dedekind and Emmy Noether; and the importance of purifying mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail. |
| nature of mathematics book: Mathematics and the Laws of Nature John Tabak, 2011 This volume of the History of Mathematics series delves into the topic of how mathematical concepts are very much ingrained in the laws of nature. |
| nature of mathematics book: Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being George Lakoff, Rafael E. Nunez, 2000-11-02 A study of the cognitive science of mathematical ideas. |
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