Mathematics Today Twelve Informal Essays

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Mathematics Today Twelve Informal Essays

Author : L.A. Steen
Publisher : Springer Science & Business Media
ISBN 13 : 146139435X
Total Pages : 365 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematics Today Twelve Informal Essays by : L.A. Steen

Download or read book Mathematics Today Twelve Informal Essays written by L.A. Steen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathe matical concepts, particularly those that have found application in current scientific research. The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Soci ety, the Mathematical Association of America, and the Society for Indus trial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Richard D. Anderson of Louisiana State University, George E. Carrier of Harvard University, Hirsh G. Cohen ofthe International Business Machines Corporation, Richard C. DiPrima of Rensselaer Polytechnic Institute, Robion C. Kirby of the University of California at Berkeley, William H. Kruskal of the University of Chicago, and George D. Mostow of Yale University. The JPCM decided to make production of this volume its first major proj ect and requested the Conference Board of the Mathematical Sciences (CBMS), of which its three sponsoring societies are all member organiza tions, to approach the National Science Foundation on its behalffor support of the undertaking. A proposal submitted by the C BMS in December 1974 and in revised form in July 1975 was granted by the Foundation in May 1976, and work on assembling the volume got under way.

Natural Sciences and Human Thought

Author : Robert Zwilling
Publisher : Springer Science & Business Media
ISBN 13 : 3642786855
Total Pages : 228 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Natural Sciences and Human Thought by : Robert Zwilling

Download or read book Natural Sciences and Human Thought written by Robert Zwilling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leaving aside for once all utilitarian considerations, this book attempts to demonstrate the role and influence of the natural sciences in the development of human thought and in shaping the way in which we perceive the world. This seems to be particularly necessary in the present day and age, in view of the fact that a large section of the public is scarcely aware of the great cultural contribution that the natural sciences make towards moulding our conception of the world and scarcely acknowledges their function in helping us to find our bearings in a world that is becoming increasingly complex.

Paradoxical Life

Author : Andreas Wagner
Publisher : Yale University Press
ISBN 13 : 0300156375
Total Pages : 271 pages
Book Rating : 4.3/5 (1 download)

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Book Synopsis Paradoxical Life by : Andreas Wagner

Download or read book Paradoxical Life written by Andreas Wagner and published by Yale University Press. This book was released on 2009-09-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: What can a fingernail tell us about the mysteries of creation? In one sense, a nail is merely a hunk of mute matter, yet in another, it's an information superhighway quite literally at our fingertips. Every moment, streams of molecular signals direct our cells to move, flatten, swell, shrink, divide, or die. Andreas Wagner's ambitious new book explores this hidden web of unimaginably complex interactions in every living being. In the process, he unveils a host of paradoxes underpinning our understanding of modern biology, contradictions he considers gatekeepers at the frontiers of knowledge. Though we tend to think of concepts in such mutually exclusive pairs as mind-matter, self-other, and nature-nurture, Wagner argues that these opposing ideas are not actually separate. Indeed, they are as inextricably connected as the two sides of a coin. Through a tour of modern biological marvels, Wagner illustrates how this paradoxical tension has a profound effect on the way we define the world around us. Paradoxical Life is thus not only a unique account of modern biology. It ultimately serves a radical--and optimistic--outlook for humans and the world we help create.

Mathematics Tomorrow

Author : L.A. Steen
Publisher : Springer Science & Business Media
ISBN 13 : 1461381274
Total Pages : 245 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematics Tomorrow by : L.A. Steen

Download or read book Mathematics Tomorrow written by L.A. Steen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics today is approaching a state of cnSIS. As the demands of science and society for mathematical literacy increase, the percentage of American college students intending to major in mathematics plummets and achievement scores of entering college students continue thelt unremit ting decline. As research in core mathematics reaches unprecedented heights of power and sophistication, the growth of diverse applied special ties threatens to fragment mathematics into distinct and frequently hostile mathematical sciences. These crises in mathematics presage difficulties for science and engineer ing, and alarms are beginning to sound in the scientific and even in the political communities. Citing a trend towards "virtual scientific and techno logical illiteracy" and a "shrinking of our national commitment to excel lence . . . in science, mathematics and technology," a recent study con ducted for the President by the U. S. National Science Foundation and Department of Education warns of serious impending shortcomings in public understanding of science. "Today people in a wide range of non scientific . . . professions must have a greater understanding of technology than at any time in our history. Yet our educational system does not now provide such understanding. " The study goes on to conclude that present trends pose great risk of manpower shortages in the mathematical and engineering sciences. "The pool from which our future scientific and engineering personnel can be drawn is . . . in danger of becoming smaller, even as the need for such personnel is increasing. " It is time to take a serious look at mathematics tomorrow.

An Historical Introduction to the Philosophy of Mathematics: A Reader

Author : Russell Marcus
Publisher : Bloomsbury Publishing
ISBN 13 : 1472529480
Total Pages : 896 pages
Book Rating : 4.4/5 (725 download)

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Book Synopsis An Historical Introduction to the Philosophy of Mathematics: A Reader by : Russell Marcus

Download or read book An Historical Introduction to the Philosophy of Mathematics: A Reader written by Russell Marcus and published by Bloomsbury Publishing. This book was released on 2016-02-11 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Writing Math Research Papers - 5th Ed.

Author : Robert Gerver
Publisher : IAP
ISBN 13 : 1641131128
Total Pages : 277 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Writing Math Research Papers - 5th Ed. by : Robert Gerver

Download or read book Writing Math Research Papers - 5th Ed. written by Robert Gerver and published by IAP. This book was released on 2017-12-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics research papers provide a forum for all mathematics enthusiasts to exercise their mathematical experience, expertise and excitement. The research paper process epitomizes the differentiation of instruction, as each student chooses their own topic and extends it as far as their motivation and desire takes them. The features and benefits of the research paper process offer a natural alignment with all eight Common Core State Standards for Mathematical Practice. Writing Math Research Papers serves both as a text for students and as a resource for instructors and administrators. The Writing Math Research Papers program started at North Shore High School in 1991, and it received the 1997 Chevron Best Practices in Education Award as the premier high school math course in the United States. Author Robert Gerver’s articles on high school mathematics research programs were featured in the National Council of Teachers of Mathematics publication Developing Mathematically Promising Students, the NCTM’s 1999 Yearbook, Developing Mathematical Reasoning in Grades K – 12, and in the September 2017 issue of the Mathematics Teacher.

Mathematical Reasoning

Author : Raymond Nickerson
Publisher : Taylor & Francis
ISBN 13 : 1136945393
Total Pages : 597 pages
Book Rating : 4.1/5 (369 download)

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Book Synopsis Mathematical Reasoning by : Raymond Nickerson

Download or read book Mathematical Reasoning written by Raymond Nickerson and published by Taylor & Francis. This book was released on 2011-02-25 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Teaching Mathematics Using Interactive Mapping

Author : Sandra L. Arlinghaus
Publisher : CRC Press
ISBN 13 : 1003804209
Total Pages : 251 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Teaching Mathematics Using Interactive Mapping by : Sandra L. Arlinghaus

Download or read book Teaching Mathematics Using Interactive Mapping written by Sandra L. Arlinghaus and published by CRC Press. This book was released on 2023-12-11 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Mathematics Using Interactive Mapping offers novel ways to learn basic math topics such as simple relational measures or measuring hierarchies through customized interactive mapping activities. These activities focus on interactive web-based Geographic Information System (GIS) and are relevant to today’s problems and challenges. Written in a guided, hands-on, understandable manner, all activities are designed to build practical and problem-solving skills that rest on mathematical principles and move students from thinking about maps as references that focus solely on "where is" something, to analytical tools, focusing primarily on the "whys of where." Success with this transition through interaction permits most readers to master mathematical concepts and GIS tools. FEATURES Offers custom-designed geographical activities to fit with specific mathematical topics Helps students become comfortable using mathematics in a variety of professions Provides an innovative, engaging, and practical set of activities to ease readers through typically difficult, often elementary, mathematical topics: fractions, the distributive law, and much more Uses web-based GIS maps, apps, and other tools and data that can be accessed on any device, anywhere, at any time, requiring no prior GIS background Written by experienced teachers and researchers with lifelong experience in teaching mathematics, geography, and spatial analysis Features an accompanying Solution Guide, available on the book's product page, that is beneficial for instructors, students, and other readers as an aid to gauging progress. This textbook applies to undergraduate and graduate students in universities and community colleges including those in basic mathematics courses, as well as upper-level undergraduate and graduate students taking courses in geographic information systems, remote sensing, photogrammetry, geography, geodesy, information science, engineering, and geology. Professionals interested in learning techniques and technologies for collecting, analyzing, managing, processing, and visualizing geospatial datasets will also benefit from this book as they refresh their knowledge in mathematics.

Excursions in the History of Mathematics

Author : Israel Kleiner
Publisher : Springer Science & Business Media
ISBN 13 : 0817682686
Total Pages : 347 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Excursions in the History of Mathematics by : Israel Kleiner

Download or read book Excursions in the History of Mathematics written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

Turning Points in the History of Mathematics

Author : Hardy Grant
Publisher : Birkhäuser
ISBN 13 : 1493932640
Total Pages : 109 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Turning Points in the History of Mathematics by : Hardy Grant

Download or read book Turning Points in the History of Mathematics written by Hardy Grant and published by Birkhäuser. This book was released on 2016-04-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Mathematical Problems

Author : Craig Smoryński
Publisher : Springer Nature
ISBN 13 : 3030509176
Total Pages : 406 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Mathematical Problems by : Craig Smoryński

Download or read book Mathematical Problems written by Craig Smoryński and published by Springer Nature. This book was released on 2020-09-19 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The life and soul of any science are its problems. This is particularly true of mathematics, which, not referring to any physical reality, consists only of its problems, their solutions, and, most excitingly, the challenges they pose. Mathematical problems come in many flavours, from simple puzzles to major open problems. The problems stimulate, the stories of their successful solutions inspire, and their applications are wide. The literature abounds with books dedicated to mathematical problems — collections of problems, hints on how to solve them, and even histories of the paths to the solutions of some famous ones. The present book, aimed at the proverbial “bright high-school student”, takes a different, more philosophical approach, first dividing mathematical problems into three broad classes — puzzles, exercises, and open problems — and discussing their various roles in one’s mathematical education. Various chapters are devoted to discussing examples of each type of problem, along with their solutions and some of the developments arising from them. For the truly dedicated reader, more involved material is offered in an appendix. Mathematics does not exist in a vacuum, whence the author peppers the material with frequent extra-mathematical cultural references. The mathematics itself is elementary, for the most part pre-calculus. The few references to the calculus use the integral notation which the reader need not truly be familiar with, opting to read the integral sign as strange notation for area or as operationally defined by the appropriate buttons on his or her graphing calculator. Nothing further is required. Advance praise for Mathematical Problems "There are many books on mathematical problems, but Smoryński’s compelling book offers something unique. Firstly, it includes a fruitful classification and analysis of the nature of mathematical problems. Secondly, and perhaps most importantly, it leads the reader from clear and often amusing accounts of traditional problems to the serious mathematics that grew out of some of them." - John Baldwin, University of Illinois at Chicago "Smoryński manages to discuss the famous puzzles from the past and the new items in various modern theories with the same elegance and personality. He presents and solves puzzles and traditional topics with a laudable sense of humor. Readers of all ages and training will find the book a rich treasure chest." - Dirk van Dalen, Universiteit Utrecht

Encyclopedia of Mathematics Education

Author : Louise Grinstein
Publisher : Routledge
ISBN 13 : 1136787232
Total Pages : 912 pages
Book Rating : 4.1/5 (367 download)

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Book Synopsis Encyclopedia of Mathematics Education by : Louise Grinstein

Download or read book Encyclopedia of Mathematics Education written by Louise Grinstein and published by Routledge. This book was released on 2001-03-15 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.

Gaither's Dictionary of Scientific Quotations

Author : Carl C. Gaither
Publisher : Springer Science & Business Media
ISBN 13 : 1461411149
Total Pages : 2800 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Gaither's Dictionary of Scientific Quotations by : Carl C. Gaither

Download or read book Gaither's Dictionary of Scientific Quotations written by Carl C. Gaither and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 2800 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unprecedented collection of 27,000 quotations is the most comprehensive and carefully researched of its kind, covering all fields of science and mathematics. With this vast compendium you can readily conceptualize and embrace the written images of scientists, laymen, politicians, novelists, playwrights, and poets about humankind's scientific achievements. Approximately 9000 high-quality entries have been added to this new edition to provide a rich selection of quotations for the student, the educator, and the scientist who would like to introduce a presentation with a relevant quotation that provides perspective and historical background on his subject. Gaither's Dictionary of Scientific Quotations, Second Edition, provides the finest reference source of science quotations for all audiences. The new edition adds greater depth to the number of quotations in the various thematic arrangements and also provides new thematic categories.

Where's the Wonder in Elementary Math?

Author : Judith McVarish
Publisher : Routledge
ISBN 13 : 1135908893
Total Pages : 198 pages
Book Rating : 4.1/5 (359 download)

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Book Synopsis Where's the Wonder in Elementary Math? by : Judith McVarish

Download or read book Where's the Wonder in Elementary Math? written by Judith McVarish and published by Routledge. This book was released on 2012-08-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues that even in today's high-stakes testing environment, 'teaching to the test' need not be teachers’ only focus as they introduce young children to mathematics. Judith McVarish demonstrates how building a community of learners and using problem solving to engage students can help teachers encourage students’ disposition to creative thinking and reasoning—skills that can otherwise become lost due to the pressure of the many other expectations placed upon both teachers and students. This book offers strategies for infusing mathematics learning and reasoning into elementary school classrooms while meeting curriculum and testing mandates. The teacher researcher component of each chapter provides a vehicle for teachers to bring their own expertise and questions back into the teaching and learning equation.

Negative Math

Author : Alberto A. Martínez
Publisher : Princeton University Press
ISBN 13 : 0691187827
Total Pages : 280 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Negative Math by : Alberto A. Martínez

Download or read book Negative Math written by Alberto A. Martínez and published by Princeton University Press. This book was released on 2018-06-05 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features? Uses history, puzzles, and lively debates to devise new mathematical systems Shows how departures from rules can underlie new practical applications Clear and accessible Requires a background only in basic high school algebra

A Divine Language

Author : Alec Wilkinson
Publisher : Farrar, Straus and Giroux
ISBN 13 : 1250168589
Total Pages : 219 pages
Book Rating : 4.2/5 (51 download)

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Book Synopsis A Divine Language by : Alec Wilkinson

Download or read book A Divine Language written by Alec Wilkinson and published by Farrar, Straus and Giroux. This book was released on 2022-07-12 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: A New York Times Book Review Editors' Choice "Wilkinson has accomplished something more moving and original, braiding his stumbling attempts to get better at math with his deepening awareness that there’s an entire universe of understanding that will, in some fundamental sense, forever lie outside his reach." —Jennifer Szalai, The New York Times "There is almost no writer I admire as much as I do Alec Wilkinson. His work has enduring brilliance and humanity.” —Susan Orlean, author of The Library Book A spirited, metaphysical exploration into math's deepest mysteries and conundrums at the crux of middle age. Decades after struggling to understand math as a boy, Alec Wilkinson decides to embark on a journey to learn it as a middle-aged man. What begins as a personal challenge—and it's challenging—soon transforms into something greater than a belabored effort to learn math. Despite his incompetence, Wilkinson encounters a universe of unexpected mysteries in his pursuit of mathematical knowledge and quickly becomes fascinated; soon, his exercise in personal growth (and torture) morphs into an intellectually expansive exploration. In A Divine Language, Wilkinson, a contributor to The New Yorker for over forty years, journeys into the heart of the divine aspect of mathematics—its mysteries, challenges, and revelations—since antiquity. As he submits himself to the lure of deep mathematics, he takes the reader through his investigations into the subject’s big questions—number theory and the creation of numbers, the debate over math’s human or otherworldly origins, problems and equations that remain unsolved after centuries, the conundrum of prime numbers. Writing with warm humor and sharp observation as he traverses practical math’s endless frustrations and rewards, Wilkinson provides an awe-inspiring account of an adventure from a land of strange sights. Part memoir, part metaphysical travel book, and part journey in self-improvement, A Divine Language is one man’s second attempt at understanding the numbers in front of him, and the world beyond.

CRC Concise Encyclopedia of Mathematics

Author : Eric W. Weisstein
Publisher : CRC Press
ISBN 13 : 1420035223
Total Pages : 3253 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis CRC Concise Encyclopedia of Mathematics by : Eric W. Weisstein

Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d