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Mathematical Fallacies Flaws And Flimflam
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Book Synopsis Mathematical Fallacies, Flaws, and Flimflam by : Edward Barbeau
Download or read book Mathematical Fallacies, Flaws, and Flimflam written by Edward Barbeau and published by MAA. This book was released on 2000-06-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition can often be misleading. This book collects and analyses a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves.
Book Synopsis Mathematical Fallacies, Flaws, and Flimflam by : Edward J. Barbeau
Download or read book Mathematical Fallacies, Flaws, and Flimflam written by Edward J. Barbeau and published by American Mathematical Soc.. This book was released on 2000-12-31 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of mathematical errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves.
Book Synopsis Magnificent Mistakes in Mathematics by : Alfred S. Posamentier
Download or read book Magnificent Mistakes in Mathematics written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2013-08-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.
Book Synopsis The Trisectors by : Underwood Dudley
Download or read book The Trisectors written by Underwood Dudley and published by American Mathematical Soc.. This book was released on 2019-07-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another--angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. According to Dudley: ""Hardly any mathematical training is necessary to read this book. There is a little trigonometry here and there, but it may be safely skipped. There are hardly any equations. There are no exercises and there will be no final examination. The worst victim o.
Book Synopsis Remarkable Mathematicians by : Ioan James
Download or read book Remarkable Mathematicians written by Ioan James and published by Mathematical Association of America. This book was released on 2003-02-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed. Ioan James is a professor at the Mathematical Institute, University of Oxford. He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford.
Book Synopsis Pell’s Equation by : Edward J. Barbeau
Download or read book Pell’s Equation written by Edward J. Barbeau and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.
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
Author :Steve Batterson Publisher :The Mathematical Association of America ISBN 13 :0883855909 Total Pages :244 pages Book Rating :4.8/5 (838 download)
Book Synopsis American Mathematics 1890-1913 by : Steve Batterson
Download or read book American Mathematics 1890-1913 written by Steve Batterson and published by The Mathematical Association of America. This book was released on 2017-06-29 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the turn of the twentieth century, mathematical scholarship in the United States underwent a stunning transformation. In 1890 no American professor was producing mathematical research worthy of international attention. Graduate students were then advised to pursue their studies abroad. By the start of World War I the standing of American mathematics had radically changed. George David Birkhoff, Leonard Dickson, and others were turning out cutting edge investigations that attracted notice in the intellectual centers of Europe. Harvard, Chicago, and Princeton maintained graduate programs comparable to those overseas. This book explores the people, timing, and factors behind this rapid advance. Through the mid-nineteenth century most American colleges followed a classical curriculum that, in mathematics, rarely reached beyond calculus. With no doctoral programs of any sort in the United States until 1860, mathematical scholarship lagged far behind that in Europe. After the Civil War, visionary presidents at Harvard and Johns Hopkins broadened and deepened the opportunities for study. The breakthrough for mathematics began in 1890 with the hiring, in consecutive years, of William F. Osgood and Maxime Bôcher at Harvard and E. H. Moore at Chicago. Each of these young men had studied in Germany where they acquired vital mathematical knowledge and taste. Over the next few years Osgood, Bôcher, and Moore established their own research programs and introduced new graduate courses. Working with other like-minded individuals through the nascent American Mathematical Society, the infrastructure of meetings and journals were created. In the early twentieth century Princeton dramatically upgraded its faculty to give the United States the stability of a third mathematics center. The publication by Birkhoff, in 1913, of the solution to a famous conjecture served notice that American mathematics had earned consideration with the European powers of Germany, France, Italy, England, and Russia.
Book Synopsis Teaching Secondary School Mathematics: Techniques And Enrichment by : Alfred S Posamentier
Download or read book Teaching Secondary School Mathematics: Techniques And Enrichment written by Alfred S Posamentier and published by World Scientific. This book was released on 2020-09-18 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.
Book Synopsis Real Infinite Series by : Daniel D. Bonar
Download or read book Real Infinite Series written by Daniel D. Bonar and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Download or read book I, Mathematician written by Peter Casazza and published by The Mathematical Association of America. This book was released on 2015-03-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.
Book Synopsis Illustrated Special Relativity through Its Paradoxes: A Fusion of Linear Algebra, Graphics, and Reality by : John dePillis
Download or read book Illustrated Special Relativity through Its Paradoxes: A Fusion of Linear Algebra, Graphics, and Reality written by John dePillis and published by American Mathematical Soc.. This book was released on 2013-12-31 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Assuming a minimum of technical expertise beyond basic matrix theory, the authors introduce inertial frames and Minkowski diagrams to explain the nature of simultaneity, why faster-than-light travel is impossible, and the proper way to add velocities. We resolve the twin paradox, the train-in-tunnel paradox, the pra-shooter paradox along with the lesser-known bug-rivet paradox that shows how rigidity is incompatible with special relativity. Since Einstein in his seminal 1905 paper introducing special relativity, acknowledged his debt to Clerk Maxwell, we fully develop Maxwell's four equations that unify the theories of electricity, optics, and magnetism. These equations also lead to a simple calculation for the frame independent speed of electromagnetic waves in a vacuum."--Cover.
Author :C. Edward Sandifer Publisher :The Mathematical Association of America ISBN 13 :0883855844 Total Pages :254 pages Book Rating :4.8/5 (838 download)
Book Synopsis How Euler Did Even More by : C. Edward Sandifer
Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.
Download or read book Phi, Pi, e and i written by David Perkins and published by The Mathematical Association of America. This book was released on 2017 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, e and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyám, Newton, Wallis, and Euler. The book is written with the goal that an undergraduate student can read the book solo. With this goal in mind, the author provides endnotes throughout, in case the reader is unable to work out some of the missing steps. Those endnotes appear in the last chapter, Extra Help. Each chapter concludes with a series of exercises, all of which introduce new historical figures or content.
Book Synopsis Calculus Without Hocus Pocus by : K. Razi Naqvi
Download or read book Calculus Without Hocus Pocus written by K. Razi Naqvi and published by K. Razi Naqvi. This book was released on 2019-07-03 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus is a subject that needs to be studied many times over, ideally with a different book in each new round. Using Ezra Pound’s analogy (in ABC of Reading), we may think of the learner as an apprentice carpenter, and of calculus as a stool or table; the learner must keep going until the piece of furniture has three legs and will stand up, or four legs and won’t tip over too easily. Most people cannot follow this plan, because life is short and the list of other demands on their time just too long. This book has been written with a view to making calculus more interesting and intelligible to those who left college, recently or a long time ago, without becoming an adept; those who are familiar with the contents of undergraduate calculus, but not altogether content with their own grasp of the central concepts; those who are aware that the structure put together by them during their apprenticeship is too wobbly, and liable to tip over when the number of independent variables is increased from one to just two. An absurd simile? Not in the opinion of a distinguished mathematician and educator (quoted verbatim in the preface), who acknowledged that the customary definition of a differential in the theory of functions of a single variable breaks down when one extends it to functions of several variables and considers double integrals. He continued: “Students are rightly baffled when they attempt to convert such an integral to polar coordinates and are told that no longer is it permissible to [apply a straightforward extension of the relevant formula for a change of variable in a single integral]. The Jacobian must be used instead, and at this point the logical structure which was built so carefully collapses entirely. If we wish to make calculus an intellectually honest subject and not a collection of convenient tricks, it is time we made a fresh start.” Calculus Without Hocus Pocus aims to elucidate those (and only those) issues that are not treated adequately in standard textbooks. It offers more cogent explanations of the conundrums and paradoxes which have been nagging the minds of students and teachers of calculus for generations. The author, who has been using calculus as a teacher and researcher for over fifty years, has tried to produce a condensed and readable book that throws light from various directions upon the difficult parts of this very technical (and somewhat unpopular) subject; to show some of the reasons why calculus has been cast in the mould in which we find it; and to recommend some minor changes in notation and nomenclature that would remove nearly all of the hocus-pocus which almost every learner of calculus has had to endure so far.
Book Synopsis The G. H. Hardy Reader by : Donald J. Albers
Download or read book The G. H. Hardy Reader written by Donald J. Albers and published by Cambridge University Press. This book was released on 2016-04-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: G. H. Hardy ranks among the greatest twentieth-century mathematicians. This book introduces this extraordinary individual and his writing.
Book Synopsis Essays on Mathematical Reasoning by : Jerzy Pogonowski
Download or read book Essays on Mathematical Reasoning written by Jerzy Pogonowski and published by . This book was released on 2020 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
