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Author : Roger B. Nelsen
Publisher : MAA
Page : 166 pages
File Size : 54,9 Mb
Release : 1993
Category : Logic, Symbolic and mathematical
ISBN : 0883857006
Author : Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 42,8 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9781470451899
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
Author : Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 49,5 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9780883857908
Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Author : Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 42,5 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9781614441212
Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 173 pages
File Size : 41,8 Mb
Release : 2006-12-31
Category : Mathematics
ISBN : 9781614441007
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.
Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 42,8 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author : Arthur T. Benjamin,Jennifer J. Quinn
Publisher : American Mathematical Society
Page : 210 pages
File Size : 50,6 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470472597
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author : Sanjoy Mahajan
Publisher : MIT Press
Page : 152 pages
File Size : 45,9 Mb
Release : 2010-03-05
Category : Education
ISBN : 9780262265591
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Author : Roger B. Nelsen
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475730760
Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Author : Sabrina Bendjaballah,Noam Faust,Mohamed Lahrouchi,Nicola Lampitelli
Publisher : John Benjamins Publishing Company
Page : 387 pages
File Size : 40,8 Mb
Release : 2014-12-15
Category : Language Arts & Disciplines
ISBN : 9789027269485
This volume brings together articles by some major figures in various linguistics domains — phonology, morphology and syntax — aiming at explaining the form of linguistic items by exploring the structures that underlie them. The book is divided in 5 parts: vowels, syllables, templates, syntax-morphology interface and Afro-Asiatic languages. Specific topics are the internal structure of vowels and its relation to harmony; the logic of recurrent vocalic patterns; syllabic prominence; the interaction of syllabic and templatic structure and segmental realization; the innateness of templates and paradigms; the limits of phonology; and various morpho-syntactic implications on phonological form. The volume renders homage to Jean Lowenstamm’s work, by underlining the importance of seeking structural and intermodular insight in the study of linguistic form.
Author : Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 42,6 Mb
Release : 2018-08-07
Category : Mathematics
ISBN : 9781470448462
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. [Author]; Roger Nelsen is a long-time contributor of ``Proofs Without Words'' in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
Author : Ulrich Daepp,Pamela Gorkin
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 44,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215600
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.
Author : Philip Ording
Publisher : Princeton University Press
Page : 272 pages
File Size : 50,7 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691218977
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
Author : Alejandro Camacho,Robert Glicksman
Publisher : NYU Press
Page : 366 pages
File Size : 53,7 Mb
Release : 2019-08-27
Category : Law
ISBN : 9781479829675
A pioneering model for constructing and assessing government authority and achieving policy goals more effectively Regulation is frequently less successful than it could be, largely because the allocation of authority to regulatory institutions, and the relationships between them, are misunderstood. As a result, attempts to create new regulatory programs or mend under-performing ones are often poorly designed. Reorganizing Government explains how past approaches have failed to appreciate the full diversity of alternative approaches to organizing governmental authority. The authors illustrate the often neglected dimensional and functional aspects of inter-jurisdictional relations through in-depth explorations of several diverse case studies involving securities and banking regulation, food safety, pollution control, resource conservation, and terrorism prevention. This volume advances an analytical framework of governmental authority structured along three dimensions—centralization, overlap, and coordination. Camacho and Glicksman demonstrate how differentiating among these dimensions better illuminates the policy tradeoffs of organizational alternatives, and reduces the risk of regulatory failure. The book also explains how differentiating allocations of authority based on governmental function can lead to more effective regulation and governance. The authors illustrate the practical value of this framework for future reorganization efforts through the lens of climate change, an emerging and vital global policy challenge, and propose an “adaptive governance” infrastructure that could allow policy makers to embed the creation, evaluation, and adjustment of the organization of regulatory institutions into the democratic process itself.
