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The Calculus Gallery
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Book Synopsis The Calculus Gallery by : William Dunham
Download or read book The Calculus Gallery written by William Dunham and published by Princeton University Press. This book was released on 2018-11-13 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching—a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.
Download or read book Euler written by William Dunham and published by American Mathematical Society. This book was released on 2022-01-13 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.
Book Synopsis Calculus Reordered by : David M. Bressoud
Download or read book Calculus Reordered written by David M. Bressoud and published by Princeton University Press. This book was released on 2021-05-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Book Synopsis The Calculus of Happiness by : Oscar E. Fernandez
Download or read book The Calculus of Happiness written by Oscar E. Fernandez and published by Princeton University Press. This book was released on 2019-07-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: How math holds the keys to improving one's health, wealth, and love life? What's the best diet for overall health and weight management? How can we change our finances to retire earlier? How can we maximize our chances of finding our soul mate? In The Calculus of Happiness, Oscar Fernandez shows us that math yields powerful insights into health, wealth, and love. Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. Moreover, the important formulas are linked to a dozen free online interactive calculators on the book's website, allowing one to personalize the equations. Fernandez uses everyday experiences--such as visiting a coffee shop--to provide context for his mathematical insights, making the math discussed more accessible, real-world, and relevant to our daily lives. Every chapter ends with a summary of essential lessons and takeaways, and for advanced math fans, Fernandez includes the mathematical derivations in the appendices. A nutrition, personal finance, and relationship how-to guide all in one, The Calculus of Happiness invites you to discover how empowering mathematics can be.
Book Synopsis Professor Stewart's Cabinet of Mathematical Curiosities by : Ian Stewart
Download or read book Professor Stewart's Cabinet of Mathematical Curiosities written by Ian Stewart and published by Profile Books. This book was released on 2010-09-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: School maths is not the interesting part. The real fun is elsewhere. Like a magpie, Ian Stewart has collected the most enlightening, entertaining and vexing 'curiosities' of maths over the years... Now, the private collection is displayed in his cabinet. There are some hidden gems of logic, geometry and probability -- like how to extract a cherry from a cocktail glass (harder than you think), a pop up dodecahedron, the real reason why you can't divide anything by zero and some tips for making money by proving the obvious. Scattered among these are keys to unlocking the mysteries of Fermat's last theorem, the Poincar Conjecture, chaos theory, and the P/NP problem for which a million dollar prize is on offer. There are beguiling secrets about familiar names like Pythagoras or prime numbers, as well as anecdotes about great mathematicians. Pull out the drawers of the Professor's cabinet and who knows what could happen...
Book Synopsis A Tour of the Calculus by : David Berlinski
Download or read book A Tour of the Calculus written by David Berlinski and published by Vintage. This book was released on 2011-04-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review
Book Synopsis The Mathematical Universe by : William Dunham
Download or read book The Mathematical Universe written by William Dunham and published by John Wiley & Sons. This book was released on 1994-08-16 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Dunham writes for nonspecialists, and they will enjoy his piquantanecdotes and amusing asides -- Booklist "Artfully, Dunham conducts a tour of the mathematical universe. . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are." -- Nature "If you want to encourage anyone's interest in math, get them TheMathematical Universe." * New Scientist
Book Synopsis Calculus Simplified by : Oscar Fernandez
Download or read book Calculus Simplified written by Oscar Fernandez and published by Princeton University Press. This book was released on 2019-06-11 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In Calculus simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus : just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure."--Page 4 de la couverture.
Book Synopsis Count Like an Egyptian by : David Reimer
Download or read book Count Like an Egyptian written by David Reimer and published by Princeton University Press. This book was released on 2014-04-27 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively collection of fun and challenging problems in ancient Egyptian math The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can’t be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated—they technically didn’t exist in the land of the pharaohs. You’ll be counting like an Egyptian in no time, and along the way you’ll learn firsthand how mathematics is an expression of the culture that uses it, and why there’s more to math than rote memorization and bewildering abstraction. Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you’ll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing. Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation—the precursor to our modern system—and compares ancient Egyptian mathematics to today’s math, letting you decide for yourself which is better.
Book Synopsis Calculus: A Rigorous First Course by : Daniel J. Velleman
Download or read book Calculus: A Rigorous First Course written by Daniel J. Velleman and published by Courier Dover Publications. This book was released on 2017-01-18 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness. No background in calculus is necessary. Prerequisites include proficiency in basic algebra and trigonometry, and a concise review of both areas provides sufficient background. Extensive problem material appears throughout the text and includes selected answers. Complete solutions are available to instructors.
Book Synopsis From Calculus to Computers by : Amy Shell-Gellasch
Download or read book From Calculus to Computers written by Amy Shell-Gellasch and published by Cambridge University Press. This book was released on 2005 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classroom resource material allowing the integration of mathematics history into undergraduate mathematics teaching.
Book Synopsis Mathematics and Art by : Lynn Gamwell
Download or read book Mathematics and Art written by Lynn Gamwell and published by Princeton University Press. This book was released on 2016 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.
Book Synopsis A Course in Complex Analysis by : Saeed Zakeri
Download or read book A Course in Complex Analysis written by Saeed Zakeri and published by Princeton University Press. This book was released on 2021-11-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--
Book Synopsis The Calculus Collection by : Caren L. Diefenderfer
Download or read book The Calculus Collection written by Caren L. Diefenderfer and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.
Download or read book The Calculus written by Otto Toeplitz and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers insights in current theoretical discussions, observations, and reflections from internationally and regionally celebrated scholars on the theory and practice of teaching English informed by a new school of thought, English as an International Language (EIL). This volume provides readers (scholars, teachers, teacher-educators, researchers in the relevant fields) with: Knowledge of the changing paradigm and attitudes towards English language teaching from teaching a single variety of English to teaching intercultural communication and English language variation. Current thoughts on the theory of teaching English as an international language by internationally-celebrated established scholars and emergent scholars. Scholarly descriptions and discussions of how English language educators and teacher-educators translate the paradigm of English as an International Language into their existing teaching. Delineation of how this newly emerged paradigm is received or responded to by English language educators and students when it is implemented. Readers have a unique opportunity to observe and read the tensions and dilemmas that educators and students are likely to experience in teaching and learning EIL -- back cover.
Download or read book Gamma written by Julian Havil and published by Princeton University Press. This book was released on 2017-10-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this.
Download or read book Calculus written by Michael Spivak and published by . This book was released on 1980 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
