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Author : George F. Simmons
Publisher : MAA
Page : 386 pages
File Size : 53,7 Mb
Release : 2007-08-02
Category : Biography & Autobiography
ISBN : 0883855615
Demonstrates the profound connections that join mathematics to the history of philosophy.
Author : George F. Simmons
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 51,6 Mb
Release : 2020-03-17
Category : Education
ISBN : 9781470451288
Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices ("Biographical Notes" and "Variety of Additional Topics") found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, "What is mathematics for?" and in Simmons' answer, "To delight the mind and help us understand the world". The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, "Brief Lives", is a biographical history of mathematics from earliest times (Thales, 625–547 BC) through the late 19th century (Weierstrass, 1815–1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, "Memorable Mathematics", is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Some of these sections have a few problems for the student to solve. Students can gain perspective on the mathematical experience and learn some mathematics not contained in the usual courses, and instructors can assign student papers and projects based on the essays. The book teaches by example that mathematics is more than computation. Original illustrations of influential mathematicians in history and their inventions accompany the brief biographies and mathematical discussions.
Author : Amy Shell-Gellasch,Dick Jardine
Publisher : Cambridge University Press
Page : 276 pages
File Size : 46,9 Mb
Release : 2005
Category : Mathematics
ISBN : 0883851784
To date, much of the literature prepared on the topic of integrating mathematics history into undergraduate teaching contains, predominantly, ideas from the 18th century and earlier. This volume focuses on nineteenth- and twentieth-century mathematics, building on the earlier efforts but emphasizing recent history in the teaching of mathematics, computer science, and related disciplines. From Calculus to Computers is a resource for undergraduate teachers that provides ideas and materials for immediate adoption in the classroom and proven examples to motivate innovation by the reader. Contributions to this volume are from historians of mathematics and college mathematics instructors with years of experience and expertise in these subjects. Examples of topics covered are probability in undergraduate statistics courses, logic and programming for computer science, undergraduate geometry to include non-Euclidean geometries, numerical analysis, and abstract algebra.
Author : George Finlay Simmons
Publisher : MAA Press
Page : 355 pages
File Size : 53,7 Mb
Release : 2020
Category : Calculus
ISBN : 1470451298
Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices ('Biographical Notes' and 'Variety of Additional Topics') found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, 'What is mathematics for?' and in Simmons' answer, 'To delight the mind and help us understand the world'. The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, 'Brief Lives', is a biographical history of mathematics from earliest times (Thales, 625-547 BC) through the late 19th century (Weierstrass, 1815-1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, 'Memorable Mathematics', is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Some of these sections have a few problems for the student to solve. Students can gain perspective on the mathematical experience and learn some mathematics not contained in the usual courses, and instructors can assign student papers and projects based on the essays. The book teaches by example that mathematics is more than computation. Original illustrations of influential mathematicians in history and their inventions accompany the brief biographies and mathematical discussions.
Author : Steven Strogatz
Publisher : Eamon Dolan Books
Page : 389 pages
File Size : 55,7 Mb
Release : 2019
Category : History
ISBN : 9781328879981
From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus - how it works and why it makes our lives immeasurably better. Without calculus, we wouldn't have cell phones, TV, GPS, or ultrasound. We wouldn't have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz's brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it's about simplicity. It harnesses an unreal number--infinity--to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to make electricity with magnets; how to ensure your rocket doesn't miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.
Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 42,8 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191379
How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Author : Calvin C. Clawson
Publisher : Springer
Page : 301 pages
File Size : 55,5 Mb
Release : 2014-01-04
Category : Mathematics
ISBN : 9781489964335
Author : Jonathan Shectman
Publisher : Bloomsbury Publishing USA
Page : 368 pages
File Size : 43,8 Mb
Release : 2003-09-30
Category : Science
ISBN : 9780313072437
The 18th century saw the emergence of the industrial and chemical revolutions and witnessed the near-universal acceptance of applied science. It was a time of revolutionary, lasting transformation for the practice of science and mathematics. Most procedures and precepts of modern science took hold during the 18th century, when scientists first paired scientific research with practical application to astonishing results. In over 60 alphabetical entries, Shectman examines at the tremendous scientific discoveries, inventions, and inquiries of the period. Familiar topics such as the steam engine and hot air balloon are covered, along with lesser-known topics such as the Watt copy press and Newton's experimentum crucis. A thorough discussion of each entry's scientific impact provides readers with an understanding of the lasting social and political importance of these advancements. Narratives enrich the entries by adding context and perspective to the century's fascinating scientific history. Students and researchers will find this reference book easy to use. Included are an appendix of entries listed by scientific field, a glossary of terms, indexes by name and subject.
Author : Dick Jardine,Amy Shell-Gellasch
Publisher : MAA
Page : 305 pages
File Size : 53,6 Mb
Release : 2011
Category : Computer science
ISBN : 9780883859841
Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Readers will find articles and activities from mathematics history that enhance the learning of topics covered in the undergraduate or secondary mathematics curricula. Each capsule presents at least one topic or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide teachers with historical background and classroom activities designed for immediate use in the classroom, along with further references and resources on the chapter subject. --Publisher description.
Author : Nathaniel Grossman
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240907
Dear Reader, Here is your book. Take it, run with it, pass it, punt it, enjoy all the many things that you can do with it, but-above all-read it. Like all textbooks, it was written to help you increase your knowledge; unlike all too many textbooks that you have bought, it will be fun to read. A preface usually tells of the author's reasons for writing the book and the author's goals for the reader, followed by a swarm of other important matters that must be attended to yet fit nowhere else in the book. I am fortunate in being able to include an insightful prepublication review that goes directly to my motivations and goals. (Look for it following this preface.) That leaves only those other important matters. In preparing the text, I consulted a number of books, chief of which included these: • S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale Uni versity Press, 1969. • J .M.A. Danby, Fundamentals of Celestial Mechanics, Macmil lan, 1962. Now available in a 2nd edition, 3rd printing, revised, corrected and enlarged, Willmann-Bell, 1992. • Y. Hagihara, Theories of Equilibrium Figures of a Rotating Ho mogeneous Fluid Mass, NASA, 1970. • R.A. Lyttleton, The Stability of Rotating Liquid Masses, C- ix x PREFACE bridge University Press, 1953. • C.B. Officer, Introduction to Theoretical Geophysics, Springer Verlag, 1974. • A.S. Ramsey, Newtonian Attraction, Cambridge University Press, 1949. • W.M. Smart, Celestial Mechanics, Longmans, Green, and Co, 1953.
Author : Sadri Hassani
Publisher : Springer Science & Business Media
Page : 828 pages
File Size : 47,7 Mb
Release : 2008-10-27
Category : Science
ISBN : 9780387095035
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.
Author : Frank Burk
Publisher : John Wiley & Sons
Page : 312 pages
File Size : 41,5 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118030981
A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration. Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.
Author : David Perkins
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 46,7 Mb
Release : 2018-10-10
Category : Electronic
ISBN : 9781470447991
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, Khayyam, Newton, Wallis, and Euler.
Author : Lawrence W. Baggett
Publisher : MAA
Page : 220 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780883855812
A memoir that describes the groundbreaking life and career of blind mathematician Larry Baggett, interspersed with musings on mathematics.
Author : Mark V. Lawson
Publisher : CRC Press
Page : 424 pages
File Size : 55,5 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9781000402506
Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra. New to the second edition Several updated chapters, plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short ‘essays’ that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035