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Author : George F. Simmons
Publisher : MAA
ISBN 13 : 9780883855614
Total Pages : 386 pages
Book Rating : 4.8/5 (556 download)
Download or read book Calculus Gems written by George F. Simmons and published by MAA. This book was released on 2007-08-02 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates the profound connections that join mathematics to the history of philosophy.
Author : George F. Simmons
Publisher : American Mathematical Soc.
ISBN 13 : 147045128X
Total Pages : 355 pages
Book Rating : 4.4/5 (74 download)
Download or read book Calculus Gems: Brief Lives and Memorable Mathematics written by George F. Simmons and published by American Mathematical Soc.. This book was released on 2020-03-17 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George Finlay Simmons
Publisher : McGraw-Hill Science, Engineering & Mathematics
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)
Download or read book Calculus Gems written by George Finlay Simmons and published by McGraw-Hill Science, Engineering & Mathematics. This book was released on 1992 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first half of Calculus Gems is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows how science - and mathematics in particular - is something that people do, and not merely a mass of observed data and abstract theory. He demonstrates the profound connections that join mathematics to the history of philosophy and also to the broader intellectual and social history of Western civilization. The second half contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes, meaning that it can be used as a supplement in a Calculus course, or a History of Mathematics course. The overall aim of this book is to answer the question, 'What is mathematics for?' and with its inevitable answer, 'To delight the mind and help us understand the world.'
Author : George Finlay Simmons
Publisher : MAA Press
ISBN 13 : 9781470451295
Total Pages : 355 pages
Book Rating : 4.4/5 (512 download)
Download or read book Calculus Gems written by George Finlay Simmons and published by MAA Press. This book was released on 2020 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George Finlay Simmons
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.0/5 ( download)
Download or read book Precalculus Mathematics in a Nutshell written by George Finlay Simmons and published by . This book was released on 1997 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book that explains the fundamentals of geometry, algebra, and trigonometry with as fewest words as the author deems it possible.
Author : Reuben Hersh
Publisher : Princeton University Press
ISBN 13 : 9781400836116
Total Pages : 432 pages
Book Rating : 4.8/5 (361 download)
Download or read book Loving and Hating Mathematics written by Reuben Hersh and published by Princeton University Press. This book was released on 2010-12-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
Author : Ian Stewart
Publisher : Profile Books
ISBN 13 : 1847651283
Total Pages : 320 pages
Book Rating : 4.8/5 (476 download)
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...
Author : Sanjoy Mahajan
Publisher : MIT Press
ISBN 13 : 0262265591
Total Pages : 152 pages
Book Rating : 4.2/5 (622 download)
Download or read book Street-Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Stuart Hollingdale
Publisher : Courier Corporation
ISBN 13 : 0486174506
Total Pages : 464 pages
Book Rating : 4.4/5 (861 download)
Download or read book Makers of Mathematics written by Stuart Hollingdale and published by Courier Corporation. This book was released on 2014-06-10 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 edition.
Author : Dick Jardine
Publisher : MAA
ISBN 13 : 088385984X
Total Pages : 305 pages
Book Rating : 4.8/5 (838 download)
Download or read book Mathematical Time Capsules written by Dick Jardine and published by MAA. This book was released on 2011 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691191999
Total Pages : 336 pages
Book Rating : 4.6/5 (911 download)
Download or read book Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author : William P. Berlinghoff
Publisher : American Mathematical Soc.
ISBN 13 : 147046456X
Total Pages : 331 pages
Book Rating : 4.4/5 (74 download)
Download or read book Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition written by William P. Berlinghoff and published by American Mathematical Soc.. This book was released on 2021-04-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
Author : Ken Bain
Publisher : Harvard University Press
ISBN 13 : 0674065549
Total Pages : 218 pages
Book Rating : 4.6/5 (74 download)
Download or read book What the Best College Teachers Do written by Ken Bain and published by Harvard University Press. This book was released on 2011-09-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: What makes a great teacher great? Who are the professors students remember long after graduation? This book, the conclusion of a fifteen-year study of nearly one hundred college teachers in a wide variety of fields and universities, offers valuable answers for all educators. The short answer is—it’s not what teachers do, it’s what they understand. Lesson plans and lecture notes matter less than the special way teachers comprehend the subject and value human learning. Whether historians or physicists, in El Paso or St. Paul, the best teachers know their subjects inside and out—but they also know how to engage and challenge students and to provoke impassioned responses. Most of all, they believe two things fervently: that teaching matters and that students can learn. In stories both humorous and touching, Ken Bain describes examples of ingenuity and compassion, of students’ discoveries of new ideas and the depth of their own potential. What the Best College Teachers Do is a treasure trove of insight and inspiration for first-year teachers and seasoned educators.
Author : Tim Glynne-Jones
Publisher : Arcturus Publishing
ISBN 13 : 1848584407
Total Pages : 310 pages
Book Rating : 4.8/5 (485 download)
Download or read book The Book of Numbers written by Tim Glynne-Jones and published by Arcturus Publishing. This book was released on 2011-06-30 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: From zero to infinity, The Book of Numbers is a handy-sized volume which opens up a new realm of knowledge. Where else in one place could you find out how the illegal numbers racket worked, what makes some people see numbers as colours, why the standard US rail gauge exactly matches the axle width of an ancient Roman chariot, and the numerological connection between Adolf Hitler and Osama Bin Laden?
Author : Carlo Cercignani
Publisher : OUP Oxford
ISBN 13 : 0191606987
Total Pages : 348 pages
Book Rating : 4.1/5 (916 download)
Download or read book Ludwig Boltzmann written by Carlo Cercignani and published by OUP Oxford. This book was released on 2006-01-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved: others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject.
Author : Steven Strogatz
Publisher : Eamon Dolan Books
ISBN 13 : 1328879984
Total Pages : 389 pages
Book Rating : 4.3/5 (288 download)
Download or read book Infinite Powers written by Steven Strogatz and published by Eamon Dolan Books. This book was released on 2019 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
