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Calculus Gems: Brief Lives and Memorable Mathematics

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Brand new. We distribute directly for the publisher. The first half of Calculus Gems entitles, Brief Lives is a biographical history of mathematics from the earliest times to the ... late nineteenth century. The author shows that 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 of the book contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes. G.H. Hardy once said, " A mathematician, like painter or poet, maker patterns. If his patterns more permanent than theirs, it is because they are made with ideas.? This part book contains wide variety these patterns, arranged an roughly corresponding to order ideas in most calculus courses. Some of the sections even have a few problems.Professor Simmons tells us in the Preface of Calculus Gems: "I hold the na??ve but logically impeccable view that there are only two kinds of students in our colleges and universities, those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types." The overall aim of the 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." Read more Show Less

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Overview

A classic book is back in print! It can be used as a supplement in a Calculus course, or a History of Mathematics course.

The first half of Calculus Gems entitles, Brief Lives is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows that 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 of the book contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes. G.H. Hardy once said, "A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." This part of the book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems.

Professor Simmons tells us in the Preface of Calculus Gems: "I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities, those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. The overall aim of the 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."

Read More Show Less

Product Details

  • ISBN-13: 9780883855614
  • Publisher: Mathematical Association of America
  • Publication date: 5/18/2008
  • Series: MAA-Spectrum Series
  • Edition description: New Edition
  • Pages: 372
  • Product dimensions: 6.20 (w) x 9.10 (h) x 1.00 (d)

Read an Excerpt

On coming to the end of my work on this book and thinking again about its nature and purpose, I am reminded of W.H. Fowler's Preface to his great Modern English Usage: "I think of it as it should have been, with its prolixities docked, and its dullnesses enlivened, its fads eliminated, its truths multiplied." And also of W.H. Auden's rueful admission: "A poem is never finished, only abandoned."

Some readers will recognize that this book had been reconstructed out of two massive appendices in my 1985 calculus book, with many additions, rearrangements and minor adjustments. Its direct practical purpose is to provide auxiliary material for students taking calculus courses, or perhaps courses on the history of mathematics. There have been a number of requests that this material be made separately available, and I have been happy to take advantage of this occasion to fill in some gaps and reconsider my opinions. I had a friend who said to me once, "I should probably spend about an hour a week revising my opinions." I treasure the remark and value the opportunity to act upon it.

My overall aims are bound up with the question, "What is mathematics for?" and with its inevitable answer, "To delight the mind and help us understand the world." I hold the naïve but logically impeccable view that there are only two kinds of students in our colleges and universities: those who are attracted to mathematics; and those who are not yet attracted, but might be. My intended audience embraces both types. Part A. This half of the book, entitled Brief Lives, amounts to a biographical history of mathematics from the earliest times to the late nineteenth century. It has two main purposes.

First, I hope in this way to "humanize" the subject, to make it transparently clear that great human beings created it by great efforts of genius, and thereby to increase students' interest in what they are studying. Science-and in particular mathematics-is something that men and women do, and not merely a mass of observed data and abstract theory. The minds of most people turn away from problems-veer off, draw back, avoid contact, change the subject, think of something else at all costs. The people-the great majority of the human race-find solace and comfort in the known and the familiar, and avoid the unknown and unfamiliar as they would deserts and jungles. It is hard for them to think steadily about a difficult problem as it is to hold together the north poles of two strong magnets. In contrast to this, a tiny minority of men and women are drawn irresistibly to problems: their minds embrace them lovably and wrestle with them tirelessly until they yield their secrets. It is those who have taught the rest of us most of what we know and can do, from the wheel and the lever to metallurgy and the theory of relativity. I have written about some of these people from our past in the hope of encouraging a few in the next generation.

My second purpose is connected with the fact that many students from the humanities and social sciences are compelled against their will to study calculus as a means of satisfying academic requirements. The profound connections that join mathematics to the history of philosophy, and also to the broader intellectual and social history of Western civilization, are often capable of arousing the passionate interest of these otherwise indifferent students.

Part B. In teaching calculus over a period of many years, I have collected a considerable number of miscellaneous topics from number theory, geometry, science, etc., which I have used for the purpose of opening doors and forging links with other subjects - and also for breaking the routing and lifting the spirits. Many of my students have found these "nuggets" interesting and eye-opening. I have collected most of these topics in this part in the hope of making a few more converts to the view that mathematics, while sometimes rather dull and routine, can often be supremely interesting. The English mathematician G.H. Hardy said, "A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.: Part B of this book contains a wide variety of these patterns, arranged in an order roughly corresponding to the order of the ideas in most calculus courses. Some of the sections even have a few problems, to give additional focus to the efforts of students who may read them: Sections A.14., B.1., B.2, B.16, B.21, B.25.

I repeat the fervent hope I have expressed in other books, that any readers who detect flaws or errors of fact or judgment will do me the great kindness of letting me know so that repairs can be made.

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Table of Contents

Preface; Part A. Brief Lives: The ancients; The forerunners; The early moderns; The mature moderns; Part B. Memorable Mathematics: Answers to problems; Index.

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