Demonstrates the profound connections that join mathematics to the history of philosophy.

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.

Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.

Classroom resource material allowing the integration of mathematics history into undergraduate mathematics teaching.

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.

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.

This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides.

A Passion for Mathematics is an educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mind-bending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike. In each chapter, Clifford Pickover provides factoids, anecdotes, definitions, quotations, and captivating challenges that range from fun, quirky puzzles to insanely difficult problems. Readers will encounter mad mathematicians, strange number sequences, obstinate numbers, curious constants, magic squares, fractal geese, monkeys typing Hamlet, infinity, and much, much more. A Passion for Mathematics will feed readers’ fascination while giving them problem-solving skills a great workout!

Exploring Mathematics: Investigations with Functions is intended for a one- or two-term course in mathematics for college students majoring in the social sciences, English, history, music, art, education, or any of the other majors within liberal arts. The mathematics course of this scope, with an algebra prerequsite, is a popular selection for liberal arts students. This 9-chapter textbook offers modern applications of mathematics in the liberal arts as well as aesthetic features of this rich facet of history and ongoing advancement of human society. With a central theme around the use of the concept of functions, and the inclusion of unique topics and chapters, Exploring Mathematics enables students to explore the next level of mathematics. It attempts to answer the questions, "How does mathematics help us to better our society and understand the world around us?" and "What are some of the unifying ideas of mathematics?" The central theme helps to impress upon the student the feeling that mathematics is more than a disconnected potpourri of rules and tricks. Although it would be inappropriate to force a functional connection in every single section, the theme is used whenever possible to provide conceptual bridges between chapters. Developing the concept of a function augments the presentation of many topics in every chapter. The Text's Objectives: The author chose the topics based on meeting the specific NCTM curriculum standards to: 1. Strengthen estimation and computational skills. 2. Utilize algebraic concepts. 3. Emphasize problem-solving and reasoning. 4. Emphasize pattern and relationship recognition. 5. Highlight importance of units in measurement. 6. Highlight importance of the notion of a mathematical function. 7. Display mathematical connections to other disciplines.

This book offers a short and accessible account of the history of mathematics, written for the intelligent layman to gain a better appreciation of its beauty, relevance, and place in history. It traces the development of the subject throughout the centuries, starting with the so-called Lebombo bone, the oldest known mathematical object that was estimated to be at least 43,000 years old, and ending with the 21st century.The presentation is informal, and no prior knowledge of mathematics is needed to enjoy the systematic chronological insights. A collection of appendices is included for more technical material — though still at the level of secondary school mathematics — and is concerned with the historically important proofs and concepts that can be explained in a simple way.