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More About This Textbook
Overview
Editorial Reviews
Booknews
New edition of a text representing a collection of topics chosen to meet the criteria of applicability to reallife problems, accessibility, inclusion of modern mathematics, and aesthetics. Sixteen chapters discuss the mathematics of social choice, management science, growth and symmetry, and statistics. Exercises address a broad spectrum of levels of difficulty. Annotation c. by Book News, Inc., Portland, Or.Product Details
Related Subjects
Meet the Author
Read an Excerpt
The "excursions" in this book represent a collection of topics chosen to meet a few simple criteria.
The material in the book is divided into four independent parts. Each of these parts in turn contains four chapters dealing with interrelated topics.
An important goal for this book is that it be flexible enough to appeal to a wide range of readers in a variety of settings. The exercises, in particular, have been designed to convey the depth of the subject matter by addressing a broad spectrum of levels of difficultyāfrom the routine drill to the ultimate challenge. For convenience (but with some trepidation) the exercises are classified into three levels of difficulty:
Traditional exercises sometimes are not sufficient to convey the depth and richness of a topic. A new feature in this edition is the addition of a Projects and Papers section following the exercise sets at the end of each chapter. One of the nice things about the "excursions" in this book is that they often are just a starting point for further exploration and investigation. This section offers some potential topics and ideas for some of these explorations, often accompanied with suggested readings and leads for getting started. In most cases, the projects are well suited for group work, be it a handful of students or an entire small class.
What Is New in This Edition?
The two most visible additions to this edition are the Projects and Papers section discussed above and a biographical profile at the end of each chapter (in the chapter on Apportionment, a historical section detailing the checkered story of apportionment in the U.S. House of Representatives was added instead). Each biographical profile features a scientist (they are not always mathematicians) who made a significant contribution to the subject covered in the chapter. In keeping with the spirit of modernity, most are contemporary and in many cases still alive.
Other changes in this edition worth mentioning are:
Table of Contents
Preface
PREFACE
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.Ā Ivars Peterson, The Mathematical Tourist
Excursions in Modern Mathematics is, as we hope the title might suggest, a collection of "trips" into that vast and alien frontier that many people perceive mathematics to be. While the purpose of this book is quite conventionalāit is intended to serve as a textbook for a collegelevel liberal arts mathematics courseits contents are not. We have made a concerted effort to introduce the reader to an entirely different view of mathematics from the one presented in a traditional general education mathematics curriculum. The notion that general education mathematics must be dull, unrelated to the real world, highly technical, and deal mostly with concepts that are historically ancient is totally unfounded.
The "excursions" in this book represent a collection of topics chosen to meet a few simple criteria.
OUTLINE
The material in the book is divided into four independent parts. Each of these parts in turn contains four chapters dealing with interrelated topics.
EXERCISES
We have endeavored to write a book that is flexible enough to appeal to a wide range of readers in a variety of settings. The exercises, in particular, have been designed to convey the depth of the subject matter by addressing a broad spectrum of levels of difficultyfrom the routine drill to the ultimate challenge. For convenience (but with some trepidation) we have classified them into three levels of difficulty:
THE FOURTH EDITION
This fourth edition of Excursions in Modern Mathematics retains the topics and organization of the third edition, in a more attractive and hopefully more user friendly package. The exercise sets at the end of each chapter have been significantly reorganized and expanded. The Walking exercises are now classified and listed according to topic, and there is now a much wider variety of exercises to choose from in each topic.
TEACHING EXTRAS AVAILABLE WITH THE FOURTH EDITION
A FINAL WORD
This book grew out of the conviction that a liberal arts mathematics course should teach students more than just a collection of facts and procedures. The ultimate purpose of this book is to instill in the reader an overall appreciation of mathematics as a discipline and an exposure to the subtlety and variety of its many facets: problems, ideas, methods, and solutions. Last, but not least, we have tried to show that mathematics can be fun.
ACKNOWLEDGMENTS
This book is now in its fourth edition, and there are many people who contributed in significant ways to help it along the way. We are thankful to each and every one of them.
Thanks go to St. Cloud State University mathematics faculty for their invaluable insight. Their dedication and resulting comments have helped shape many of the improvements in this revision.
The exercise sets have grown over time, with valuable contributions at various stages from Vahack Haroutunian, Ronald Wagoner, Carlos Valencia, and L. T. Ullmann.
We extend special thanks to Professor Benoit Mandelbrot of Yale University who read the manuscript for Chapter 12 and made several valuable suggestions.
For this fourth edition, the contributions of our copy editor Kathy SessaFederico and our production editor Barbara Mack were invaluable, and much of the improvements in presentation and readability are due to their work.
Last, but not least, the person most responsible for the success of this book is Sally Yagan. There is an editor behind every book, but few that can match her vision, "cando" attitude, and leadership.