The New Mathematics

Description

The New Mathematics by Irving Adler Nearly a decade and a half after this book first gave wide currency to the term “the new mathematics,” it remains perhaps the most concise and clearest exposition of the subject for teachers, parents, and mathematics buffs alike. It has sold more than 475,000 copies in United States editions, and has been translated into ten languages. Now, in this enlarged edition, Irving Adler has made numerous revisions of the text and has added two sections: a supplement of do-it-yourself exercises, and an essay on “The Changes Taking Place in Mathematics.” This book reveals that the concepts of advanced mathematics lie hidden in the elementary mathematics we all learned in school. The author brings these concepts out of their hiding places as he traces the steps by which our number system has grown from the ordinary whole numbers we use for counting, through integers, rational numbers, and real numbers, to the complex numbers with which the electrical engineer describes an alternating current. In this way he shows the familiar origin of such unfamiliar concepts and terms of the new mathematics as groups, rings, fields, vector spaces, algebras, homomorphisms, isomorphisms, and homeomorphisms. As he reads, and takes pencil and paper to work the “Do-It-Yourself” sections, the reader will become aware that he is merely nibbling at the corner of a great rug that has a beautiful but intricate design woven into it. If what he sees from the corner arouses his curiosity about the central design, this book will prepare him to move toward it through systematic study of advanced texts. This is a book for the layman who has had elementary algebra and plane geometry and who wants to enter a fascinating new world of knowledge. It will be particularly valuable to the high school teacher who wants to enrich the curriculum, gain new insights into old structures, and keep pace with the most modern standards of mathematics teaching. Contents Foreword 7 I. Numbers for Counting 13 II. Number Systems Without “Numbers” 35 III. New Numbers From Old 44 IV. Numbers for Measuring 73 V. Filling Out the Line 90 VI. Spilling Into the Plane 125 VII. The Rank and File: Matrices 148 VIII. Arrows That Are Numbers 160 Bibliography 181 Summary of Basic Definitions 183 Appendix I. Do It Yourself Supple­ment 185 Appendix II. The Changes Taking Place in Mathematics 195 Index 219