Monographs On Topics Of Modern Mathematics Relevant To The Elementary Field J. W. a. Young Author - new book

MONOGRAPHS ON TOPICS OF MODERN MATHEMATICS RELEVANT TO THE ELEMENTARY FIELD EDITED BY J. W. A. YOUNG WITH A NEW INTRODUCTION BY MORRIS KLINE, PROFESSOR OF MATHEMATICS, NEW YORK UNIVERSITY DOVER PUBLICATIONS, INC. Copyright 1911 by Longmans, Green and Co. Copyright 1955 by Dover Publications, Inc. All rights reserved under Pan American and International Copyright Conventions This new Dover edition, printed in 1955, is an unabridged republication of the first edition with a new introduction by Professor Morris Kline. Published by special arrangement with Longmans, Green and Co. Printed in the United States of America. 73 EDITORS PREFACE THE purpose of this collection of monographs may be indi cated by the following citation from the letter that was sent to those who were requested to act as authors. Among the various publications on mathematics that are being made, it would seem that there is room for a serious effort to bring within reach of secondary teachers in service or in training, college students, and others at a like stage of mathematical advancement, a scientific treatment of some of the regions of advanced mathematics that have points of contact with the elementary field. Undoubtedly one of the most crying needs of our secondary instruction in mathematics to-day, is that the scientific attainments of the teachers be enlarged and their mathematical horizon widened and I believe that there is a large body of earnest teachers and stu dents that are eager to extend their mathematical knowledge if the path can be made plain and feasible for them. A volume of monographs dealing with selected topics of higher mathematics might well be a useful contribution to the meeting of this need.Such monographs would aim to bring the reader into touch with some characteristic results and viewpoints of the topics considered, and to point out their bearing on elementary mathematics. They would there fore contain KWflSftS CITY MO. PUBLIC LIBRARY 1 A considerable body of results proved in full, so that the reader can materially extend his mathematical acquisitions by the reading of the monograph alone. o o 6809393 vi PREFACE 2 Statement without proof of some leading methods and results, so as to give a birds-eye view of the subject. 3 A small number of references indicating what the reader may profitably take up after he has mastered the contents of the monograph. Both the plan itself, and the invitation to act as author, were most cordially received work on the monographs was promptly begun, has been carried through substantially as planned, and the results are presented herewith. The manuscripts have, whenever feasible, been read care fully by at least one collaborator other than myself, and in consequence various questions and suggestions have been submitted to the authors and acted upon by them. Each author, however, retains sole responsibility for his monograph as it now appears. No attempt has been made to secure uniformity in style of treatment each monograph is an inde pendent unit, that can be read without reference to the others. The amount of technical mathematical knowledge that is presupposed on the part of the reader varies with the different subjects. A large part of the book presupposes only knowledge of elementary geometry and algebra, together with a certain measure of mathematical maturity. On the other hand, there is much that will repay careful and detailedstudy by advanced students. So far as the subject-matter permits, the less difficult topics are taken up first in each monograph. J. W. A. YOUNG. INTRODUCTION The reasons given by the editor for organizing and pub lishing in 1911 the present survey of topics in advanced mathematics are all the more cogent for reprinting this vol ume in 1954. The mathematical student body is now much vaster, and mathematics itself is a more vital activity...