TITLES AND AUTHORS I. THE FOUNDATIONS OF GEOMETRY. By OSWALD VEBLEN, Ph.D., Professor of Mathe matics in Princeton University. II. MODERN PURE GEOMETRY. By Thomas F. Holgate, Ph.D., LL.D., Professor of Mathematics in Northwestern University. VIII. Non-EUCLIDEAN GEOMETRY. By FREDERICK S. Woods, Ph.D., Professor of Mathe matics in the Massachusetts Institute of Technology. IV. THE FUNDAMENTAL PROPOSITIONS OF ALGEBRA. By EDWARD V. HUNTINGTON, Ph.D., Assistant Pro fessor of Mathematics in Harvard University. V. THE ALGEBRAIC EQUATION. By G. A. Miller, Ph.D., Professor of Mathematics in the University of Illinois. + VI. THE FUNCTION CONCEPT AND THE FUNDA MENTAL NOTIONS OF THE CALCULUS. of Mathematics in the Universtiy of Chicago. VII. THE THEORY OF NUMBERS. By J. W. A. YOUNG, Ph.D., Associate Professor of the Pedagogy of Mathematics in the University of Chicago. VIII. CONSTRUCTIONS WITH RULER AND COMPASSES; REGULAR POLYGONS. in the University of Chicago. By David EUGENE Smith, Ph.D., LL.D., Professor of Mathematics in Teachers College, Columbia University. ON TOPICS OF MODERN MATHEMATIS RELEVANT TO THE ELEMENTARY FIELD EDITED BY J. W. A. YOUNG LONGMANS, GREEN, AND CO. FOURTH AVENUE & 30TH STREET, NEW YORK LONDON, BOMBAY, AND CALCUTTA 1911 510.45 COPYRIGHT, 1911, BY LONGMANS, GREEN, & CO. 108799 THE SCIENTIFIC PRESS BROOKLYN, N. Y. EDITOR'S PREFACE The purpose of this collection of monographs may be indicated 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 students 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 therefore contain: (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. |