Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

TITLES AND AUTHORS

I. THE FOUNDATIONS OF GEOMETRY.

By OSWALD VEBLEN, Ph.D., Professor of Mathematics in Princeton University.

II. MODERN PURE GEOMETRY.

By THOMAS F. HOLGATE, Ph.D., LL.D., Professor of
Mathematics in Northwestern University.

III. NON-EUCLIDEAN GEOMETRY.

By FREDERICK S. WOODS, Ph.D., Professor of Mathematics in the Massachusetts Institute of Technology.

IV. THE FUNDAMENTAL PROPOSITIONS OF ALGEBRA. By EDWARD V. HUNTINGTON, Ph.D., Assistant Professor 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.

By GILBERT AMES BLISS, Ph.D., Associate Professor 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.

By L. E. DICKSON, Ph.D., Professor of Mathematics in the University of Chicago.

IX. THE HISTORY AND TRANSCENDENCE OF π.

By DAVID EUGENE SMITH, Ph.D., LL.D., Professor of Mathematics in Teachers College, Columbia University,

ON TOPICS OF

MODERN MATHEMATICS

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

COPYRIGHT, 1911,

BY

LONGMANS, GREEN, & CO.

THE SCIENTIFIC PRESS
ROBERT DRUMMOND AND COMPANY
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.

V

(2) Statement without proof of some leading methods and results, so as to give a bird's-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 carefully 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 independent 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 detailed study 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.

« ΠροηγούμενηΣυνέχεια »