**American Mathematical Society Colloquium**was held at Buffalo in 1896. The Fifth such Colloquium was held at Yale University in 1906 and the lecture courses by E H Moore, E J Wilczynski, and M Mason were published in the volume

*The New Haven Mathematical Colloquium*(Yale University Press, New Haven, 1910). The Preface to the volume contains details of the three courses presented in the volume, details of the aims of the Colloquium as set out before the first Colloquium was held, and details of the four earlier Colloquia.

Preface to *The New Haven Mathematical Colloquium*

*The New Haven Mathematical Colloquium*

The American Mathematical Society held its Fifth Colloquium in connection with its Thirteenth Summer Meeting, under the auspices of Yale University, during the week September 3-8, 1906. At this Colloquium the following courses of lectures were given:

Professor **Eliakim H Moore**, of the University of Chicago: three lectures on

*The Theory of Bilinear Functional Operators.*

Professor **Ernest J Wilczynski**, of the University of California: three lectures on

*Projective Differential Geometry.*

Professor **Max Mason**, of Yale University: three lectures on

*Selected Topics in the Theory of Boundary Value Problems of Differential Equations.*

The present volume contains these lectures as prepared by their respective authors for publication.

The aim and scope of the **Colloquia of the American Mathematical Society** are well set forth in the following extract taken from an official circular issued prior to the first Colloquium:-

The colloquia preceding the fifth are the following:The objects now attained by the Summer Meeting are two-fold: an opportunity is offered for presenting before discriminating and interested auditors the results of research in special fields, and personal acquaintance and mutual helpfulness are promoted among the members in attendance. These two are the prime objects of such a gathering. It is believed however that a third no less desirable result lies within reach. From the concise, unrelated papers presented at any meeting only few derive substantial benefit. The mind of the bearer is too un-prepared, the impression is of too short duration to produce accurate knowledge of either the content or the method. ...Positive and exact knowledge, scientific knowledge, is rarely increased in these short and stimulating sessions.

On the other hand, the courses of lectures in our best universities, even with topics changing at intervals of a few weeks, do give exact knowledge and furnish a substantial basis for reading and investigation. ...

To extend the time of a lecture to two hours, and to multiply this time by three or by six, would be practicable within the limits of one week. An expert lecturer could present, in six two-hour lectures, a moderately extensive chapter in some one branch of mathematics. With some new matter, much that is old could be mingled, including for example digests of recent or too much neglected publications. There would be time for some elementary details as well as for more profound discussions. In short, lectures could be made profitable to all who have a general knowledge of the higher mathematics.

**I. THE BUFFALO COLLOQUIUM, 1896.**

(a) Professor MAXIME BÔCHER, of Harvard University

*Linear Differential Equations, and their Application.*

This colloquium has not been published, but several papers appeared at about the time of the colloquium, in which the author dealt with topics treated in the lectures.

(b) Professor JAMES PIERPONT, of Yale University:

*Galois's Theory of Equations.*

This colloquium was published in the *Annals of Mathematics*, ser. 2, vols. 1 and 2 (1900).

**II. THE CAMBRIDGE COLLOQUIUM, 1898.**

(a) Professor WILLIAM F OSGOOD, of Harvard University:

*Selected Topics in the Theory of Functions.*

This colloquium was published in the *Bulletin of the Amer. Math. Soc.*, ser. 2, vol. 5 (1898), p. 59.

(b) Professor ARTHUR G WEBSTER, of Clark University:

*The Partial Differential Equations of Wave Propagation.*

**III. THE ITHACA COLLOQUIUM, 1901.**

(a) Professor OSKAR BOLZA, of the University of Chicago:

*The Simplest Type of Problems in the Calculus of Variations.*

Published in amplified form under the title:

*Lectures on the Calculus of Variations*, Chicago, 1904.

(b) Professor ERNEST W BROWN, of Haverford College:

*Modern Methods of Treating Dynamical Problems, and in Particular the Problem of Three Bodies.*

**IV. THE BOSTON COLLOQUIUM, 1903.**

(a) Professor HENRY S WHITE, of Northwestern University: three lectures on

*Linear Systems of Curves on Algebraic Surfaces.*

(b) Professor FREDERICK S WOODS, of the Massachusetts Institute of Technology: three lectures on

*Forms of Non-Euclidean Space.*

(c) Professor EDWARD B VAN VLECK, of Wesleyan University: six lectures on

*Selected Topics in the Theory of Divergent Series and Continued Fractions.*

This colloquium was published in full, under the title *The Boston Colloquium.* Lectures on Mathematics. The Macmillan Co., N.Y., 1905.

The expense incurred in publishing the present volume was defrayed by a grant, from Yale University.

The editor wishes to express his thanks to *The New Era Printing Co.* for their efforts to secure the typographical excellence of the present volume, and for their unfailing patience in spite of many unavoidable delays in printing.