**Colloquium Publications**

Volume: 1;
1905;
188 pp;
Softcover
Secondary 14; 53; 40

Print ISBN: 978-0-8218-4588-2

Product Code: COLL/1

List Price: $49.00

Individual Member Price: $39.20

**Electronic ISBN: 978-1-4704-3151-8
Product Code: COLL/1.E**

List Price: $49.00

Individual Member Price: $39.20

# The Boston Colloquium

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*Frederick Shenstone Woods; Henry Seely White; Edward Burr Van Vleck*

The 1903 colloquium of the American Mathematical Society was held as
part of the summer meeting that took place in Boston. Three sets of
lectures were presented: Linear Systems of Curves on Algebraic
Surfaces, by H. S. White, Forms of Non-Euclidean Space, by
F. S. Woods, and Selected Topics in the Theory of Divergent Series
and of Continued Fractions, by Edward B. Van Vleck.

White's lectures are devoted to the theory of systems of curves on
an algebraic surface, with particular reference to properties that are
invariant under birational transformations and the kinds of surfaces
that admit given systems.

Woods' lectures deal with the problem of the classification of
three-dimensional Riemannian spaces of constant curvature. The author
presents and discusses Riemann postulates characterizing manifolds of
constant curvature, and explains in detail the results of Clifford, Klein,
and Killing devoted to the local and global classification problems.

The subject of Van Vleck's lectures is the theory of divergent series.
The author presents results of Poincaré, Stieltjes, E. Borel, and others
about the foundations of this theory. In particular, he shows "how to
determine the conditions under which a divergent series may be manipulated
as the analytic representative of an unknown function, to develop the
properties of the function, and to formulate methods of deriving a
function uniquely from the series." In the concluding portion of these
lectures, some results about continuous fractions of algebraic functions
are presented.

#### Table of Contents

# Table of Contents

## The Boston Colloquium

#### Readership

Graduate students and research mathematicians interested in analysis.