Colloquium Publications, Volume: 1
1905; 187 pp; softcover
ISBN-10: 0-8218-4588-8
ISBN-13: 978-0-8218-4588-2
Expected publication date is July 14, 2008.
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 Poincare, 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.
Graduate students and research mathematicians interested in analysis.
H. S. White -- Linear systems of curves on algebraic surfaces
F. S. Woods -- Forms of non-Euclidean space
E. B. Van Vleck -- Selected topics in the theory of divergent series and of continued fractions
Bibliography
Colloquium Publications Volume: 2
1910; 222 pp; softcover
ISBN-10: 0-8218-4591-8
ISBN-13: 978-0-8218-4591-2
Expected publication date is July 14, 2008.
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. This book contains the lecture notes
for the three courses that were given at this colloquium: "Introduction
to a Form of General Analysis" by Eliakim H. Moore, "Projective
Differential Geometry" by Ernest J. Wilczynski, and "Selected
Topics in the Theory of Boundary Value Problems of Differential Equations"
by Max Mason.
Graduate students and research mathematicians interested geometry and topology, analysis, and differential equations.
E. H. Moore -- Introduction to a Form of General Analysis
E. J. Wilczy?ski -- Projective Differential Geometry
M. Mason -- Selected Topics in the Theory of Boundary Value Problems of Differential Equations
Colloquium Publications, Volume: 3
1913; 224 pp; softcover
ISBN-10: 0-8218-4641-8
ISBN-13: 978-0-8218-4641-4
Expected publication date is July 14, 2008.
Following the early tradition of the American Mathematical Society, the
sixth colloquium of the Society was held as part of the summer meeting
that took place at Princeton University. Two sets of lectures were presented:
Fundamental Existence Theorems, by G. A. Bliss, and Geometric Aspects of
Dynamics, by Edward Kasner.
The goal of Bliss's Colloquium Lectures is an overview of contemporary existence theorems for solutions to ordinary or partial differential equations. The first part of the book, however, covers algebraic and analytic aspects of implicit functions. These become the primary tools for the existence theorems, as Bliss builds from the theories established by Cauchy and Picard. There are also applications to the calculus of variations.
Kasner's lectures were concerned with the differential geometry of dynamics, especially kinetics. At the time of the colloquium, it was more common in kinematics to consider geometry of trajectories only in the absence of an external force. The lectures begin with a discussion of the possible trajectories in an arbitrary force field. Kasner then specializes to the study of conservative forces, including wave propagation and some curious optical phenomena. The discussion of constrained motions leads to the brachistochrone and tautochrone problems. Kasner concludes by looking at more complicated motions, such as trajectories in a resisting medium.
Graduate students and research mathematicians interested in fundamental existence theorems and geometric aspects of dynamics.
G. A. Bliss -- Fundamental existence theorems
E. Kasner -- Differential geometric aspects of dynamics
Colloquium Publications
1914; 230 pp; softcover
Volume: 4
ISBN-10: 0-8218-4598-5
ISBN-13: 978-0-8218-4598-1
List Price: US52
Member Price: US42
Order Code: COLL/4
Temporarily out of stock.
Expected publication date is July 14, 2008. Suggest to a Colleague Following the tradition of the American Mathematical Society, the seventh colloquium of the Society was held as part of the summer meeting that took place at the University of Wisconsin, in Madison. Two sets of lectures were presented: On Invariants and the Theory of Numbers, by L. E. Dickson, and Functions of Several Complex Variables, by W. F. Osgood.
Dickson considers invariants of quadratic forms, with a special emphasis
on invariants of forms defined in characteristic p, also called modular
invariants, which have number-theoretic consequences. He is able to find
a fundamental set of invariants for both settings. For binary forms, Dickson
introduces semi-invariants in the modular case, and again finds a fundamental
set. These studies naturally lead to the important study of invariants
of the standard action of the modular group. The lectures conclude with
a study of "modular geometry", which is now known as geometry
over mathbf{F}_p.
The lectures by Osgood review the state of the art of several complex variables. At this time, the theory was entirely function-theoretic. Already, though, Osgood can introduce the ideas and theorems that will be fundamental to the subject for the rest of the century: Weierstrass preparation, periodic functions and theta functions, singularities--including Hartogs' phenomenon, the boundary of a domain of holomorphy, and so on.
Graduate students and research mathematicians interested in number theory and analysis.
L. E. Dickson -- On Invariants and the theory of numbers
W. F. Osgood -- Topics in the theory of functions of several complex variables
Colloquium Publications, Volume: 6
1927; 150 pp; softcover
ISBN-10: 0-8218-4599-3
ISBN-13: 978-0-8218-4599-8
List Price: US35
Member Price: US28
Order Code: COLL/6
Temporarily out of stock.
Expected publication date is July 14, 2008. Suggest to a Colleague This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.
Graduate students and research mathematicians interested in differential equations.
Preliminary concepts. Stieltjes integrals and Fourier series
Functions harmonic within a circle
Necessary and sufficient conditions. The Dirichlet problems for the circle
Potentials of a single layer and the Neumann problem
General simply connected plane regions and the order of their boundary points
Plane regions of finite connectivity
Related problems
Index