PH. D.
Class D.—This class meets three times each week throughout the
session. The topics discussed are: The Theory of the Number System;
Determinants; the Infinitesimal and Finite Calculus and the general
Theory of Functions.
Reference Books.—Scott's Determinants: Laurent Traité d'Analyse; Chrystal's
Algebra; Boole's Finite Differences; Tannery's Théorie des Fonctions d'une
Variable, and Harkness and Morley's Theory of Functions; Picard, Traité
d'Analyse.
Class E.—The first half-year will be devoted to a course on the Applications
of the Differential and Integral Calculus to Geometry, with
special reference to the Theory of Surfaces—and curves on surfaces.
During the second half-year a course in Pure Geometry, beginning
with Projective Geometry and proceeding to elementary Higher
Geometry, will be offered.
This class, and the following one, meet three times a week, and the
subjects will be presented by lectures.
Reference Books.—Joachimsthal's Anwendung der Differential and Integralrechnung
auf die Allgemeine Theorie der Flächen, und der Linien Doppelter
Krümmung, Salmon's Geometry of Three Dimensions: Darboux's Théorie
Général des Surfaces; Reye's Geometrie der Lage; Klein's Höhere Geometrie,
Volume I; Page's Differential Equations.
Class F.—In this class will be presented a course in Lie's Theory of
Transformation Groups, with Applications to Differential Equations
and to Higher Geometry.
Reference Books.—Lie's Works on Transformation Groups; Klein's Höhere
Geometrie, Volume II.
The candidate for the Ph. D. degree is required to complete the
work of all the classes in the graduate courses, and to present a thesis
which shall be acceptable to the faculty.
