University of Virginia Library

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's 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 und 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.

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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.