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 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
Krūmmung;" Salmon's "Geometry of Three Dimensions;" Darboux's "Theorie
Génēral des Surfaces;" Reye's "Geometrie der Lage;" Klein's Lectures on "Hohere
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 Lectures on
"Hohere 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.