University of Virginia Library

GRADUATE COURSES.

M. A.

Class C.—This class meets three times each week (four and a half hours)
throughout the session. It begins with the study of Analytical Geometry of
three dimensions, and takes a systematic course in the Differential and Integral
Calculus, and completes the course with a study of Differential Equations.

Text-Books.—Charles Smith's Solid Geometry; Williamson's Differential and
Integral Calculus; Murray's Differential Equations.

This course is required for graduation in the M. A. course of Mathematics.

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.

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.