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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 Differ-
ential and Integral Calculus; Johnson'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, and Harkness and Morley's
Theory of Functions.
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
Integralrechung 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 Lectures on "Höhere Geometrie," Volume I.
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 "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.
In addition to the regular courses of instruction the
Mathematical Club of the University affords valuable
instruction in its formal and informal discussion of mathematical
topics and of the papers read.
During the present session Mr. Lovett delivers the
following lectures:
A course on the Geometry of Transformations embracing
the following subjects: Historic point and curve transformations
as principles of correspondence; the elementary
notions lineal-element, element-association, and contact-transformation
of Lie's geometry in the plane; determination of
all proper contact-transformations in the plane; definition
of contact transformations by means of differential equations;
an account of the applications of contact-transformations
with examples; the projective transformation; the
transformation by reciprocal radii; the pedal transformations;
the transformations by reciprocal polars; pentaspheric
coördinates; contact-transformations in ordinary space;
Lie's transformation of straight lines into spheres; transformations
in spaces of higher dimensions.
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