 | University of Virginia |  |
SCHOOL OF MATHEMATICS.
Professor Echols,
Associate Professor Page.
The work of the School of Mathematics is divided into two parts:
Part I.—The Undergraduate Course, leading to the degree of B. A.,
fundamental principles of mathematics to those who pursue it as a
component part of a general education, and as a preparation to those
who desire a working knowledge of the subject for use in subsequent
studies in Physics, Astronomy, and Engineering.
Part II.—The Graduate Course, leading to the degrees of M. A. and
Ph. D., has a twofold design. In the first place its object is to require
a thorough and systematic study of the chief branches of pure mathematics
as exhibited in the writings of the best authors; and in the
second place, to inculcate a serious and thoughtful contemplation of
pure mathematics as an art, a science, and a branch of philosophy.
In this school, as at present designed, there are six classes.
B. A. COURSE.
In this course there are two classes, each of which meets three times
a week throughout the session.
Class A.—This class meets three times a week (three hours), and
devotes about three months to each of the three subjects, Algebra,
Geometry, and Trigonometry.
In Algebra the class begins with Ratio and Proportion, proceeding
to the progressions, the Binominal Formula, Convergence and Divergence
of Series, Logarithms, Determinants, and the Theory of Equations.
In Geometry the work begins with the Solution of numerous original
exercises in Plane Geometry, proceeds through Solid Geometry, with
exercises, and terminates with a short course in Geometrical Conic
Sections.
The year is closed by a course in elementary Plane Trigonometry,
embracing the Solution of Triangles by means of Logarithms, the
usual applications to the problems of Heights and Distances, etc.
The preparation necessary to enter this class is a good knowledge of
Arithmetic, of Algebra through Simultaneous Quadratic Equations,
and of Plane Geometry.
Text-Books.—Charles Smith's Algebra; Venable's Legendre's Geometry,
with Exercises; Venable's Notes on Geometric Conic Sections; Wells's Plane
and Spherical Trigonometry.
Class B.—The preparation for this class consists in a thorough
knowledge of the topics worked over in Class A.
This class devotes about three months to each of the three subjects,
Trigonometry, Analytical Geometry, and Calculus. Four and a half
hours each week.
The subject of Trigonometry, plane and spherical, is carefully
worked over and followed by the study of the Conic Sections analytically.
study of the elementary principles and applications of the Differential
and Integral Calculus.
Text-Books.—Loney's Trigonometry, Part I; Charles Smith's Conic Sections;
Echols's Calculus.
GRADUATE COURSES.
M. A.
Class C.—This class meets three times a 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'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.
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.
| University of Virginia | |