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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.,
is designed with a view of giving an intelligent comprehension of the
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
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 (three hours) throughout the session.
Class A.—This class meets three times a week; 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 Binomial 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; and Wells'
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.
The subject of Trigonometry, plane and spherical, is carefully
worked over and followed by the study of the Conic Sections analytically.
The last three months of the session are devoted to the 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;
Osborne's Calculus.
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
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 and 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.
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