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SCHOOL OF MATHEMATICS
Professor Echols.
Adjunct 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 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
(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
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 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.
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