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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 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, or Bailey and Wood's Analytic Geometry. In the Calculus a book
of the grade of Osborne's Calculus is used.

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.