University of Virginia Library

Primarily for Undergraduates.

Course 1A: Admission to the School prerequisite. This class meets
three times a week, and devotes about three months to each of the three
subjects—Geometry, Trigonometry, and Algebra.

In Geometry the work begins with the solution of numerous
original exercises in Plane Geometry, and proceeds through Solid
Geometry with constant drill in original exercises.

In Trigonometry, a complete course in Plane and Spherical Trigonometry
is pursued with constant drill in the solution of problems, and
exercises in the use of logarithms.

In Algebra, the work begins with the Progressions and proceeds
with the study of the Binomial Formula, Convergence and Divergence
of Series, with special study of the Binomial, Exponential, and Logarithmic

Series. The study of Inequalities and Determinants prepares
for the Theory of Equations with which the course is closed.

In addition to the regular examinations held during the session, there
will be held a special examination on the work of Course 1A on the first
day of each session, to which any student registered in the School of Mathematics
will be admitted. To a student successfully passing this examination
will be given a certificate of proficiency in the work required in Course
1A. Professor Page.

Text-Books.—Venable, Legendre's Geometry, with Exercises; Loney, Trigonometry,
Part I; Murray, Spherical Trigonometry; Charles Smith, Treatise on Algebra.

Course 2B: Course 1A prerequisite.—The class devotes three months
to Analytical Geometry and six months to the Differential and Integral
Calculus.

In Analytical Geometry, the Cartesian method of representing a function
by points, lines, and surfaces is considered, and a special study of the
conic sections is made. In three dimensions, as far as the time permits,
the straight line, the plane and the conicoids are introduced and discussed.

In the Calculus a careful study of the functions of one variable is
made, and is followed by the study of functions of two and three variables
as far as the time allows.

In this class both the educational and the practical value of the topics
considered, as well as their importance with regard to all further work in
mathematics, are clearly brought to view. Constant drill at the board and
frequent examination and repetition of principles are insisted on. Professor
Echols.

Text-Books.—Charles Smith, Conic Sections; Notes on Analytical Geometry of
Three Dimensions; Echols, Differential and Integral Calculus.