University of Virginia :: March, 1907 :: University of Virginia Library

Required for Admission to the Work of the School: The General
Entrance Examination, and in addition an examination for classification:
the latter covers algebra through quadratics and the whole of Plane
Geometry.

In this School as at present organized there are seven courses.

Primarily for Undergraduates.

Course 1: The examination for classification 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 1 on the first day

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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 1. Prof. Page.

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

Course 2: Course 1 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.
Prof. Echols.

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

For Undergraduates and Graduates.

Course 3: Course 2 prerequisite.—This course begins with the study
of Analytical Geometry of Three Dimensions. The Differential and
Integral Calculus is taken up, at the point left off in Course 2, and is
systematically studied along broad lines. A course of parallel reading on
the History of Mathematics is assigned and an examination held in this
subject. The course closes with the study of Ordinary Differential Equations.
Prof. Echols.

Text-Books.—Charles Smith, Solid Geometry; Echols, Differential and
Integral Calculus; Williamson, Differential Calculus; Williamson, Integral
Calculus; Murray, Differential Equations; Cajori, History of Mathematics.

For Graduates Only.

The candidate for the degree of Doctor of Philosophy, who chooses
Mathematics for his major subject, is required to complete the work of
the four following courses, as well as that of Course 3, and to present a
thesis which shall be acceptable to the Faculty.

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Course 4: A Course in Geometry: Course 3 prerequisite.—In this
is offered a preparatory course in Descriptive Geometry, which is followed
by courses in Projective and Kinematical Geometry.

A study is made of the foundations on which Geometry is based after
the methods of Hilbert, Lobatschewsky, Riemann, etc. Prof. Echols.

Course 5: A Course in Differential Geometry: Course 3 prerequisite.—In
this the year will be devoted to a course in the Applications
of the Differential and Integral Calculus to Geometry, with special reference
to the theory of the General Space Curve, the Surface, and the Surface
Curve. Prof. Page.

Course 6: A Course in Differential Equations: Course 3 prerequisite.—In
this there will be presented a course in Ordinary and Partial
Differential Equations. In the discussion of the Ordinary Differential
Equation, particular attention is paid to the theory of integration of such
equations as admit of a known Transformation Group, and the classic
methods of integration are compared with those which flow from the
Theory of Transformation Groups. A similar method is adopted in the
study of the Simultaneous System, with its equivalent Linear Partial
Differential Equation of the First Order. As far as the time admits, the
theories of integration of the Complete System, as well as those of the
General Partial Differential Equation of the First and Second Orders,
will be discussed. Prof. Page.

Course 7: A Course in the Theory of Functions: Course 3 prerequisite.—In
this class is offered to advanced students a course in Mathematical
Analysis. The treatment of the subject is arranged under three
heads, as follows:

The design of the numbers of analysis and the laws of the operations
to which they are subject are studied after the methods of Dedekind and
Tannery, Cantor and Weierstrass, as introductory to the study of functions.

The study of the Theory of Functions of a Real Variable, including
series, products, and continued fractions, the Calculus of Finite Differences
and of Variations, lead up to the need of the complex variable.

The General Theory of Functions of a Complex Variable is studied
after the methods of Cauchy, Riemann, and Weierstrass.

A special study is made of the series of Taylor and of Fourier.
Prof. Echols.

The work in Courses 4, 5, 6, and 7 is carried on by means of lectures,
notes, and the systematic reading of the standard authors in texts and in
journals.