 | The University of Virginia record February, 1908 |  |
SCHOOL OF MATHEMATICS.
Professor Echols.
Professor Page.
Dr. Stone.
Mr. Luck.
Mr. Michie.
Mr. Givens.
Required for Admission to the Work of the School: The four
blocks set in Mathematics at the General Entrance Examinations.
In this School as at present organized there are eight courses.
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
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.
For Undergraduates and Graduates.
Course 3C: Course 2B 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 2B, 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.
Professor Echols.
For Graduates Only.
Text-Books.—Charles Smith, Solid Geometry; Echols, Differential and Integral
Calculus; Williamson, Differential Calculus; Williamson, Integral Calculus; Murray,
Differential Equations; Cajori, History of Mathematics.
The candidate for the degree of Doctor of Philosophy, who chooses
Mathematics for his major subject, is required to complete the work of
the five following courses, as well as that of Course 3C, and to present a
dissertation which shall be acceptable to the Faculty.
Course 4D: A Course in Geometry: Course 3C prerequisite.—An
advanced course in analytic geometry, in homogeneous, tangential and
radial coördinates, with applications to kinematics and the theory of
homogeneous displacement. A study is made of the foundations on which
Geometry is based after the methods of Hilbert, Lobatschewsky, Riemann,
etc. Professor Echols.
Course 5D: A Course in Differential Geometry: Course 3C 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. Professor Page.
Course 6D: A Course in the Theory of Continuous Groups:
Course 3C prerequisite.—In this will be presented an outline of the General
Theory of Continuous Groups of point and contact transformations. Numerous
application to Geometry and Differential Equations will be adduced.
Professor Page.
Course 7D: A Course in Differential Equations: Course 3C 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 Continuous Groups. A similar method is adopted in the study
of the 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. Professor Page.
[Not more than two of the Courses 5D, 6D, 7D, are offered in one
session.]
Course 8D: A Course in the Theory of Functions: Course 3C
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 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. Professor
Echols.
The work in Courses 4D, 5D, 6D, 7D and 8D is carried on by means
of lectures, notes, and the systematic reading of the standard authors in
texts and in journals.
| The University of Virginia record February, 1908 | |