 | University of Virginia record February, 1911 |  |
SCHOOL OF MATHEMATICS.
Professor Echols.
Professor Page.
Mr. Smith.
Mr. Echols.
Mr. Beard.
Mr. Wilson.
Required for Admission to the Work of the School: Mathematics
A, B and C, of the general requirements, p. 71.
In this School, as at present organized, there are ten courses. The
class in Course 1A meets in two sections.
For Undergraduates.
[Students entering January 1 may begin the study of Trigonometry
in Course 1A, or College Algebra in Course 2A. Students entering about
March 15 may begin College Algebra in Course 1A, or Elementary Analytical
Geometry in Course 2A.]
Course 1A, Sections I and II: Admission to the School prerequisite.
Each Section 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. Section I.
Tuesday, Thursday, Saturday, 9-10. Section II. Tuesday, Thursday, Saturday,
10-11. Cabell Hall. Professor Page.
Course 2A: Mathematics A, B, C and D, of the general entrance
requirements, prerequisite.
This section meets three times a week, and devotes about three months
to each of the three subjects, Trigonometry, Algebra, and elementary
Analytical Geometry.
The first two terms of the session are devoted to Trigonometry and
Algebra, respectively; and the courses covered in these subjects are
exactly the same as those described above for Sections I and II of
Course 1A. In elementary Analytical Geometry, to which the third term
systems of Coördinates, with numerous exercises in the graphical representation
of equations. Especial attention is paid to the straight line and the
general equation of the first degree in two variables. The course is intended
to prepare for the study of the Analytical Geometry of the Conic
Section. Monday, Wednesday, Friday, 9-10. Cabell Hall. Professor Page.
Text-Books.—Venable, Legendre's Geometry, with Exercises; Loney, Trigonometry,
Part I; Murray, Spherical Trigonometry; Rietz and Crathorne, College
Algebra; Fine and Thompson, Coördinate Geometry.
In addition to the regular examination held during the session, there
will be held special examinations on the work of Courses 1A and 2A
Tuesday, September 18, to which any student registered in the School of
Mathematics will be admitted. To a student successfully passing one of
these examinations will be given a certificate of proficiency in the work
required in Course 1A or 2A. Advanced standing on the work of Course
1A or 2A will be granted a student entering from a secondary school only
after he has passed here the prescribed examination on the course in
question.
Course 3B: 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. Tuesday, Thursday, Saturday, 12-1. Cabell Hall. Professor Echols.
Course 4B: This course is required of all engineering students,
Course 2A being prerequisite. All engineering students applying for
advanced standing in this course must pass a written examination on the
topics of Course 2A. The work of the course begins the analytical
geometry of the conic sections with the study of the circle or parabola
and takes up the Differential Calculus early in November, concluding it
in March. The remainder of the session is devoted to the Integral Calculus.
In this course less attention is given to the educational and theoretical
Wednesday, Friday, 12-1. Cabell Hall. Professor Echols.
Text-Books.—Charles Smith, Conic Sections; Echols, Notes on Analytical
Geometry of Three Dimensions; Echols, Differential and Integral Calculus.
For Graduates and Undergraduates.
Course 5C: Course 3B 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.
Monday, Wednesday, Friday, 11-12. Cabell Hall. Professor 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.
Primarily for Graduates.
Course 6D: A Course in Geometry: Course 3C prerequisite.—An
advanced course in analytical geometry, in homogeneous, tangential and
radial coördinates, with applications to kinematics and the theory of
homogeneous displacement. Hours by appointment. Professor Echols.
Course 7D: 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. Hours by appointment. Professor Page.
Course 8D: 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
applications to Geometry and Differential Equations will be adduced.
Hours by appointment. Professor Page.
Course 9D: 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. Hours by appointment. Professor
Page.
[Not more than two of the Courses 7D, 8D, 9D, are offered in one
session.]
Course 10D: 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. Tuesday,
Thursday, Saturday, 11-12. Professor Echols.
The work in Courses 6D, 7D, 8D, 9D, and 10D is carried on by means
of lectures, notes, and the systematic reading of the standard authors in
texts and in journals.
| University of Virginia record February, 1911 | |