 | University of Virginia record February, 1910 |  |
SCHOOL OF MATHEMATICS.
Professor Echols.
Professor Page.
Mr. Givens.
Mr. Brooke.
Mr. Didlake.
Mr. Smith.
Required for Admission to the Work of the School: Mathematics
A, B and C, of the general entrance requirements, p. 71.
In this School, as at present organized, there are nine 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
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 is devoted, the class begins with a study of the Cartesian
and polar systems of Coördinates, with numerous exercises in the
grapical 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;
Loney, Analytical 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 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 one of these examinations will be given a certificate of
proficiency in the work required in Courses 1A or 2A.
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
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, 11-12. Cabell
Hall. Professor Echols.
Course 4B: This course is required of all engineering students,
the Course 2A, being prerequisite. All engineering students applying
for advanced study in this course must pass a written examination
on the topics of the Course 2A. The work of the course begins the
analytical geometry of the conic sections with the study of the circle
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 value of Mathematics and more to the utilitarian
aspect. Monday, Wednesday, Friday, 11-12. Cabell Hall. Professor
Echols.
Text-Books.—Charles Smith, Conic Sections; Notes on Analytical Geometry of
Three Dimensions; Echols, Differential and Integral Calculus.
Special Course in Analytical Geometry. A special course in
Analytical Geometry, repeating the work of the first term of Course
3B above, is given, beginning in January, and running for two hours
a week till the close of the session. Hours by appointment. Professor
Echols.
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,
12-1. 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
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.]
| University of Virginia record February, 1910 | |