 | University of Virginia record February, 1912 |  |
SCHOOL OF MATHEMATICS.
Professor Echols.
Professor Page (J. M.)
Mr. Beard.
Mr. Smith.
Mr. Gaver.
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 A1 meets in two sections.
For Undergraduates.
[Students entering January 1 may begin the study of Trigonometry
in Course A1, or College Algebra in Course A2. Students entering
about March 15 may begin College Algebra in Course A1, or
Elementary Analytical Geometry in Course A2.]
Course A1, 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. (B. A. or B. S. credit, 3 session-hours.) Section I. Tuesday,
Thursday, Saturday, 9-10. Section II. Tuesday, Thursday, Saturday,
10-11. Cabell Hall. Professor Page.
Course A2: 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 A1. 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
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 1; Murray, Spherical Trigonometry; Rietz and Grathorne, 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 A1
and A2 at the opening of the 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 Course A1 or A2. Advanced
standing on the work of Course A1 or A2 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 B1: (Course A1 prerequisite).—This class meets three
times each week throughout the session. The work of the course
at the point left in course A1. The major portion of the
session's work, however, is given to the study of analytical geometry
of two dimensions in cartesian and polar coördinates. A special
study of the conic sections is followed by the study of a number of
classical curves. This course is required of all students who elect
mathematics for an undergraduate degree. (B. A. or B. S. credit,
3 session-hours.) Monday, Wednesday, Friday, 11-12. Cabell Hall.
Professor Page.
Course B2: (Course B1 prerequisite.)—This course is devoted
to a preliminary study of the Differential and Integral Calculus.
It extends throughout the session, the class meeting one hour three
times each week during the nine months. The treatment of the
subject involves the operations of differentiation and integration of
functions, with applications to the expansion of functions in series,
evaluation of illusory forms, maximum and minimum values, the
applications to geometry of curves in the problems of tangency,
contact and curvature, curve tracing, arc length, and areas, the volumes
of revolutes and of special forms of other surfaces, areas of
surfaces of revolution, and finally the solutions of the more important
simple problems in ordinary differential equations. This
course is an elective-at-large for students applying for undergraduate
degrees. (B. A. or B. S. credit, 3 session-hours.) Tuesday, Thursday,
Saturday, 12-1. Cabell Hall. Professor Echols.
Course B3: (Course A2 prerequisite).—This course is intended
for engineering students only. The class meets three times each
week throughout the session. The subject of analytical geometry
is taken up at the point left off in course A2 and finished preliminary
to the calculus. The subject of differential and integral calculus is
taken up about November first and pursued during the remainder
of the session. Less stress is laid on the principles of the subject
than in course B2 the main interest being the formal application of
the operations of the calculus to the solution of problems with the
view of making the student familiar with these operations to enable
him to apply them to the problems of applied mathematics which
he is to meet in engineering. (B. A. or B. S. credit, 3 session-hours.)
Monday, Wednesday, Friday, 12-1.[2]
Cabell Hall. Professor Echols.
For Graduates and Undergraduates.
Course C1: Courses B1 and B2 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 B2, and is systematically studied along broad lines. A course
of parallel reading on the History of Mathematics is assigned and
study of Ordinary Differential Equations. Tuesday, Thursday, Saturday,
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 D1: A Course in Differential Geometry: Course C1 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 D2: A Course in Differential Equations: Course C1 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.
[Only one of the courses D1 and D2 will be offered in 1912-13.]
Course D3: A Course in the Theory of Functions: Course C1
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 D1, D2, and D3 is carried on by means of
lectures, notes, and the systematic reading of the standard authors
in texts and in journals.
For summer-school courses in Mathematics, on which college-credit
will be allowed, see p. 258.
| University of Virginia record February, 1912 | |