University of Virginia record :: February 1, 1915 :: University of Virginia Library

Students entering January 1 may begin the study of Geometry in
Mathematics A1, or College Algebra in Mathematics A2. Students entering
about March 15 may begin College Algebra in Mathematics A1, or
Elementary Analytical Geometry in Mathematics A2.

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Mathematics A1: Mathematics A, B, and C of the entrance requirements,
prerequisite.

First Term: 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.

Second Term: 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.

Third Term: 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. Section III, Tuesday,
Thursday, Saturday, 11-12. Section IV, Monday, Wednesday, Friday,
9-10. Cabell Hall. Professor Page.

Mathematics A2: Mathematics A, B, C, and D, of the entrance requirements,
prerequisite.

The first two terms of the session are devoted to Trigonometry and
Algebra, respectively; and the first and third terms covered in these subjects
are exactly the same as those described above for the first and third
terms of Mathematics 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. (B. A. or B. S. credit, 3 session-hours.) Monday,
Wednesday, Friday, 9-10. Cabell Hall. Professor Page.

Text-Books: Venable, Legendre's Geometry, with Exercises; Loney, Trigonometry,
Part I; Murray, Spherical Trigonometry; Reitz and Crathorne, College
Algebra; Fine and Thompson, Coördinate Geometry.

In addition to the regular examinations held during the session, there
will be held special examinations on the work of Mathematics 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 Mathematics A1 or A2. Advanced standing on the work of
Mathematics 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.

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Mathematics B1: Mathematics A1 prerequisite.—The work of the
course consists of an advanced course in trigonometry, taking up the subject
where left off in Mathematics 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. (B. A. or B. S.
credit, 3 session-hours.) Monday, Wednesday, Friday, 11-12. Cabell Hall.
Professor Page.

Mathematics B2: Mathematics B1 prerequisite.—This course is devoted
to a preliminary study of the Differential and Integral Calculus.
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, are 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. (B. A. or B. S. credit, 3 session-hours.) Tuesday,
Thursday, Saturday, 12-1. Cabell Hall. Professor Echols.

Mathematics B3: Mathematics A2 prerequisite.—This course is intended
for engineering students only. The subject of Analytical Geometry
is taken up at the point left off in Mathematics 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 Mathematics 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 so that he can apply them to the problems
of applied mathematics which he is to meet in engineering. Credit to
engineering students for work done elsewhere covering this course or any
portion of it must be obtained through application to and with the approval
of the Engineering Faculty. (B. A. or B. S. credit, 3 session-hours.) Monday,
Wednesday, Friday, 12-1.[1] Cabell Hall. Professor Echols.

[1]

For examination dates, see Engineering Schedule, p. 252, Mathematics
103-4-5.

For Undergraduates and Graduates.

Mathematics C1: Mathematics 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
Mathematics B2, 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

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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.

For Graduates.

Mathematics D1: Differential Geometry: Mathematics C1 prerequisite.—In
this course the year will be devoted to 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.

Mathematics D2: Differential Equations: Mathematics C1 prerequisite.—In
this course there will be presented a study of 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 1915-1916.]

Mathematics D3: Theory of Functions: Mathematics C1 prerequisite.—In
this course is offered to advanced students a study of 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.
Monday, Wednesday, Friday, 11-12. Professor Echols.

The work in Mathematics 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.

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For summer-school courses in Mathematics, on which college credit
will be allowed, see p. 273.