University of Virginia Library

SCHOOL OF MATHEMATICS

Mathematics C1: Mathematics B1 and B2 or Mathematics A2 or A3 and
B2, prerequisite.—Analytical geometry of three dimensions; advanced differential
and integral calculus; differential equations. Professor Echols.

Mathematics C2: Higher Algebra: Mathematics B2, prerequisite.—First
term: Operations with and transformations of matrices, determinants, vectors
and tensors. Second term: Invariants and covariants of polynomials, particularly
of bilinear forms and of quadratic forms. Third term: One-to-one
quadratic transformations and an introduction to contact transformations. Numerous
applications will be made to analytical geometry, projective geometry,
non-Euclidean geometry and mechanics. Hours by appointment. Associate Professor
Linfield.

Mathematics C3: Higher Geometry: Mathematics C2, prerequisite.—
First term: Algebraic plane curves with particular attention to curves of the
3rd degree or the 3rd class. Second term: Circle and sphere geometry and circular
transformations. Third term: Line geometry with a brief study of the
theory of screws. Hours by appointment. Associate Professor Linfield. Only
one of the courses C2 and C3 will be given in any one year.

Mathematics C4: Projective Geometry: An introductory course. Hours
by appointment. Professor Luck.

Mathematics D1: Mathematics C1 and a reading knowledge of German
prerequisite.—Differential Geometry: This course opens with a brief study of
ordinary differential equations from the Lie group standpoint and continues with

a study of the metric differential properties of plane and space curves and of
surfaces, including important curve families on surfaces such as lines of curvature,
asymptotic curves, geodesics, etc. Hours by appointment. Professor Luck.
Only one of the courses C4 and D1 will be given in any one year.

Mathematics D2: Mathematics C1, prerequisite.—Ordinary and partial differential
equations. Hours by appointment. Professor Page.

Mathematics D3: Mathematics C1 and C2, prerequisite.—Analysis (Functions
of real variables). The course will begin with a study of the definitions of
the seven algebraic operations and of the limit of a sequence. Continuous, differentiable
or integrable functions of real variables will then be defined through
the use of the limits of sequences and their important properties deduced from
these definitions. The third term will be devoted to a study of some particular
transcendental functions of real variables. Great emphasis will be laid throughout
the course on detailed rigorous proof. Hours by appointment. Associate
Professor Linfield.

Mathematics D4: Mathematics C1 and D3, prerequisite.—Theory of functions
of a complex variable. Vector Analysis. Hours by appointment. Professor
Echols.