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136 ACADEMIC DEPARTMENT.
by a full discussion of the conditions and criteria for integrability of
any given function. Definite integrals, and methods for their evalua
tion. Various functions defined by definite integrals such as the
gamma function and the logarithmic integral. Curvilinear and
multiple integrals. Two hours. Dr. Hutchinson.
[18 Theory of Groups of a Finite Order. Begins with a study
of the substitution groups that can be represented by a small number
of elements. This is followed by a study of the abstract groups whose
orders involve a small number of prime factors, the cyclical groups,
the groups whose order is a power of a prime number, etc. The latter
part of the course is devoted to applications, the Galois theory of
equations receiving the most attention. Requires courses 12 and pre
ferably 29. To be given in igoo-'oi. Three hours. Dr. Miller.]
19. General Theory of Algebraic Curves and Surfaces. Re
quires courses 12, 13, 15, and 17. Necessary to courses 25, 32, 33,
and preferably to all the courses that follow.
{a)
Algebraic Curves. Based on Clebsch and Salmon. The
principal subjects treated will be : systems of coordinates ; conditions
which determine a curve ; Pliicker's numbers ; symbolic notation ;
poles and polars ; singularities ; the forms of curves of the third and
fourth order. Two hours. Dr. Snyder.
[{b) Surfaces and Twisted Curves. Winter and spring terms.
Three hours.]
20. Algebraic Invariants. Requires courses 12, 15, and 17 ;
courses 11, 13, 14, and 18 are also desirable. This course is given
chiefly by lectures. The general linear transformation is applied, first
to a single binary quantic,
and later to a system of simultaneous
quantics in n variables ; and the necessary and sufficient conditions for
invariants, covariants, etc., are investigated. Simultaneous invariants
are shown to include covariants as a special case, and such invariants
are represented as functions of the coefficients, of the roots, and also
in the symbolic notation. Hilbert's proof of Gordan's theorem on the
finiteness of the number of irreducible invariants is given, both for
the binary quantics, and also for any number of quantics in n variables.
Much of Elliott's Algebra of Quantics is read by the class in connec
tion with the lectures,
and some attention is paid to the geometric
side of the subject. Two hours. Assistant Professor Tanner.
21. Differential Equations. A course devoted {a) to the inte
gration of special equations not discussed in course 11 ; and {b) to the
general theory of linear differential equations.
Part {a) requires course 11 as a prerequisite; and part {b), an
elementary knowledge of the varitheory
of functions of a complex