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ACADEMIC DEPARTMENT. 137
able. The latter part of the course is based upon the works of Craig,
Jordan, Picard, and Schlesinger. Necessary to all the courses that
follow : and particularly useful in mathematical physics. Three
hours. Dr. Murray.
22. Finite Differences. This course treats of factorials, interpo
lation formulas, summation of series and difference equations, with
practical applications. The course is based on the treatises of Boole
and Markoff on finite differences. An elementary knowledge of the
differential and integral calculus is a prerequisite for this course.
Requires course 21. Two hours. Dr. Murray.
23. Theory of Groups of an Infinite Order. Begins with the
study of the linear substitution groups, the congruence groups, etc.
This is followed by a study of the theory of Lie's continuous groups
and their application to the theory of differential equations. Requires
courses 11, 17, and preferably 18 and 29. Threehours. Dr. MILLER.
25. Theory of Functions. Requires courses 12, 17, 19, 21, and
preferably 23. Useful in all the courses that follow.
{a) First year. General Function-theory. Based on Forsyth's
of Functions. Three hours. Dr. Snyder.
Theory
{b)
Second year. Theta and Abelian Functions. Theta func
tions of p variables with rational characteristics will be studied in
detail with reference to their classification and the relations existing
among them, special attention being given to functions of two and
three variables with half integer characteristics. Classification and
properties of abelian integrals,
and the application of the theta func
tions to the solution of the inversion problem. Double abelian inte
grals. Applications to geometry, particularly to hyperelliptic surfaces
and the generalized Kummer surface. Three hours. Dr. Hutchinson.
29. Theory of Numbers. Includes theory of congruences, quad
ratic residues, quadratic forms and cyclotomic numbers. Based on
the works of Bachman, Dirichlet,
and Dedekind. Requires course
12, and preferably 17, 20. Two hours. Dr. Miller.
30. Quaternions and Vector Analysis. Requires courses 12,
17, aud of mechanics. something
McMahon.
Two hours. Assistant Professor
31. Theory of Probabilities and Least Squares ; with some
applications to insurance and the theory of errors. Requires course
2 or 10. Two hours. Professor JONES.
[32. Non-Euclidian Geometry. Requires courses 12, 13, 15, 17,
19, 25(a). Two hours.]
33. Line Geometry. Requires courses 13, 15, 17, 20,
hours. Dr. Snyder.
21. Two