Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups

Abstract

THE theory of continuous groups should appeal to all who are interested in mathematics; it is based on the fundamental ideas involved in cases of change of the algebraic notation, and as such is an illuminating synthesis of a large number of our elementary operations; and the principal notions of the theory, once laid bare, are so simple and admit of so many familiar applications that these should form an integral part of elementary teaching, particularly in analytical geometry and differential equations. As to its philosophical import, the theory is of the greatest value in the analysis of our geometrical conceptions, being an indispensable part of that algebraic scheme which, at present running parallel with these, may modify them still more than hitherto before the parallelism is recognised again as an identity.

Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups.

By John Edward Campbell, Fellow and Tutor of Hertford College, Oxford, and Mathematical Lecturer at University College, Oxford. Pp. xx + 416. (Oxford: Clarendon Press, 1903.) Price 14s. net.