(1) THE solution of a given equation is a problem which has attracted the attention of many of the greatest mathematicians. In this tract we have a short summary of the results arrived at. The solution depends on the properties of a certain permutation group called the Galoisian group; if this group is soluble, the equation is solvable by radicals. Interesting types of soluble groups are cyclical, Abelian, and metacyclic groups. To each of the corresponding equations is devoted a chapter in which are explained the application of cyclical groups to cyclotomy, the dependence of Abelian on cyclical equations, and Kronecker's solution of the metacyclic equation. Prof. Mathews's masterly epitome of the subject is not very easy reading, and he assumes some knowledge of Tschirnhausen's transformation, the theory of permutation groups, &c. The student will probably have to prepare himself for the study of this tract by reading some more elementary treatise on the same subject (e.g. Dickson's “Algebraic Equations”), and some book on groups, such as Burnside's.
(1) Algebraic Equations.
By G. B. Mathews. Pp. viii + 64.
(2) The Theory of Optical Instruments.
By E. T. Whittaker. Pp. viii + 72. Cambridge Mathematical Tracts, Nos. 6 and 7. (Cambridge: The University Press, 1907.) Price 2s. 6d. each net.