An Introduction to the Modern Theory of Equations (Classic Reprint)

The main difference between this text and others on the same subject published in theE nglish language, consists in the selection of the material. In proceeding from the elementary to the more advanced properties of equations, the subject of invariants and covariants is here omitted, to make room for a discussion of the elements of substitutions and substitution-groups, of domains of rationality, and of their application to equations. Thereby the reader acquires some familiarity with the fundamental results on the theory of equations, reached by Gauss, A bel, Galois, and Kronecker. The Galois theory of equations is usually found by the beginner to be quite difficult of comprehension. In the present text the effort is made to render the subject more concrete by the insertion of numerous exercises. I f, in the work of the class room, this text be found to possess any superiority, it will be due largely to these exercises. Most of them are my own; some are taken from the treatises named below. In the mode of presentation I can claim no originality. The following texts have been used in the preparation of this book: Bachmann, p. KreistJ ieilung. Leipzig, 1872. BuRNS iDB, W. Theory of Groups, Cambridge, 1897. BuBNS iDB, W. S., and Panton, A. W. Theory of Equations, Vol. I, 1899; Vol. II, 1901. Dickson, L. E. Theory of Algebraic Equations, New York, 1903. EASTON, B. S. The Constructive Development of Group-T heory, Philadelphia, 1902. Encyklopadie derM athematischen Wissenschcften.
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