Turnbull H.W. Theory of Equations

New York: Interscience Publisher, 1947. - 189 Pages.This book is founded on the lecture course given in the University of St Andrews to students reading for an Ordinary Degree in Mathematics and to first-year Honours students. It contains a short and elementary account of algebraic equations, both from the theoretical and the practical side, together with the algebra of polynomials and rational fractions. It includes classes of number, partitions, identities, the G.C.M. process, partial fractions arid recurring series, but it omits continued fractions and indeterminate equations. Cubic and biquadratic equations are discussed, together with more general types, elimination, and symmetric functions, but the theory of invariants and of groups is left untouched. An elementary knowledge of algebra is presupposed, particularly of long division, quadratic equations and the binomial theorem, together with elementary determinants, coordinate geometry and differential calculus. The more advanced determinantal and matrical theory of p. 48 and p. 141 may be omitted on a first reading. The book has been written with the historical development of algebra constantly in mind ; and many of the topics have been selected for their importance, not only as part of a general mathematical education, but also as
preliminaries to the study of all higher algebra. I acknowledge with gratitude the help which I have derived from the well-known treatises on algebra and equations written in England, Ireland, America and Germany : more particularly from the works of Todhunter and of Professor P. B. Fischer. I also thank the editors of the present series, my colleagues, and the printers for their helpful co-operation.