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Introduction to the Theory of Equations

Nature volume 162, page 87 (17 July 1948) | Download Citation



THE contents of this volume fall into three clearly marked sections. Chapters 1–4 (pp. 1–105) lead up to the location and calculation of the real roots of a real algebraic equation ; the cubic and quartic equations are studied in Chapter 2, as a preliminary to theorems on the general equation. Sturm‘s theorem provides for locating the roots of the general equation, but the only method of calculation expounded is that of Horner, explained very lucidly with attention to the justification of contracted processes. Chapters 5–7 (pp. 106–235) deal with determinants, introduced for orders 2 and 3 and extended to order n, and with systems of linear equations. The connexion between a set of solutions of such a system and the rank of the augmented matrix of the system is set out carefully ; but some hints on what can be done to alleviate the tedious process of solving a numerical set of linear equations would have been welcome. Chapter 8 sets out the axiomatic theory of the complex number, familiarity with the technique having been assumed in the early chapters. Chapter 9 deals with symmetric functions of the roots of an algebraic equation, a topic the academic elegance of which has caused it to be over-elaborated in some text-books ; Prof. Griffiths rightly relegates it to the subordinate position it should occupy in an introductory account.

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