Recent Works on the Theory of Determinants

Abstract

THREE of these works are introductory text-books of from fifty to eighty pages, and may consequently be dismissed in a few lines. The first is a skilfully arranged and well-written manual, furnished with suitable exercises, and ought to be found exceedingly serviceable in the secondary schools of Portugal. That by Prof. Mansion, of Ghent, has already been referred to in NATURE; the fact that it is now in the fourth French edition and second German edition is sufficient proof of its value. The third, by Gymnasial-Professor Sickenberger, is the largest and yet the most elementary, having been intended (not very wisely, we are disposed to think) for pupils very imperfectly prepared in algebra. Twelve pages, including a collection of thirty exercises, are devoted to determinants of the second order, thirty-eight pages to those of the third order, and the remaining thirty pages to determinants in general, the whole being pre pared with endless pains and much preceptorial skill. Introductory works of this kind have for a number of years been appearing in Germany at the rate of 1.3. … per annum: in England we have not had one since 1875. Our insular way of doing things, however, is so different from that of the Germans that it may be fairly questioned whether we are any the worse for the deficiency. It would certainly be very erroneous to conclude that the advance of the theory of determinants in the two countries during the period referred to has shown the same marked contrast.

Primeiros Principlos da. Theoria dos Determinantes.

Por J.-A. Albuquerque. (Porto, 1884.)

Die Determinanlen in genetischer Behandlung.

Von Adolf Sickenberger. (München, 1885.)

Vorlesungen über Invariantentheorie.

Bd. 1. Determinanten. Von Paul Gordan. (Leipzig, 1885.)

Elemente der Theorie der Determinanten.

Von Paul Mansion. 2te vermehrte Auflage. (Leipzig, 1886.)

An Elementarey Treatise on the Theory of Determinants.

By Paul H. Hanus (Boston, 1886.)

Beitrage sur Theorie der Determinanten.

Von Wilhelm Schrader. (Halle, 1887.)