The theory of determinants in the historical order of development, by Sir Thomas Muir.

DETERMINANTS IN GENERAL (DIEKMANN, 1875, 1876) 59

DIEKMANN, J. (1875, 1876): FALK, M. (1876):
GULDBERG, A. S. (1876).
[Die Determinanten als Unterricht auf Gymnasien und Realschulen.
Zeitschriftf. math. u. naturv. Unterricht, vi. pp. 1-21, 124-137,
193-211.]
[EINLEITUNG IN DIE LEHRE VON DEN DETERMINANTEN, und ihre
Anwendung auf dem Gebiete der niederen Mathematik. Zum
Gebrauch an Gymnasien, Realschulen u. andern hohern
Lehranstalten, sowie zum Selbstunterricht. viii + 88 pp.
Essen.]
[LAROBOK I DETERMINANT-TEORIENS FORSTA GRUNDER, f6r hogre
laroanstalter och till sjelfstudium. iv+96 pp. Upsala.]
[DETERMINANTERNES TEORI. Udgivet med bidrag af videnskabernes selskab i Trondhjem. viii+88 pp. Kristiania.]
In his first publication Diekmann pressed on teachers his views
as to the part that ought to be taken by determinants in a school
course; he then almost immediately after brought out a booklet
planned and written in accordance therewith. Less than a third
part of the exposition is devoted to determinants pure and simple,
but the little elementary knowledge thus acquired is utilized to the
utmost in the remaining pages. In some respects it is not an
advance on similar booklets already in use. The general question
which he raised, however, was both timely and appropriate, and
was certain sooner or later to be amply discussed by intemperate
advocates of a novelty and by natural opponents of change.
Falk's publication, though meant for the same kind of readers
as Diekmann's, is of a quite different character, about two-thirds
of it being occupied with the establishment and illustration of
twelve carefully formulated theorems, including three on Jacobians,
and the remainder with forty exercises, worked and unworked,
culled from well-known sources.
Guldberg's is still less of an elementary introduction, being indeed
a reversion to an earlier type and intended apparently for such
readers as Brioschi and Baltzer had in view. It makes no pretensions to freshness of manner or matter.