Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888).
The theories of determinants and of symmetric functions and of the algebra of differential operations have an important bearing upon this comparatively new branch of mathematics.
Pp. 8 0 -94, 95112) showed by his calculus of hyper-determinants that an infinite series of such functions might be obtained systematically.
So that A breaks u p into a sum of determinants, and we also obtain a theorem for the addition of determinants which have rows in common.