From the Preface: The longest paper in volume I is 'On the Theory of the Syzygetic Relations of Two Rational Integral Functions, comprising an application to the Theory of Sturm's Functions', and to this many of the shorter papers in the volume are contributory...the volume contains also Sylvester's dialytic method of elimination, his Essay on Canonical Forms, and early investigations in the theory of Invariants. It also contains celebrated theorems as to Determinants and investigations as to the Transformation of Quadratic Forms and the recognition of the Invariant factors of a matrix.Among the Papers contained in Volume 2 are the author's Lecture on Geometry, delivered before the Gresham Committee, the author's seven lectures on the Partition of Numbers, in outline, the long memoir on Newton's Rule, the Presidential Address to the Mathematical and Physical section of the British Association at Exeter, and a set of papers 'Nugae Mathematicae.'Volume 3 deals very largely with the author's enumerative method of obtaining the complete system of concomitants of a system of quantics, with the help of generating functions; the brief but very luminous papers...on the Constructive Theory of Partitions. ..his Commemoration Day Address at Johns Hopkins University (1877)...investigations on chemistry and algebra, the paper on Certain Ternary Cubic-Form Equations, and the paper on Subinvariants and Perpetuants.Volume 4 contains Sylvester's Constructive Theory of Partitions, papers on Binary Matrices, and the Lectures on the Theory of Reciprocants. There is an added Index to the four volumes, and Biographical Notice of Sylvester.
James Joseph Sylvester (1814-1897), a mathematician, poet, and wit, was one of the contributors to the nineteenth-century English tradition in algebra. He was also an early figure in the establishment of graduate education in mathematics in the United States. One of his main contributions, with Arthur Cayley, was to initiate the theory of algebraic invariants. Among Sylvester's classic results are his theory of elementary divisors and his law of inertia of quadratic forms. This four-volume set contains his collected works.