Hussey 1-14-50 16348 The following work is designed for the use of the higher classes of Schools and the junior students in the Universities. Although the book is complete in itself, it is expected that students who use it will have previously read some more elementary work on Algebra: the simpler parts of the subject are therefore treated somewhat briefly. I have ventured to make one important change from the usual order adopted in English text-books on Algebra, namely by considering some of the tests of the convergency of infinite series before making any use of such series: this change will, I feel sure, be generally approved. The order in which the different chapters of the book may be read is, however, to a great extent optional. A knowledge of the elementary properties of Determinants is of great and increasing practical utility; and I have therefore introduced a short discussion of their fundamental properties, founded on the Treatises of Dostor and Muir. No pains have been spared to ensure variety and interest in the examples. With this end in view, hundreds of examination papers have been consulted; including, with very few exceptions, every paper which has been set in Cambridge for many years past. Amongst the examples will also be found many interesting theorems which have been taken from the different Mathematical Journals. I am indebted to many friends for their kindness in looking over the proof-sheets, for help in the verification of the examples, and for valuable suggestions. My especial thanks are due to the following members of Sidney Sussex College : Mr S. R. Wilson, M.A., Mr J. Edwards, M.A., Mr S. L. Loney, M.A., and Mr J. Owen, B.A. CHARLES SMITH. CAMBRIDGE, December 12th, 1887. Multiplication of monomial expressions The factors of a product may be taken in any order . 26 27 28 29 PAGE Factors found by comparing with known identities . Factors of quadratic expressions found by inspection Factors of general quadratic expression Factors found by rearrangement and grouping of terins An expression of the nth degree cannot vanish for more than n values of x, unless it vanishes for all values of x 77 83 83 85 |