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This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
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In the early part of this century it was possible for an industrious student to acquire a comprehensive if not minute knowledge of the entire realm of mathematical science. The more eminent minds of that time, Hke Lagrange, Laplace, and Gauss, were about equally familiar with all branches of pure and applied mathematics. Since that epoch the tendency has been constantly towards specialization; and additions to pure theory along with extensions of apphcations have been made with increasing rapidity, until now the mere quantity of information available presents a formidable obstacle to the simultaneous attainment of the breadth and depth of knowledge which characterized the mathematician of a generation ago. It would appear, however, that. this obstacle is due to the bewildering mass of details rather than to any considerable increase in the number of fundamental principles. Hence the student who seeks to gain a comprehensive view of the mathematics of the present day needs most of all that sort of guidance which fixes his attention on essentials and prevents him from wasting valuable time and energy in the pursuit of nonessentials. During the past twenty years a marked change of opinion has occurred as to the aims and methods of mathematical instruction. The old ideas that mathematical studies should be pursued to discipH ne the mind, and that such studies were ended when an elementary course in the calculus had been covered, have for the most part disappeared.
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