Fundamental Conceptions of Modern Mathematics: Variables and Quantities; With a Discussion of the General Conception of Functional Relation (Classic Reprint) - Tapa blanda

Excerpt from Fundamental Conceptions of Modern Mathematics: Variables and Quantities; With a Discussion of the General Conception of Functional Relation

As an illustration of the difficulties in the way of acquiring a thorough knowledge of a branch of mathematics, we may mention that Hamilton, assuredly no tyro in Vector Analysis, found the Ausdehnungslehre so obscure that he avowed himself unable to understand Grassmann's system in all its details. And Herschel, in turn, after reading three chapters of Hamilton's Lectures on Quaternions, was obliged to give up in despair his hope of master ing the subject. This was some years ago, but what change has since taken place in methods of mathematical exposition has not been a change for the better.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Fundamental Conceptions of Modern Mathematics: Variables and Quantities; With a Discussion of the General Conception of Functional Relation

The present work is essentially one of constructive criticism. It is, we believe, the first attempt made on any extensive scale to examine critically the fundamental conceptions of Mathematics as embodied in the current definitions. The purpose of our examination is not solely or even chiefly to show the presence of error, but to promote the development of a more scientific doctrine. In expounding our own views we have often been obliged to find fault with those of others; but we have not gone out of our way for the sake of mere criticism; we have merely cleared away false doctrine preparatory to replacing it with true. Our work, though in a sense dealing with definitions, does not have as its essential scope questions as to the words to be used in expressing something about which there is universal agreement; it really deals with the conceptions underlying the definitions where there is, as will be shown, a great diversity of view. Further than a discussion of definitions (in this sense) we do not go, and though we have at times occasion to enunciate axioms and theorems we never set down a demonstration. It is indeed undeniable that a discipline consisting of definitions alone would be perfectly futile, but this is no argument against deeming the definitions of a science worthy of a separate exposition.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.