Author: Simon Newcomb

Publisher: Forgotten Books

Published: 2015-06-12

Total Pages: 484

ISBN-13: 9781330288528

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Excerpt from Algebra for Schools and Colleges The course of algebra embodied in the present work is substantially that pursued by students in our best preparatory and scientific school and colleges, with such extensions as seemed necessary to afford an improved basis for more advanced studies. For the convenience of teachers the work is divided into two parts, the first adapted to well-prepared beginners and comprising about what is commonly required for admission to college; and the second designed for the advanced general student. As the work deviates in several points from the models most familiar to our teachers, a statement of the principles in which it is constructed may be deemed appropriate. One well-known principle underlying the acquisition of knowledge is that an idea cannot be fully grasped by the youthful mind unless it is presented under a concrete form. Whenever possible an abstract idea must be embodied in some visible representation, and all general theorems must be presented in a variety of special forms in which they may be seen inductively. In accordance with this principle, numerical examples of nearly all algebraic operations and theorems have been presented. For the purpose of illustration, numbers have been preferred to literal symbols when they would serve the purpose equally well. The relations of positive and negative algebraic quantities have been represented by lines and directions from the beginning in order that the pupil might be able to give, not only a numerical, but a visible, meaning to all algebraic quantities. Should it appear to any one that we thus detract from the generality for algebraic quantities, it is sufficient to reply that the system is the same which mathematicians use to assist their conceptions of advanced algebra, and without which they would never have been able to grasp the complicated relations of imaginary quantities. 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.

Download or read book Algebra for Schools and Colleges written by Simon Newcomb and published by Forgotten Books. This book was released on 2015-06-12 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Algebra for Schools and Colleges The course of algebra embodied in the present work is substantially that pursued by students in our best preparatory and scientific school and colleges, with such extensions as seemed necessary to afford an improved basis for more advanced studies. For the convenience of teachers the work is divided into two parts, the first adapted to well-prepared beginners and comprising about what is commonly required for admission to college; and the second designed for the advanced general student. As the work deviates in several points from the models most familiar to our teachers, a statement of the principles in which it is constructed may be deemed appropriate. One well-known principle underlying the acquisition of knowledge is that an idea cannot be fully grasped by the youthful mind unless it is presented under a concrete form. Whenever possible an abstract idea must be embodied in some visible representation, and all general theorems must be presented in a variety of special forms in which they may be seen inductively. In accordance with this principle, numerical examples of nearly all algebraic operations and theorems have been presented. For the purpose of illustration, numbers have been preferred to literal symbols when they would serve the purpose equally well. The relations of positive and negative algebraic quantities have been represented by lines and directions from the beginning in order that the pupil might be able to give, not only a numerical, but a visible, meaning to all algebraic quantities. Should it appear to any one that we thus detract from the generality for algebraic quantities, it is sufficient to reply that the system is the same which mathematicians use to assist their conceptions of advanced algebra, and without which they would never have been able to grasp the complicated relations of imaginary quantities. 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.