Higher Geometry

Excerpt from Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry The present book is the outgrowth of lectures given at various times to students of the later undergraduate and earlier graduate years. It aims to present some of the general concepts and methods which are necessary for advanced work in algebraic geometry (as distinguished from differential geometry), but which are not now accessible to the student in any one volume, and thus to bridge the gap between the. usual text in analytic geometry and treatises or articles on special topics. With this object in view the author has assumed very little mathematical preparation on the part of the student beyond that acquired in elementary courses in calculus and plane analytic geometry. In addition it has been necessary to assume a slight knowledge of determinants, especially as applied to the solution of linear equations, such as may be acquired in a very short course on the subject. But it has not been assumed that the student has had a course in higher algebra, including matrices, linear substitutions, invariants, and similar topics, and no effort has been made to include a discussion of these subjects in the text. This restriction in the tools to be used necessitates at times modes of expression and methods of proof which are a little cumbersome, but the appeal to a larger number of readers seems to justify the occasional lack of elegance. In preparing the text one of the greatest problems has consisted in determining what matters to exclude. It is-obvious that an introduction to geometry cannot contain all that is known on any subject or even refer briefly to all general topics. The matter of selection is necessarily one of individual judgment. One large domain of geometry has been definitely excluded from the plan of the book; namely, that of differential geometry. In the field which is left the author cannot dare to hope that his choice of material will agree exactly with that which would be made by any other teacher. He hopes, however, that his choice has been sufficiently wise to make the book useful to many besides himself. 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.