Excerpt from The Elements of Written Arithmetic: Combining Analysis and Synthesis, Adapted to the Best Mode of Instruction for Beginners During the few years Eaton's Series of Arithmetics Ima been before the Educational Public, it has been demonstrated, by their cordial reception - by their circulation, already extensive and rapidly increasing - that a deep-felt want for books of iheir high character has been satisfactorily met. In the vast field at the South now being opened to educational advantages - in the extensive and rapidly growing settlements of the West, and in the cities and manufacturing districts of the older States, there is a large class of pupils whose school days are very limited. To these - next to reading and writing a - brief, practical course of Arithmetic must always form the most useful part of school training. It was to meet the wants of this class that the present work was projected by its author. Owing to an unforeseen event, its completion has devolved upon others. This has been the occasion of some delay in its publication, which however has been taken advantage of to make it as perfect as possible. This little work then is a short, practical course of Written Arithmetic, embracing the topics actually necessary to be mastered to enable one to pursue with intelligence the ordinary business avocations of life. Special attention has been bestowed upon the Fundamental Rules, United States Money and Percentage, and a simple but full exposition of the new Metric System is also presented. 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.

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.