The mosfc important are in 80-82, which I have rewritten in accord ance with suggestions made by Mr S. Pollard. The earlier editions contained no satisfactory account of the genesis of the circular functions. I have made some attempt to meet this objection in 158 and Appendix III. Appendix IV is also an addition. It is curious to note how the character of the criticisms I have had to meet has changed. I was too meticulous and pedantic for my pupils of fifteen years ago: I am altogether too popular for the Trinity scholar of to-day. I need hardly say that I find such criticisms very gratifying, as the best evidence that the book has to some extent fulfilled the purpose with which it was written. G. H. H. August 1921 EXTRACT FROM THE PREFACE TO THE SECOND EDITION THE principal changes made in this edition are as follows. I have inserted inC hapter I a sketch of Dedekind stheory of real numbers, and a proof of Weierstrass stheorem concerning points of condensation; inC hapter IV an account of limits of indetermination and the general principle of convergence ;in Chapter Va proof of the Heine-B orel Theorem ,H eine stheorem concerning uniform continuity, and the fundamental theorem concerning implicit functions; inC hapter VI some additional matter concerning the integration of algebraical functions; and inC hapter VII a section on differentials. I have also rewritten in a more general form the sections which deal with the definition of the definite integral. In order to find space for these insertions I have deleted a good deal of the analytical geometry and formal trigonometry contained inC hapters II and III of the first edition. These changes have naturally involved a large number of minor alterations. G. H. H.

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**Book Description **Forgotten Books, United States, 2018. Paperback. Condition: New. Language: English. Brand new Book. Excerpt from A Course of Pure Mathematics I have endeavoured to make Chapter IV one of the principal features of the book. The notion of a limit is one that has always presented grave difficulties to mathematical students even of great ability. It has been my good fortune during the last eight or nine years to have a share in the teaching of a good many of the ablest candidates for the Mathematical Tripos; and it is very rarely indeed that I have encountered a pupil who could face the simplest problem involving the ideas of infinity, limit, or continuity, with a vestige of the confidence with which he would deal with questions of a different character and of far greater intrinsic difficulty. I have indeed in an examination asked a dozen candidates, including several future Senior Wranglers, to sum the series 1 ]m+m2+ and not received a single answer that was not practically worthless - and this from men quite capable of solving difficult problems connected with the curvature and torsion of twisted curves. I cannot believe that this is due solely to the nature of the subject. There are difficulties in these ideas, no doubt: but they are not so great as many other difficulties inherent in mathematics that every young mathematician completely overcomes. The fault is not that of the subject or of the student, but of the text-book and the teacher. It is not enough for the latter, if he wishes to drive sound ideas on these points well into the mind of his pupils. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at 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. ***** Print on Demand *****. Seller Inventory # AAV9781440079078

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**Book Description **Forgotten Books, 2017. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Excerpt from A Course of Pure Mathematics I have endeavoured to make Chapter IV one of the principal features of the book. The notion of a limit is one that has always presented grave difficulties to mathematical students even of great ability. It has been my good fortune during the last eight or nine years to have a share in the teaching of a good many of the ablest candidates for the Mathematical Tripos; and it is very rarely indeed that I have encountered a pupil who could face the simplest problem involving the ideas of infinity, limit, or continuity, with a vestige of the confidence with which he would deal with questions of a different character and of far greater intrinsic difficulty. I have indeed in an examination asked a dozen candidates, including several future Senior Wranglers, to sum the series 1 +m+m2+ and not received a single answer that was not practically worthless - and this from men quite capable of solving difficult problems connected with the curvature and torsion of twisted curves. I cannot believe that this is due solely to the nature of the subject. There are difficulties in these ideas, no doubt: but they are not so great as many other difficulties inherent in mathematics that every young mathematician completely overcomes. The fault is not that of the subject or of the student, but of the text-book and the teacher. It is not enough for the latter, if he wishes to drive sound ideas on these points well into the mind of his pupils. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at 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. Seller Inventory # AAV9781440079078

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**Book Description **Forgotten Books. Paperback. Condition: New. 466 pages. Dimensions: 9.0in. x 6.0in. x 1.1in.The mosfc important are in 80-82, which I have rewritten in accord ance with suggestions made by Mr S. Pollard. The earlier editions contained no satisfactory account of the genesis of the circular functions. I have made some attempt to meet this objection in 158 and Appendix III. Appendix IV is also an addition. It is curious to note how the character of the criticisms I have had to meet has changed. I was too meticulous and pedantic for my pupils of fifteen years ago: I am altogether too popular for the Trinity scholar of to-day. I need hardly say that I find such criticisms very gratifying, as the best evidence that the book has to some extent fulfilled the purpose with which it was written. G. H. H. August 1921 EXTRACT FROM THE PREFACE TO THE SECOND EDITION THE principal changes made in this edition are as follows. I have inserted inC hapter I a sketch of Dedekind stheory of real numbers, and a proof of Weierstrass stheorem concerning points of condensation; inC hapter IV an account of limits of indetermination and the general principle of convergence ;in Chapter Va proof of the Heine-B orel Theorem , H eine stheorem concerning uniform continuity, and the fundamental theorem concerning implicit functions; inC hapter VI some additional matter concerning the integration of algebraical functions; and inC hapter VII a section on differentials. I have also rewritten in a more general form the sections which deal with the definition of the definite integral. In order to find space for these insertions I have deleted a good deal of the analytical geometry and formal trigonometry contained inC hapters II and III of the first edition. These changes have naturally involved a large number of minor alterations. G. H. H. (Typographical errors above are due to OCR software and dont occur in the book. )About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Scie This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9781440079078

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