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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.
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Reseña del editor
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 don't occur in the book.)
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- EditorialForgotten Books
- Año de publicación2018
- ISBN 10 1440079072
- ISBN 13 9781440079078
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas466
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Paperback. Condición: New. Print on Demand. This book delves into the fundamental ideas of calculus and related fields of mathematics, offering a rigorous yet accessible exploration suitable for first-year university students aiming for scholarship-level understanding. While the author emphasizes the core concepts of infinitesimal calculus, differential and integral calculus, the scope extends beyond the typical English calculus treatise. The book incorporates topics often separated into higher algebra or trigonometry, presenting a more comprehensive view of mathematical analysis. The author's treatment of limits, a notoriously challenging concept for many students, stands out as a key feature. He acknowledges the difficulty and stresses the need for thorough explanation and extensive practice to build a robust understanding of these essential ideas. The book also includes a detailed examination of various classes of functions and their graphical representation, exploring the relationship between geometry and analysis. Ultimately, this book provides a foundation for a deeper understanding of mathematical analysis, offering a comprehensive and insightful exploration of key concepts, including limits and functions. It is a valuable resource for aspiring mathematicians seeking a rigorous and comprehensive approach to these fundamental topics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781440079078_0
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