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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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A Course of Pure Mathematics (Classic Reprint)
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Paperback. Condition: 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. Seller Inventory # 9781440079078_0
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Paperback. Condition: Brand New. 466 pages. 9.00x6.00x1.05 inches. This item is printed on demand. Seller Inventory # zk1440079072
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Condition: New. KlappentextrnrnExcerpt from A Course of Pure MathematicsrnrnI 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 . Seller Inventory # 2148537719
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