Excerpt from Subjects for Mathematical Essays
The object of what are here called "mathematical essays" is to co-ordinate a pupil"s knowledge on certain subjects which are not specially dealt with in text-books. The essays, of which outlines are given in the first part of this book, are of the following types:
(i) A group of theorems on one subject, the theorems in ordinary text-books being often scattered in one or several volumes (e.g., Essays 19, 26, 70, 91);
(ii) A series of questions leading up to the solution of an important problem (e.g., Essays 79, 87, 90, 93);
(iii) A collection of different methods of proving the same theorem (e.g., Essays 28, 61, 75, 78);
(iv) A series of applications of the same theorem (e.g., Essays 37, 48, 75);
(v) A classification of tests of the same geometrical condition (e.g. Essays 3, 4, 40, 41).
The subjects given in the first part (Essays 1-100) are, as a rule, of an elementary character. In several of these, a question, which throws light on different subjects, is repeated, Those given in the second part (Essays 101-200) are taken from papers set for entrance scholarships in the Trinity and Pembroke groups of Cambridge colleges from 1905 and 1907 respectively.
I should be grateful for notices of any errors that may be found in the text or answers, and for any suggestions from teachers for the improvement of the book.
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