A Course of Pure Mathematics (Classic Reprint)

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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