This is the first of a series of problem books in analysis, analytic geometry, and higher algebra. The main purpose of this series is to provide the student with a rich collection of carefully selected material designed to increase his understanding and skill in handling problems in the above fields. To this end a large number of problems are presented and their solutions are given in full detail. To improve understanding, some problems of more difficult character are included, the solution of which requires deeper insight in the topics treated.
More than 1200 problems are presented in this book. Some of these were taken from examination papers of the Technion, Israel Institute of Technology. Others were drawn from various sources and there seems to be no point in endeavoring to trace their origins.
The order of exposition adopted here seems quite natural; however, care has been taken so that the book may be used in a course in which the topics are arranged differently.
Every section begins with a brief explanation of the basic notions and theorems to be used. In general, the theorems are given without proof. The main part of every section is devoted to problems, a large number of which are immediately followed by solutions; others have solutions to be found only at the end of the book. It is believed that this will encourage the reader to solve the problem by himself and only afterwards to look for the printed solution. The comparison of solutions will often be beneficial, as it will afford a check on the work and, occasionally, encounters with new methods.
Some problems, of course, have a variety of solutions and it may easily happen that the one given here is not the simplest possible. Remarks in this and other regards will be welcomed by the author.
My thanks are due to Dr. M. Edelstein, who read the manuscript and made many valuable suggestions, and to Dr. Emory P. Starke who supervised the production of the book.
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