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Student Mathematical Library 2000; 380 pp; softcover Volume: 4 ISBN10: 0821820508 ISBN13: 9780821820506 List Price: US$57 Institutional Members: US$45.60 All Individuals: US$45.60 Order Code: STML/4 See also: Problems in Mathematical Analysis II: Continuity and Differentiation  W J Kaczor and M T Nowak Problems in Mathematical Analysis III: Integration  W J Kaczor and M T Nowak Moscow Mathematical Olympiads, 19931999  Roman Fedorov, Alexei Belov, Alexander Kovaldzhi and Ivan Yashchenko  We learn by doing. We learn mathematics by doing problems. This book is the first volume of a series of books of problems in mathematical analysis. It is mainly intended for students studying the basic principles of analysis. However, given its organization, level, and selection of problems, it would also be an ideal choice for tutorial or problemsolving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for selfstudy. Each section of the book begins with relatively simple exercises, yet may also contain quite challenging problems. Very often several consecutive exercises are concerned with different aspects of one mathematical problem or theorem. This presentation of material is designed to help student comprehension and to encourage them to ask their own questions and to start research. The collection of problems in the book is also intended to help teachers who wish to incorporate the problems into lectures. Solutions for all the problems are provided. The book covers three topics: real numbers, sequences, and series, and is divided into two parts: exercises and/or problems, and solutions. Specific topics covered in this volume include the following: basic properties of real numbers, continued fractions, monotonic sequences, limits of sequences, Stolz's theorem, summation of series, tests for convergence, double series, arrangement of series, Cauchy product, and infinite products. Also available from the AMS are Problems in Mathematical Analysis II and Problems in Analysis III in the Student Mathematical Library series. Readership Undergraduates, graduate students, and instructors interested in analysis. Reviews "A valuable resource."  American Mathematical Monthly "Would be an ideal choice for tutorial or problemsolving seminars. The volume is also suitable for selfstudy ... presentation of material is designed to help student comprehension and to encourage them to ask their own questions and to start research ... a really useful book for practice in mathematical analysis."  Zentralblatt MATH "Belongs to the great tradition of Eastern European problem books ... if you love mathematics and are serious about understanding analysis, this book is a must."  MAA Online Table of Contents



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