Softcover ISBN:  9780821820506 
Product Code:  STML/4 
List Price:  $57.00 
Individual Price:  $45.60 
Electronic ISBN:  9781470421243 
Product Code:  STML/4.E 
List Price:  $57.00 
Individual Price:  $45.60 

Book DetailsStudent Mathematical LibraryVolume: 4; 2000; 380 ppMSC: Primary 00; 40;
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.ReadershipUndergraduates, graduate students, and instructors interested in analysis.

Table of Contents

Problems

Chapter 1. Real numbers

Chapter 2. Sequence of real numbers

Chapter 3. Series of real numbers

Solutions

Chapter 1. Real numbers

Chapter 2. Sequences of real numbers

Chapter 3. Series of real numbers


Additional Material

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


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 Book Details
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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.
Undergraduates, graduate students, and instructors interested in analysis.

Problems

Chapter 1. Real numbers

Chapter 2. Sequence of real numbers

Chapter 3. Series of real numbers

Solutions

Chapter 1. Real numbers

Chapter 2. Sequences of real numbers

Chapter 3. Series of real numbers

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