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Problems in Mathematical Analysis I: Real Numbers, Sequences and Series
 
W. J. Kaczor Marie Curie-Sklodowska University, Lublin, Poland
M. T. Nowak Marie Curie-Sklodowska University, Lublin, Poland
Front Cover for Problems in Mathematical Analysis I
Available Formats:
Softcover ISBN: 978-0-8218-2050-6
Product Code: STML/4
380 pp 
List Price: $57.00
Individual Price: $45.60
Electronic ISBN: 978-1-4704-2124-3
Product Code: STML/4.E
380 pp 
List Price: $57.00
Individual Price: $45.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
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Front Cover for Problems in Mathematical Analysis I
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  • Front Cover for Problems in Mathematical Analysis I
  • Back Cover for Problems in Mathematical Analysis I
Problems in Mathematical Analysis I: Real Numbers, Sequences and Series
W. J. Kaczor Marie Curie-Sklodowska University, Lublin, Poland
M. T. Nowak Marie Curie-Sklodowska University, Lublin, Poland
Available Formats:
Softcover ISBN:  978-0-8218-2050-6
Product Code:  STML/4
380 pp 
List Price: $57.00
Individual Price: $45.60
Electronic ISBN:  978-1-4704-2124-3
Product Code:  STML/4.E
380 pp 
List Price: $57.00
Individual Price: $45.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $85.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 42000
    MSC: 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 problem-solving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for self-study.

    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.

  • 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 problem-solving seminars. The volume is also suitable for self-study … 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
  • Request Review Copy
  • Get Permissions
Volume: 42000
MSC: 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 problem-solving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for self-study.

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.

  • 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 problem-solving seminars. The volume is also suitable for self-study … 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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