Hardcover ISBN:  9781470420574 
Product Code:  GSM/166 
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MAA Member Price:  $75.60 
AMS Member Price:  $67.20 
Electronic ISBN:  9781470427818 
Product Code:  GSM/166.E 
List Price:  $79.00 
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Book DetailsGraduate Studies in MathematicsVolume: 166; 2015; 467 ppMSC: Primary 26; 28; 46; 47;
It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems.
The Problem chapters are accompanied by Solution chapters, which include solutions to twothirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most “natural” rather than the most elegant solution is presented.ReadershipGraduate students and researchers interested in learning and teaching real and functional analysis at the graduate level.

Table of Contents

Part 1. Problems

Chapter 1. Set theory and metric spaces

Chapter 2. Measures

Chapter 3. Lebesgue measure

Chapter 4. Measurable and integrable functions

Chapter 5. $L^p$ spaces

Chapter 6. Sequences of functions

Chapter 7. Product measures

Chapter 8. Normed linear spaces. Functionals

Chapter 9. Normed linear spaces. Linear operators

Chapter 10. Hilbert spaces

Part 2. Solutions

Chapter 11. Set theory and metric spaces

Chapter 12. Measures

Chapter 13. Lebesgue measure

Chapter 14. Measurable and integrable functions

Chapter 15. $L^p$ spaces

Chapter 16. Sequences of functions

Chapter 17. Product measures

Chapter 18. Normed linear spaces. Functionals

Chapter 19. Normed linear spaces. Linear operators

Chapter 20. Hilbert spaces


Additional Material

Reviews

The book is written in a very clear style and is very useful for graduate students to extend their vision of real and functional analysis.
Mohammad Sal Moslehian, Zentralblatt MATH


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 Book Details
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It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems.
The Problem chapters are accompanied by Solution chapters, which include solutions to twothirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most “natural” rather than the most elegant solution is presented.
Graduate students and researchers interested in learning and teaching real and functional analysis at the graduate level.

Part 1. Problems

Chapter 1. Set theory and metric spaces

Chapter 2. Measures

Chapter 3. Lebesgue measure

Chapter 4. Measurable and integrable functions

Chapter 5. $L^p$ spaces

Chapter 6. Sequences of functions

Chapter 7. Product measures

Chapter 8. Normed linear spaces. Functionals

Chapter 9. Normed linear spaces. Linear operators

Chapter 10. Hilbert spaces

Part 2. Solutions

Chapter 11. Set theory and metric spaces

Chapter 12. Measures

Chapter 13. Lebesgue measure

Chapter 14. Measurable and integrable functions

Chapter 15. $L^p$ spaces

Chapter 16. Sequences of functions

Chapter 17. Product measures

Chapter 18. Normed linear spaces. Functionals

Chapter 19. Normed linear spaces. Linear operators

Chapter 20. Hilbert spaces

The book is written in a very clear style and is very useful for graduate students to extend their vision of real and functional analysis.
Mohammad Sal Moslehian, Zentralblatt MATH