- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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 two-thirds 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.
Contents
Problems: Set theory and metric spaces
Measures Lebesgue measure
Measurable and integrable functions $L^p$ spaces
Sequences of functions
Product measures
Normed linear spaces
Functionals Normed linear spaces
Linear operators
Hilbert spaces
Index
