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商品描述
Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration and Martingales; measure and topology and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.
This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
商品描述(中文翻譯)
《分析學習題》將分為兩冊出版。第一冊涵蓋數學分析的五個核心主題：度量空間、拓撲空間、測度、積分與鞅、測度與拓撲，以及泛函分析。五個主題各自對應一章，內容包括基礎理論、主要定義與結果，並附有適當的評論與說明，以幫助讀者更深入理解教材。每個主題至少提供 170 道練習題／問題，並於各章末提供解答。整套練習題完整且均衡地呈現了各主題相關的應用情境，實用性十足。
這套幾乎涵蓋百科全書式數學分析練習題的著作，為同類書籍中的首創，適合廣泛讀者閱讀。研究生可利用這套問題集準備預備考試或資格考試，也能藉此檢驗自己對教材更深層的理解。練習題依難度分級。對於教授課程內容涵蓋上述一個或多個主題的教師而言，這些練習題將對課程準備提供極大幫助。分析學研究人員也可能發現，本書以易於閱讀的單冊形式，整理並總結了分析學相關理論，具有相當實用的價值。
作者簡介
Leszek Gasińksi is the Chair of Optimization and Control Theory in the Institute of Computer Science at Jagiellonian University in Krakow, Poland. He is the co-author, along with Nikolaos S. Papageorgiou, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006). Nikolaos S. Papageorgiou is a Professor of Mathematics in the School of Applied Mathematical and Physical Sciences at National Technical University in Athens, Greece. He is the co-author, along with Leszek Gasińksi, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006).
作者簡介(中文翻譯)
Leszek Gasińksi 是波蘭克拉科夫 Jagiellonian University 電腦科學研究所的最佳化與控制理論講座教授。他與 Nikolaos S. Papageorgiou 共同合著《非線性分析》（Nonlinear Analysis，CRC，2005）以及《非光滑臨界點理論與非線性邊值問題》（Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems，CRC，2006）。
Nikolaos S. Papageorgiou 是希臘雅典 National Technical University 應用數學與物理科學學院的數學教授。他與 Leszek Gasińksi 共同合著《非線性分析》（Nonlinear Analysis，CRC，2005）以及《非光滑臨界點理論與非線性邊值問題》（Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems，CRC，2006）。
