Real analysis through modern infinitesimals
著者
書誌事項
Real analysis through modern infinitesimals
(Encyclopedia of mathematics and its applications / edited by G.-C. Rota, [140])
Cambridge University Press, 2011
大学図書館所蔵 全44件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. [554]-556) and index
内容説明・目次
内容説明
Real Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses.
目次
- Preface
- Introduction
- Part I. Elements of Real Analysis: 1. Internal set theory
- 2. The real number system
- 3. Sequences and series
- 4. The topology of R
- 5. Limits and continuity
- 6. Differentiation
- 7. Integration
- 8. Sequences and series of functions
- 9. Infinite series
- Part II. Elements of Abstract Analysis: 10. Point set topology
- 11. Metric spaces
- 12. Complete metric spaces
- 13. Some applications of completeness
- 14. Linear operators
- 15. Differential calculus on Rn
- 16. Function space topologies
- Appendix A. Vector spaces
- Appendix B. The b-adic representation of numbers
- Appendix C. Finite, denumerable, and uncountable sets
- Appendix D. The syntax of mathematical languages
- References
- Index.
「Nielsen BookData」 より