Simone Secchi
A Circle-Line Study of Mathematical Analysis
A Circle-Line Study of Mathematical Analysis
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- More about A Circle-Line Study of Mathematical Analysis
The book covers the rigorous foundations of mathematical analysis, including naive set theory, real numbers, topology, sequences, series, limits, differentiation, and integration. It is suitable for graduate courses and self-study for students interested in mathematical analysis.
Format: Paperback / softback
Length: 469 pages
Publication date: 16 March 2023
Publisher: Springer International Publishing AG
The book delves into the intricate foundations of mathematical analysis, encompassing a comprehensive exploration of fundamental topics. In the first part, a thorough review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation, and integration according to Riemann is presented. This section serves as a foundational framework for the subsequent discussions.
The second part of the book takes a more mature approach to these subjects. It explores potential axiomatizations of set theory, introduces general topology with a focus on convergence in abstract spaces, constructs the abstract Lebesgue integral in the spirit of Daniell, and delves into the discussion of differentiation in normed linear spaces. This part offers a deeper understanding of the core concepts of mathematical analysis.
The book is designed for graduate courses in real and abstract analysis, providing a comprehensive and rigorous foundation for advanced study. It can also serve as a valuable resource for students embarking on a Ph.D. program in Analysis, offering a self-study guide for those seeking to deepen their understanding of the field. Additionally, the first part of the book can be recommended as a second reading for undergraduate students with a strong interest in mathematical analysis, providing a more advanced and comprehensive perspective.
In summary, the book offers a comprehensive and rigorous introduction to mathematical analysis, covering a wide range of topics and providing valuable insights for both graduate students and self-study enthusiasts. Its comprehensive nature and detailed explanations make it an essential resource for anyone seeking to advance their knowledge in this field.
Weight: 924g
Dimension: 153 x 235 x 27 (mm)
ISBN-13: 9783031197376
Edition number: 1st ed. 2022
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