Overview
- Focuses on a global vision of Modern Analysis, from Set Theory to Measure Theory
- Suitable for preparation to Ph.D. enrollment
- Contains exercises along the text
Part of the book series: UNITEXT (UNITEXT, volume 141)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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About this book
The book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann.
The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces.
The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.
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Keywords
Table of contents (16 chapters)
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Front Matter
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First Half of the Journey
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Front Matter
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Authors and Affiliations
About the author
Simone Secchi obtained a Ph.D. in Functional Analysis from SISSA, Trieste under the supervision of Prof. Antonio Ambrosetti. He is currently Associate Professor of Mathematical Analysis at Università degli Studi di Milano Bicocca. His research interests are partial differential equations, critical point theory, and topological and variational methods for PDEs.
Bibliographic Information
Book Title: A Circle-Line Study of Mathematical Analysis
Authors: Simone Secchi
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-031-19738-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-19737-6Published: 16 March 2023
eBook ISBN: 978-3-031-19738-3Published: 15 March 2023
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XIX, 469
Number of Illustrations: 1 b/w illustrations
Topics: Analysis