Paperback. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: A Circle-Line Study of Mathematical Analysis (Paperback)
Publisher: Springer International Publishing AG, Cham
Publication Date: 2023
Language: English
ISBN 10: 3031197372
ISBN 13: 9783031197376
Binding: Paperback
Edition: 1st Edition
Condition: new

About this title

Synopsis

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.

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 Universit� degli Studi di Milano Bicocca. His research interests are partial differential equations, critical point theory, and topological and variational methods for PDEs.

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