A circle-line study of mathematical analysis [electronic resource] / Simone Secchi.

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A circle-line study of mathematical analysis [electronic resource] / Simone Secchi.

9783031197383 (electronic bk.)
3031197380 (electronic bk.)
3031197372
9783031197376

Cham, Switzerland : Springer, 2023.

English

1 online resource.

10.1007/978-3-031-19738-3 doi

QA300

515

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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed March 22, 2023).

Unitext. Matematica per il 3+2.
Unitext ; 141.

Print version: 9783031197376

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