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A Circle-Line Study of Mathematical Analysis: 141 (UNITEXT, 141

A Circle-Line Study of Mathematical Analysis: 141 (UNITEXT, 141

Simone Secchi
Barcode 9783031197376
Paperback

£40.04 - £40.04
£40.04
£40.04 - £40.04
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Release Date: 16/03/2023

Edition: 1st ed. 2022
Genre: Science Nature & Math
Label: Springer International Publishing AG
Series: La Matematica per il 3+2
Language: English
Publisher: Springer International Publishing AG

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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