A Circle-Line Study of Mathematical Analysis: 141 (UNITEXT, 141
A Circle-Line Study of Mathematical Analysis: 141 (UNITEXT, 141
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Sign in or Sign up!- Release Date: 16/03/2023
- Barcode: 9783031197376
- Genre: Science Nature & Math
- Imprint: Springer International
- Publisher: Springer

A Circle-Line Study of Mathematical Analysis: 141 (UNITEXT, 141
1st ed. 2022
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DESCRIPTION
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.
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