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A circle-line study of mathematical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	A circle-line study of mathematical analysisby Simone Secchi.
Author:	Secchi, Simone.
Published:	Cham :Springer International Publishing :2022.
Description:	xix, 469 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis.
Online resource:	https://doi.org/10.1007/978-3-031-19738-3
ISBN:	9783031197383$q(electronic bk.)

A circle-line study of mathematical analysis
Secchi, Simone.

A circle-line study of mathematical analysis[electronic resource] /by Simone Secchi. - Cham :Springer International Publishing :2022. - xix, 469 p. :ill., digital ;24 cm. - UNITEXT. La matematica per il 3+2,v. 1412038-5757 ;. - UNITEXT.La matematica per il 3+2 ;v. 136..

Part I First half of the journey -- 1 An appetizer of propositional logic -- 2 Sets, relations, functions in a naïve way -- 3 Numbers -- 4 Elementary cardinality -- 5 Distance, topology and sequences on the set of real numbers -- 6 Series -- 7 Limits: from sequences to functions of a real variable -- 8 Continuous functions of a real variable -- 9 Derivatives and differentiability- 10 Riemann's integral -- 11 Elementary functions -- Part II Second half of the journey -- 12 Return to Set Theory -- 13 Neighbors again: topological spaces -- 14 Differentiating again: linearization in normed spaces -- 15 A functional approach to Lebesgue integration theory -- 16 Measures before integrals.

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.

ISBN: 9783031197383$q(electronic bk.)

Standard No.: 10.1007/978-3-031-19738-3doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A circle-line study of mathematical analysis
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505 0 $a Part I First half of the journey -- 1 An appetizer of propositional logic -- 2 Sets, relations, functions in a naïve way -- 3 Numbers -- 4 Elementary cardinality -- 5 Distance, topology and sequences on the set of real numbers -- 6 Series -- 7 Limits: from sequences to functions of a real variable -- 8 Continuous functions of a real variable -- 9 Derivatives and differentiability- 10 Riemann's integral -- 11 Elementary functions -- Part II Second half of the journey -- 12 Return to Set Theory -- 13 Neighbors again: topological spaces -- 14 Differentiating again: linearization in normed spaces -- 15 A functional approach to Lebesgue integration theory -- 16 Measures before integrals.
520 $a 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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