A circle-line study of mathematical analysis
Secchi, Simone
A circle-line study of mathematical analysis [Documento eletrónico] / by Simone Secchi. - Cham : Springer International Publishing , 2022 . - XIX, 469 p. : il.. - (La Matematica per il 3+2) ; 141 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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ISBN 978-3-031-19738-3
Mathematical analysis
LCC QA299.6-433
A circle-line study of mathematical analysis [Documento eletrónico] / by Simone Secchi. - Cham : Springer International Publishing , 2022 . - XIX, 469 p. : il.. - (La Matematica per il 3+2) ; 141 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-031-19738-3
Mathematical analysis
LCC QA299.6-433
