Understanding Analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2001
|
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it |
| Physical Description: | 1 Online-Ressource (XII, 260 p) |
| ISBN: | 9780387215068 9781441928665 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-0-387-21506-8 |
Staff View
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| spelling | Abbott, Stephen Verfasser aut Understanding Analysis by Stephen Abbott New York, NY Springer New York 2001 1 Online-Ressource (XII, 260 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it Mathematics Real Functions Mathematik Reelle Analysis (DE-588)4627581-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Reelle Analysis (DE-588)4627581-2 s 2\p DE-604 https://doi.org/10.1007/978-0-387-21506-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abbott, Stephen Understanding Analysis Mathematics Real Functions Mathematik Reelle Analysis (DE-588)4627581-2 gnd |
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| title | Understanding Analysis |
| title_auth | Understanding Analysis |
| title_exact_search | Understanding Analysis |
| title_full | Understanding Analysis by Stephen Abbott |
| title_fullStr | Understanding Analysis by Stephen Abbott |
| title_full_unstemmed | Understanding Analysis by Stephen Abbott |
| title_short | Understanding Analysis |
| title_sort | understanding analysis |
| topic | Mathematics Real Functions Mathematik Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Mathematics Real Functions Mathematik Reelle Analysis Lehrbuch |
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