000			02761nmm a22002175i 4500
005			20230705150651.0
008			150519s2015 xxu| s |||| 0|eng d
020			_a9781493927128 _9978-1-4939-2712-8
082			_a515 _223
100			_aAbbott, Stephen. _921224
245			_aUnderstanding Analysis _h[electronic resource] / _cby Stephen Abbott.
250			_a2nd ed. 2015.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2015.
300			_aXII, 312 p. 36 illus. in color. _bonline resource.
505			_aPreface -- 1 The Real Numbers -- 2 Sequences and Series -- 3 Basic Topology of R -- 4 Functional Limits and Continuity -- 5 The Derivative -- 6 Sequences and Series of Functions -- 7 The Riemann Integral -- 8 Additional Topics -- Bibliography -- Index. .
520			_aThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated t hat exposing students to it could well lead them to expect such excellence in all their textbooks. ... Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen. ... This terrific book will become the text of choice for the single-variable introductory analysis course ... " - Steve Kennedy, MAA Reviews .
650			_aMathematical analysis. _921225
650			_aAnalysis. _921226
856			_uhttps://doi.org/10.1007/978-1-4939-2712-8
942			_cEBK
999			_c13731 _d13731