Analysis I, 2nd edition I [electronic resource] / Terence Tao.
Tao, Terence| Call Number | 515 |
| Author | Tao, Terence. |
| Title | Analysis I, 2nd edition Terence Tao. |
| Edition | 2nd ed. |
| Physical Description | 1 online resource (372 pages) |
| Series | Texts and Readings in Mathematics ; 37 |
| Contents | Analysis I, 2nd edition -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 1: Introduction -- Chapter 2: Starting at the Beginning: The Natural Numbers -- Chapter 3: Set Theory -- Chapter 4: Integers and Rationals -- Chapter 5: The Real Numbers -- Chapter 6: Limits of Sequences -- Chapter 7: Series -- Chapter 8: Infinite Sets -- Chapter 9: Continuous Functions on R -- Chapter 10: Differentiation of Functions -- Chapter 11: The Riemann Integral -- Chapter A: Appendix: The Basics of Mathematical Logic -- Chapter B: Appendix: The Decimal System -- Index -- Texts and Readings in Mathematics. |
| Summary | This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. The second edition has been extensively revised and updated. |
| Subject | MATHEMATICAL ANALYSIS. Electronic books. |
| Multimedia |
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$a Analysis I, 2nd edition -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 1: Introduction -- Chapter 2: Starting at the Beginning: The Natural Numbers -- Chapter 3: Set Theory -- Chapter 4: Integers and Rationals -- Chapter 5: The Real Numbers -- Chapter 6: Limits of Sequences -- Chapter 7: Series -- Chapter 8: Infinite Sets -- Chapter 9: Continuous Functions on R -- Chapter 10: Differentiation of Functions -- Chapter 11: The Riemann Integral -- Chapter A: Appendix: The Basics of Mathematical Logic -- Chapter B: Appendix: The Decimal System -- Index -- Texts and Readings in Mathematics.
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$a This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. The second edition has been extensively revised and updated.
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| Summary | This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of number systems and set theory, then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. The second edition has been extensively revised and updated. |
| Contents | Analysis I, 2nd edition -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 1: Introduction -- Chapter 2: Starting at the Beginning: The Natural Numbers -- Chapter 3: Set Theory -- Chapter 4: Integers and Rationals -- Chapter 5: The Real Numbers -- Chapter 6: Limits of Sequences -- Chapter 7: Series -- Chapter 8: Infinite Sets -- Chapter 9: Continuous Functions on R -- Chapter 10: Differentiation of Functions -- Chapter 11: The Riemann Integral -- Chapter A: Appendix: The Basics of Mathematical Logic -- Chapter B: Appendix: The Decimal System -- Index -- Texts and Readings in Mathematics. |
| Subject | MATHEMATICAL ANALYSIS. Electronic books. |
| Multimedia |