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Practical Analysis in One Variable

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Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers¿ calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o?ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in ¿Little Rudin. ¿ I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a ¿serious¿ mathematics course for the ?rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi?erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9781441930217
  • Indbinding:
  • Paperback
  • Sideantal:
  • 648
  • Udgivet:
  • 1. December 2010
  • Størrelse:
  • 155x35x235 mm.
  • Vægt:
  • 966 g.
Leveringstid: 2-3 uger
Forventet levering: 4. Juni 2024

Beskrivelse af Practical Analysis in One Variable

Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers¿ calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o?ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in ¿Little Rudin. ¿ I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a ¿serious¿ mathematics course for the ?rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi?erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J.

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