A Problem Book in Real Analysis
Seiten
2009
Springer-Verlag New York Inc.
978-1-4419-1295-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-1295-4 (ISBN)
However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses.
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Functions.- Continuity.- Differentiability.- Integration.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.
| Erscheint lt. Verlag | 17.12.2009 |
|---|---|
| Reihe/Serie | Problem Books in Mathematics |
| Zusatzinfo | X, 254 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | alternating series test • bounded function • Cauchy criterion series • Elementary Logic • fundamentals topology • improper integral • intermediate value theorem • limits functions • lower sum • mean value theorem • Metric Spaces • Picard's iteration scheme • Real Numbers • Riemann sum • Rolle's theorem • sequences functions • series converge • series functions • set theory • Taylor's theorem • Tchebycheff polynomials • upper sum |
| ISBN-10 | 1-4419-1295-9 / 1441912959 |
| ISBN-13 | 978-1-4419-1295-4 / 9781441912954 |
| Zustand | Neuware |
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