The real numbers and real analysis
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The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. The choice of material and the flexible organization, including three different entryways into the study of the real numbers, making it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis is accessible to students who have prior experience with mathematical proofs and who have not previously studied real analysis. The text includes over 350 exercises.
Key features of this textbook:
- provides an unusually thorough treatment of the real numbers, emphasizing their importance as the basis of real analysis
- presents material in an order resembling that of standard calculus courses, for the sake of student familiarity, and for helping future teachers use real analysis to better understand calculus
- emphasizes the direct role of the Least Upper Bound Property in the study of limits, derivatives and integrals, rather than relying upon sequences for proofs; presents the equivalence of various important theorems of real analysis with the Least Upper Bound Property
- includes a thorough discussion of some topics, such as decimal expansion of real numbers, transcendental functions, area and the number p, that relate to calculus but that are not always treated in detail in real analysis texts
- offers substantial historical material in each chapter
This book will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus.
The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
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Prijs:
Taal: en
Bindwijze: Paperback
Oorspronkelijke releasedatum: 26 november 2014
Aantal pagina's: 554
Illustraties: Nee
Hoofdauteur: Ethan D. Bloch
Hoofduitgeverij: Springer-Verlag New York Inc.
Editie: 2011
Extra groot lettertype: Nee
Product breedte: 156 mm
Product hoogte: 30 mm
Product lengte: 234 mm
Studieboek: Ja
Verpakking breedte: 157 mm
Verpakking hoogte: 47 mm
Verpakking lengte: 234 mm
Verpakkingsgewicht: 1110 g
EAN: 9781489998347