The Real Numbers and Real Analysis
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The Real Numbers and Real Analysis

The Real Numbers and Real Analysis


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About the Book

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.

Table of Contents:
Preface.-To the Student.-To the Instructor.- 1. Construction of the Real Numbers.- 2. Properties of the Real Numbers.- 3. Limits and Continuity.- 4. Differentiation.- 5. Integration.- 6. Limits to Infinity.-7. Transcental Functions.-8. Sequences.- 9. Series.- 10. Sequences and Series of Functions.- Bibliography.- Index.

About the Author :
Dr. Ethan D. Bloch of Bard College is the author of two Springer publications "A First Course in Geometric Topology and Differential Geometry," and the first and second editions of, "Proofs and Fundamentals: A First Course in Abstract Mathematics." More information about Dr. Ethan D. Bloch can be found on his person web page: http://math.bard.edu/bloch

Review :
"Bloch (Bard College) has written an introductory book on analysis at the undergraduate level, with enough material for at least two semesters of studies. The author writes very carefully and includes numerous examples and historical insights. The exposition is generally excellent. The book provides all proofs with enough details for most undergraduates to follow through without undue difficulties... Overall, an excellent book. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and faculty." -D. M. Ha, Ryerson University, Choice, February 2012


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Product Details
  • ISBN-13: 9780387721767
  • Publisher: Springer-Verlag New York Inc.
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 0387721762
  • Publisher Date: 27 May 2011
  • Height: 235 mm
  • No of Pages: 554
  • Returnable: Y


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