The real numbers and real analysis by Bloch E.D.

The real numbers and real analysis



Download The real numbers and real analysis




The real numbers and real analysis Bloch E.D.
Language: English
Page: 584
Format: pdf
ISBN: 0387721762, 9780387721767
Publisher: Springer

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

From the Back Cover

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.

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