The Real Numbers and Real Analysis [Paperback]

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.

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.

From the reviews:

The authors purpose is to cover with this book the necessary mathematical background for secondary school teachers. The book is also useful for an introductory one real variable analysis course. & The book has an interesting and useful collection of exercises & . Last but not least, the historic notes are excellent. & I consider this book of great interest for the academic training of the future secondary school teachers, so the authors purpose is greatly fulfilled. (Juan Ferrera, The European Mathematical Society, April, 2013)

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 follol£®