The Real Numbers and Real Analysis

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.

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

From the reviews:

"The author's 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 author's 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 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

"The most distinctive characteristic of this text on real analysis is its three-in-one feature. It was designed specifically for three distinct groups of students. ... The book was motivated by a need for a textbook for the M.A.T. students, but is intended to have enough flexibility to serve the other groups as well. ... this is a strong text, especially for students who need more guidance and support. The book gives an instructor plenty of options for planning a course." (William J. Satzer, The Mathematical Association of America, August, 2011)