Introduction to Real Analysis

This beautifully written text starts with proofs and sets in the first 40 pages and continues in the rest of Parts I and II to maintain an ongoing emphasis on the construction of proofs, demonstrating proper skills through detailed examples using the "forward-backward" method. *One of the texts greatest strengths are the problem sets, which are many and varied. *Offers a wide range of problem material guiding readers through large projects and allowing them to explore and develop interest in near research-level topics. *Presents the most abstract subject matter in terms that relate to students experience in calculus, rather than ignoring or downplaying the value of this experience. *Depicts the structure of the real number system as a collection of closely interrelated properties, rather than simply a list of theorems.

Key Topics: After introducing the materials of analysis—emphasizing the structure of the real number system—in Parts I and II, this text reviews and extends calculus in Part III. Readers use their newly acquired knowledge of the real nu mber system in their reexamination of calculus, then move on to Part IV's “testing laboratory”where they explore the strength and basic nature of materials.