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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.

The Real Numbers and Real Analysis

Preface.- Construction of the Real Numbers.- Properties of the Real Numbers.- Limits and Continuity.- Differentiation.- Integration.- Transcendental Functions.- Limits to Infinity.- Sequences.- Series.- Sequences and Series of Functions.- Hints for Selected Exercises.- References.- Index.