Introduction to Analysis (Dover Books on Mathematics)

Because of its clarity, simplicity of exposition, and stress on easier examples, the material in Introduction to Analysis is accessible to a wide range of students of both mathematics and other fields.

Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more . Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter—1968 edition.
Instruction in Basic Real Analysis : A solid foundation for direct entry into advanced work in such fields as complex analysis, differential equations, integration theory, and general topology. Comprehensive Coverage : Provides a thorough introduction to the principles of analysis, covering essential topics like open and closed sets, convergent sequence of points and functions, limits, continuity, differentiation, and integration. Practical Examples : The exercises include easy and more complex problems, interesting examples and counter-examples, and a number of more advanced results. Foundation for Advanced Studies : Serves as a vital stepping stone for students entering more advanced mathematics and related fields. Applicability to Modern Fields : Analysis remains a critical component in disciplines such as data science, engineering, and theoretical computing, aligning the book’s content with current academic and professional trends.
Introduction to Analysis lends itself to a one- or two-quarter or one-semester course at the undergraduate level. It grew out of a course given at Berkeley since 1960. Refinement through extensive classroom use and the author’s pedagogical experience and expertise make it an unusually accessible introductory text.