Understanding Analysis PDF Download Ebook. Stephen Abbott exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The author has written an interesting book designed as a text for a one-semester course. He also expects the students to do their part by leaving to them (with copious hints) the details of many of the steps in the proofs.
This enables him to cover a surprising amount of material in an attractive and stimulating manner. Students who work their way through this text will have seen a lot of interesting analysis and have developed a good understanding of the material. Stephen Abbott appreciates that modern readers may be unfamiliar with axiomatic arguments. Thus, many courses in analysis have been made easier by making them less interesting.
The alternative is to make advanced topics accessible and focus on questions that give real analysis its value. Prerequisite knowledge has been kept to a minimum: an understanding of single variable calculus. The text is written with introductory students in mind and will certainly be persuasive in establishing the value of analysis.
The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions. The book is very clear, well presented, rigorous and should be recommended to undergraduate students as a good complement.
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