Real Analysis and Foundations

by Steven G. Krantz

A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking
Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations.

New to the Third Edition
Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises.

Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding
This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.

Genres: Mathematics, Textbooks, Science

430 pages, Hardcover

First published June 13, 2013

Reviews

[David Chmelik · Rating 5 out of 5]

Krantz said he purposely made the book '[as hard as real analysis was years or decades ago,]' and it is at least twice the size of my other Real Analysis book, but Krantz's is not impossible if one studies & focuses: I even got a B+ and B in parts 1 and 2 of 3 of a class that uses it, though I needed a B+ to continue.

[Stefan Shirley · Rating 4 out of 5]

Easy to understand and great examples to work.

[Francisco Nunes · Rating 5 out of 5]

Great book. Very well explained, with good drawings to help the student understand abstract concepts.

I would recommend it if it’s your first time studying Analysis.