Lindstrom’s Spaces: An Introduction to Real Analysis (PDF) is a contemporary introduction to real analysis at the advanced undergraduate level. It is progressive in the sense that it first and foremost intends to provide college students with the ideas and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only requirements are a solid understanding of linear algebra and calculus. Two introductory chapters will assist students with the transition from computation-based calculus to theory-based analysis. The key topics covered are metric spaces, spaces of continuous functions, normed spaces, measure and integration theory, differentiation in normed spaces, and Fourier series. Though some of the topics are more advanced than what is usually found in ebooks of this level, care is taken to offer the material in a way that is appropriate for the intended audience: concepts are wisely introduced and motivated, and proofs are presented in complete detail. Applications to Fourier analysis and differential equations are used to show the power of the theory, and exercises of all levels from usual to real challenges help students improve their understanding and skills. The textbook has been tried in classes at the University of Oslo over several years.
“The presentation is done in a manner to make the ebook eminently readable by undergraduate students..I think that reading ‘Spaces’ or taking a program based on the textbook would serve very well as a link between undergraduate level and modern graduate-level mathematics.” — Jason M. Graham, MAA Reviews
NOTE: The product only includes the ebook, Spaces: An Introduction to Real Analysis in PDF. No access codes are included.