Tom L. Lindstrom
American Mathematical Society
A modern introduction to real analysis written for advanced undergraduate students, Lindstrom’s Spaces: An Introduction to Real Analysis is available as a free PDF download. It is progressive in the sense that its primary objective is to equip college students with the conceptual frameworks and methodological approaches that they will require in order to successfully complete more advanced coursework in mathematical analysis and related disciplines. The only prerequisite is a comprehensive familiarity with linear algebra and calculus. Students will find that the transition from theory-based analysis to computation-based calculus is made easier with the inclusion of two introductory chapters. Metric spaces, spaces of continuous functions, normed spaces, measure and integration theory, differentiation in normed spaces, and Fourier series are some of the most important subjects that are discussed in this course. Although some of the topics are more advanced than what is typically found in ebooks of this level, care has been taken to present the material in a manner that is suitable for the audience for whom it is intended. Concepts are introduced in a thoughtful manner and are motivated, and proofs are presented in complete and exact detail. Applications to Fourier analysis and differential equations are utilized to highlight the strength of the theory; and tasks of all levels, from the typical to actual obstacles, help students improve both their understanding and their skills. Over the course of several years, students at the University of Oslo have had the opportunity to test out the textbook.
“The presentation is done in a manner to make the ebook eminently readable by students who are enrolled in their first year of college.
“I believe that reading ‘Spaces’ or participating in a program that is based on the textbook would serve very well as a link between undergraduate level mathematics and contemporary graduate-level mathematics.” — Jason M. Graham, as cited in MAA Reviews
PLEASE TAKE NOTE That the package only includes the PDF version of the ebook titled “Spaces: An Introduction to Real Analysis.” There are no access codes contained within.