Concrete Introduction to Real Analysis

Robert Carlson is professor of mathematics at the University of Colorado, Colorado Springs. He holds a Ph.D. in Mathematics from UCLA and has written extensively for several noted journals about graphs, differential equations, eigenvalue problems, and other mathematical topics. This is his third book.

• Real Numbers and Mathematical Proofs. Infinite Sequences. Infinite Series. Functions. Integrals. Variations on the Riemann Sums Theme. Taylor Series and Power Series. Appendix: Solutions to Select Problems.

This is the second, revised edition of a textbook for a course that would typically follow an introductory calculus course in the standard American curriculum. The intended student readers would be those planning to continue with more advanced mathematics, or those in areas that require an understanding of mathematics from a conceptual perspective. While there are many texts with this focus, and libraries may already have several, this one is a bit different. It approaches the subject in an easy-to-read and intuitive manner, rather than in the more rigidly traditional "definition, theorem, proof" approach. It doesn’t cover as much material as some other texts, since it approaches the topics through a historical, contextual lens. Even so, a library may wish to consider this book, even if it has an existing real analysis collection. It will appeal to the student who is struggling with the structured formalism of more traditional texts. Enhancing its utility for self-study, the book includes complete solutions to half of the exercises. It contains a short bibliography, mostly of classic mathematical analysis books.--D. Z. Spicer, University System of Maryland