A Concrete Introduction to Real Analysis

A Concrete Introduction to Analysis, Second Edition offers a major reorganization of the previous edition with the goal of making it a much more comprehensive and accessible for students. The standard, austere approach to teaching modern mathematics with its emphasis on formal proofs can be challenging and discouraging for many students. To remedy this situation, the new edition is more rewarding and inviting. Students benefit from the text by gaining a solid foundational knowledge of analysis, which they can use in their fields of study and chosen professions.The new edition capitalizes on the trend to combine topics from a traditional transition to proofs course with a first course on analysis. Like the first edition, the text is appropriate for a one- or two-semester introductory analysis or real analysis course. The choice of topics and level of coverage is suitable for mathematics majors, future teachers, and students studying engineering or other fields requiring a solid, working knowledge of undergraduate mathematics. Key highlights:Offers integration of transition topics to assist with the necessary background for analysisCan be used for either a one- or a two-semester courseExplores how ideas of analysis appear in a broader contextProvides as major reorganization of the first editionIncludes solutions at the end of the 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.

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.