Real Analysis and Foundations

This is a “rigorous” introduction to real analysis for more advanced undergraduate students of mathematics. The text requires only that readers have a strong background in calculus. Krantz (Washington Univ., St. Louis) has removed several advanced chapters from earlier editions (CH, Apr’92, 29-4571) to strengthen the book’s focus on basics. The only advanced topic that remains is harmonic analysis. The removal of advanced material enables the author to discuss the fundamental parts of the subject in more detail and to include more exercises (about ten per section, appearing in increasing order of difficulty). In the same spirit, there are multiple appendixes, as well as a very detailed glossary and a table of notation. The theorems, lemmas, and examples are always connected by some context, making it easy for students to see the big picture and how the discussed results fit within this picture. This reviewer’s only critical remark is that no exercises offer solutions, which makes self-study difficult.–M. Bona, University of Florida

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 65 books and more than 175 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.