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Foundations of Analysis by Joseph L. Taylor
...[C]ontent-comprehensive and pedagogically sound. There are exercises adequate to guarantee thorough grounding in the basic facts, and problems to initiate thought and gain experience in proofs and counterexamples. ... I like it a lot. --Don Tucker, University of Utah
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Higher Order Fourier Analysis by Terence Tao
The latest title from Tao, this introduction to higher order Fourier analysis covers various topics in the area in a unified manner and surveys some of the most recent developments.
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Knowing the Odds: An Introduction to Probability by John B. Walsh
John Walsh, one of the great masters of the subject, has written a superb book on probability. It covers at a leisurely pace all the important topics that students need to know, and provides excellent examples. I regret his book was not available when I taught such a course myself, a few years ago. --Ioannis Karatzas, Columbia University