Methods of Real Analysis
Richard R. Goldberg
In some presentations rigor is sacrificed for an intuitive overview of the material. This is a mistake in my view, particularly for an undergraduate course in analysis, which is the perfect environment for rigorous proof-writing skills to be developed.
Goldberg makes no such sacrifice. His proofs are great. His exposition is very clear. If I have a complaint, it's that it's not colorful enough, there aren't enough different kinds of pictures and graphs. The text DOES contain pictures and diagrams, and they are good, but they are not great. On the other hand, this might be seen as a feature, for it forces the student to work on coming up with her own, which is a very important skill to develop.
