I'm reading the book Principles of Mathematical Analysis by Walter Rudin, aka "Baby Rudin". The exercises included are very instructive and helpful, but I'd like to find a book that has more problems (with solutions) that could help me build a better understanding on the topics covered in Baby Rudin.
I found a series "Problems in Mathematical Analysis I-III" by W.J.Kaczor and M.T.Nowak, but seems to me that it does not fit Baby Rudin well. Any recommendation?
Best Answer
I used Intro to Real Analysis while reading Rudin and noticed many similarities. The structure of the book was very similar, although there are the occasional proofs shown in a different way. For example, Baby Rudin proves that every k-cell is compact by contradiction, whereas Manfred Stoll proves a slightly weaker claim (closed bounded set $[a,b]$ is compact) by using a direct proof, which constructs a set and shows that it is compact and equal to $[a,b]$.
Stoll uses a slightly different layout, it introduces sequences, followed by topology, and treats series after integration, but the book has more approachable exercises. The exercises in Rudin, while not impossible are very difficult (at least they were for me) and it can be frustrating. Manfred Stoll's book contains some easier problems near the beginning of each set of exercises, however, difficult problems do exist.
Solutions do not exist for all the problems, but I still found this book helpful to read alongside baby Rudin.