Even though I am not an undergraduate student (yet), I have to point out that this book is amazing as a first read for one good reason: Halmos forces the reader to prove some nontrivial results that are generally proved in other textbooks. I particularly like the fact that the author refers to infinite dimensional vector spaces in the first few chapters. The famous saying among problem solvers is that "problem solving can only be learnt through solving problems." Due to the fact that a mathematician needs to know how to approach problems on his or her own, he or she must be FORCED to solve problems. Working through this book is worth the time. However, some experience with proofs is a must; other that this, the book is self-contained for those who are familiar with some real analysis.

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