Paul Pollack’s book Not Always buried deep. A Second Course in Elementary Number Theory presents a specially beautiful selection of topics in Elementary Number Theory. By this we mean that all of the problems addressed can be —and, in fact, are— described in simple terms and that the mathematics involved are, for the most part, self sufficient.
There are many texts on Elementary Number Theory written for students, whether graduate or undergraduate, but there are very few books on the subject written for readers that, not being specialists, are assumed to be, mathematically speaking, adults. Paul Pollack’s book Not Always buried deep. A Second Course in Elementary Number Theory is one of them. In the choice of topics and in the way in which such topics are introduced, the author takes for granted that the reader enjoys both doing and reading about mathematics and is familiar with the essential problems and questions that have given shape to Number Theory along the discipline’s history. There is, thus, no need to start by awakening the curiosity of the reader, and Pollack can start doing beautiful and profound mathematics from the first page.
This refreshing point of view makes this book specially suitable for professional mathematicians not specialists on the subject who want to learn about contemporary Elementary Number Theory, for number theorists who want to keep up with the state of the art in the subject or just give themselves the pleasure of reading a beautiful book and as supplementary material in a second level course on Elementary Number Theory.