I was asked by the publisher to review "Sage: Beginner's Guide" by Craig Finch. They sent me a free copy; I have no other conflicts of interest. I am generally biased towards Sage itself, as an avid user and minor developer.

On Amazon you can browse the table of contents, which gives a pretty good idea of the strengths of the book, namely basic computation and plotting, numerical calculations, and data analysis. The focus was an excellent choice considering what is already available. The current free Sage Tutorial is oriented much more towards pure mathematicians. There is a Numerical Computing With Sage as part of the standard documentation, but at the moment its quite short and nowhere near as helpful as Finch's book.

I liked the style of the book a lot. There are many code examples that illustrate how to accomplish concrete tasks, along with good explanations of what they are doing. Many of these are things that are unfortunately far from obvious to a beginner (or even intermediate) Sage user. Despite using Sage heavily for the last five years, I learned some new things. The book is particularly strong in showing how to use Numpy, Scipy, and Matplotlib. Sage wraps a lot of the functionality of these projects, but if you want to do something that isn't included in the standard interfaces it can be quite mystifying.

Chapter 9, "Learning Advanced Python Programming", might have been a little ambitious. There's nothing wrong with it, but its too short to provide enough. Fortunately there are a lot of good books, some of them free, that cover Python programming in much more depth. I would have preferred some of this space and effort to be devoted to using Cython and the @interact command, which are covered very briefly in Chapter 10.

I teach several classes using Sage and I will definitely advertise this text as a useful optional supplement (I consider it a little too expensive to add on as a mandatory second text). It would be nice if some institutions considered using Sage instead of its commercial competitors such as Maple, Matlab, and Mathematica - you could probably give every student a copy of this book for the money saved from license fees!

The only thing I disliked about the book was the quality of the illustrations. Sage output that was in LaTeX was not typeset, but instead looks as if a PNG was copied from a screenshot. Some of the examples would have benefited from being in color. The quality of the plots is also somewhat poor. This is not too big a deal if one is following along with Sage, since you can reproduce the figures. None of them are bad enough to obscure the content.

Overall this is a very impressive and useful introduction to Sage that should help any beginning user a great deal.

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