It's a book, a real book, quite long. It has a lot of topics on applied math. Some of its main topics are linear algebra, probability theory, and Markov proce

It's a book, a real book, quite long. It has a lot of topics on applied math. Some of its main topics are linear algebra, probability theory, and Markov processes. Really, the book just touches on such topics. Usually in college each of those topics is worth a course of a semester or more. So, what the book has on such topics is much less than such a course. E.g., for linear algebra, the book gets quickly to the singular value decomposition but leaves its treatment of eigenvalues for an appendix and otherwise leaves out about 80% of a one semester course on linear algebra. Similarly for probability and Markov processes. Some of the topics the book has or touches on are unusual with, likely, few other sources in book form. E.g., early on the book has Gaussian distributions on finite dimensional vector spaces where the dimension is larger than is common. So, for the topics rarely covered in book form, the book could be a good reference. For topics such as from linear algebra, a reader might get misled without an actual course in linear algebra from any of the long popular books, e.g., Halmos, Strang, Hoffman and Kunze, Nering or more advanced books by Horn, Bellman, or others. Usually in universities, probability and Markov processes quickly get into graduate material with a prerequisite in measure theory and, hopefully, some on functional analysis, e.g., to discuss some important cases of convergence. So, the book seems to have some good points and some less good ones. A good point is that the book is a source of a start on some topics rarely in book form. A less good point is that the book gives very brief coverage of topics otherwise usually covered in full courses from popular texts. A student with a good math background could use the book as a reference and maybe at times get some value from the coverage of some of the topics rarely covered elsewhere. But I would suspect that students without courses in linear algebra, probability, etc. would need more background in math to find the book very useful. E.g., early in my career, I jumped into various applied math topics using very brief treatments. Later when I did careful study of good texts with relatively full coverage, I discovered that the brief treatments had been misleading. E.g., no one would try to learn heart surgery in a weekend and then try to apply it to a real person. Well, for applied math, maybe learning singular value decomposition, etc. in a weekend might not be enough to make a serious application. It is good to see a book on applied math try to be a little closer to real, recent applications than has been traditional in applied math texts. I'm not sure that the being closer is crucial or even very useful for making real applications, but maybe it will help.