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While I think the book is trying not to limit its readers' imaginations, a few more example of where expert systems are or could be implemented would be useful. These example would lend more credibility to the ideas, since they would show that the systems that are vaguely described in the book could actually be implemented.
A must read for those that want to change the world using IT.
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My favorite in this volume is The Flow and Seed Sequence, a series seven poems written by the Zen Patriarchs beginning with Bodhidharma (d. 536) with poems added to the series nearly 2 centuries later. The translations do an excellent job of retaining the concrete imagery typical of Zen poetry e.g. from Liu Chang Ching "All along the trail of moss, / I follower your wooden shoeprints". We find inventive descriptions of concret images in Liu Fang-Ping "The Big Dipper slopes; / the Great Bear bends down". There are also unusual mentions of doubt from Wang An Shih "Often I doubt the Buddhist way, / that nothing truly exists".
Despite its many good attributes, this collection failed my ultimate test: rarely was I enticed to read and reread a poem. I would still recommend A Drifting Boat or Cold Mountain first. But to even be worthy of comparison to those volumes is strong praise.
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All through the class I struggled to understand concepts. I did not. That was not due to the book since I did not even bother opening it. After finishing the course, I realized that the material of this book is of the most importance to anyone planning on continuing his/her grad degree in math, so I decided to read the book. The mission was accomplished in a matter of a couple of weeks.
I do not claim that this is the easiest book to understand the material. In fact, Lang's books are remarked for their dryness. Motivation is almost nonextant. If you, however, have a fairly good background in Linear Algebra (something like the material of Anton's "Elementary Linear Algebra" or the like) and Abstract Algebra (an excellent introduction can be sought in Herstein's "Abstract Algebra") you would much benefit from this book.
The book is a very good book for a second course in linear algebra, that is, it is not a good book for those who had no experience with matrix theory before. The reason is that the book does not mention anything about Gaussian elimination and treats the solutions of n equations in m unknowns using dimension theorems, which is not the standard way of proving existence of such solutions. One more thing is that it does not talk about elementary matrices (one can interpret column or row operations by multiplication of elementary matrices to the right or left). I am not saying the book
is bad, I am saying it is not the right book for a beginner.
The book introduces the basic notions of vector spaces, linear mappings, matrices scalar products, determinants, and eigenvalues and spaces. It then moves to unitary, symmetric, and Hermitian operators and explores their Eigenvalues. Polynomials have a whole chapter followed by triangulation of a linear map. The book concludes with applications of Linear algebra to convex geometry.
I might disagree with the definition of the determinant the author offers, but I would have to admit that his approach is the traditional one.
The subjects of the books must be mastered (or at least absorbed) by anyone who wants to go to analysis (Functional analysis to be precise), Algebra, Geometry, and Differential Equations. To ensure this you should do almost all the exercises of the book since they are so excellent and help a lot in understanding the material presented.
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