Linear Algebra, Geometry and Transformation (Textbooks in Mathematics) 1st Edition by Bruce Solomon (PDF)

Description

The Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay among Algebra, Geometry, and MappingsThe text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization. A Smooth Transition to the Conceptual Realm of Higher MathematicsThis book guides students on a journey from computational mathematics to conceptual reasoning. It takes them from simple “identity verification” proofs to constructive and contrapositive arguments. It will prepare them for future studies in algebra, multivariable calculus, and the fields that use them.Print Versions of this book also include access to the ebook version.

User’s Reviews

Editorial Reviews: Review “All the standard topics of a first course are covered, but the treatment omits abstract vector spaces. … What is unusual is the author’s aim to interpret every concept and result geometrically, thus motivating the student to learn to visualize what is going on, rather than just relying on calculations. This is a strong and useful feature. … The book has very many practice sections with over 500 exercises, most of them numerical. … As the author mentions in the preface, it was his aim to provide a sound mathematical introduction, and in the reviewer’s opinion he has succeeded in doing this.”―Zentralblatt MATH 1314 About the Author Bruce Solomon is a professor in the Department of Mathematics at Indiana University Bloomington, where he often teaches linear algebra. He has held visiting positions at Stanford University and in Australia, France, and Israel. His research articles explore differential geometry and geometric variational problems. He earned a PhD from Princeton University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book isn’t as poorly written as a number of other math textbooks typically are as a sad matter of course. I would rank it as average for any other field, but for mathematics it comes across a lot better than most. The biggest problem that I see in a lot of this book is that Solomon could offer some more examples, or put more detail into existing examples. For instance, my understanding of imagespace and onto functions was hindered by the singular example of x^2 when another example might have made it clear to me that the range is described by the mapping itself, rather than the intrinsic properties of the function. This isn’t a trivial point, since most students learn one particular and narrow notion of range in algebra and calculus where they tend to shrink the range to be as small as possible. So most students are trained, for instance, to think of the range of f(x)=x^2 as being [0, inf) rather than R. Notionally, it makes sense that students would assume this is an intrinsic quality and fail to realize that the mapping of the function is defining the range more broadly. This is actually a really interesting concept, and I think this book like most math textbooks buries this somewhat under definitions, when it should call attention to this fact. One important note: I like that this book offers a digital edition at no extra charge. Very decent of the publisher in a world where students are nickel and dimed enough.

⭐Very clean and inexpensive…..

⭐The textbook is relatively clear, but contains no solutions to any of the practice problems. This makes practicing fairly useless.

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