He says:. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the underlying mathematics of the numerical algorithms they must see. This book is intended to bridge that gap and presumably resolve the frustration and recriminations. Who would have thought that linear algebra could inflame the passions like that? I have virtually no recent experience with the preparation of incoming graduate students, but I am surprised that linear algebra would be a notable shortcoming.
I might have thought that the focus of the first book like this to appear would have been analysis or abstract algebra, since many colleges have significantly reduced requirements in those areas. The author has designed this book for several possible uses: for self study, as a text for advanced linear algebra for advanced undergraduate or first-year graduate students, as a reference book, or as study guide for Ph. The topics that the author considers are mostly standard, but his treatment of them is unusual.
Probably most of us think that the core of linear algebra is about linear transformations of vector spaces over the real or complex fields. After discussions of linear independence, dimension and linear transformations, he introduces the endomorphism algebra of a vector space. Of course, many examples and exercises in the text use actual real numbers.
But the overall level of abstraction seems inappropriate for the intended audience, particularly if the purpose of the text is at least partly remedial. The basic matrix factorizations of great importance in numerical work get only passing attention. Ill-conditioned systems are unavoidable; the art is knowing how to deal with them. The visual appearance of the text might well put off some readers.
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Indeed the pages are so full that things look all crammed together. Dimensions: This book is written with the intention of bridging that gap.
It was designed be used in one or more of several possible ways: -As a reference book; -As a self-study guide; -As a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level. The book is self-contained to the extent that it not assume any previous knowledge of linear algebra. It does, however, assume a seriousness of purpose and modicum of mathematical sophistication on the part of the reader. There are almost exercises, many of them very challenging.
There is a solutions manual to accompany this textbook which is available free to course adopters. If you would like a copy, please e-mail nicole. Add review.
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Thinking to go deeper on the subject. I am never good with proofs, so I actually prefer books that may build some skills on that.
On that regard, the book perhaps should be fairly rigorous. Right now I have several in mind: - Algebra , Artin I may try to study this slowly I do not plan to actually buy a new book, just want to study something from the library.
The Linear Algebra a Beginning Graduate Student Ought to Know | Mathematical Association of America
I am majoring in Physics , so relevant advices will also be nice. If someone can actually tell me what is mathematical maturity and how to develop it, that would also be nice. Homework Helper. Axler is fantastic. I'd recommend it.
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