Thursday, May 20, 2010

Review of Linear Algebra and its Applications by D.C. Lay

The most obvious benefit of this particular book is its size. At fewer than five hundred pages it is a comparatively light book. Despite its compact nature, it does include some clear and helpful illustrations, and features some interesting applications
However, the layout is far from appealing, and at first glance can be confusing. The answers to the random exercises can be difficult to locate, and the solutions are often too brief to be of any use. In general the proofs are difficult to follow because they are in compact notation, and like many books of this type, it makes little provision for students struggling to remember previously mentioned results and definitions. In some cases a theorem is stated on page X and then the proof of this theorem is given on page X+2 without restating the theorem. This means the reader is constantly flicking between pages X and X+2. The inclusion of repeated theorems would not hamper the confident mathematician, but would be invaluable to a less self assured student.
There seems to be little attempt made to inspire the reader, and its approach is largely clinical and less personal.

Review of Elementary Linear Algebra by Larson and Edwards

This book has an attractive layout, with its theorems and definitions clearly and repetitively presented in highlighted boxes. It is easy to follow and could certainly prove useful to a weak student.
However, many results are stated without providing proof, leaving the student to produce the proof as part of the exercise. Underpinning this type of mathematics with proof is certainly a fundamental part of the education process, but in my experience many students find this an intimidating step. I believe it is vital that students have proofs demonstrated repeatedly, until they become confident enough to formulate their own. This book could undoubtedly benefit from the inclusion of more examples.
In addition, there is a noticeable lack of illustrations, giving the book a very dense feel.
Generally speaking, while this book might provide a valuable handbook for some students, I don’t believe its style engages the attention of the reader and it doesn’t attempt to provide a thorough explanation of linear algebra.

Review of Elementary Linear Algebra by Anton and Rorres

This is a polished, well written text and features a wide variety of interesting contemporary applications towards the end of the book
Its definitions and theorems are highlighted and boxed, and it makes excellent use of illustrations.
However, after their initial introduction, the definitions and results are not reprinted. This makes the book awkward to use and the reader is often forced to search back through the book to find a particular formula or theorem. It is my opinion that the average student is unlikely to absorb this information at their first attempt, and I think it is important to repeat important points until the student is completely familiar with them.
This book also fails to summarise each chapter. My experience of students is that they find a modular approach to mathematics easier to absorb, and I think it is imperative that at the conclusion of each section, new information is condensed and consolidated before the next module commences.
Its explanations are somewhat brief in places, and it uses a compact notation. A confident mathematician would find this method of presentation clear and concise, while the nervous undergraduate finds this kind of brevity difficult to interpret.