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A Nice Approach for Die-hard Math fans
on December 4, 2001
Sheldon Axler's "Linear Algebra Done Right" is an excellent book for the strong of heart. I am an undergraduate student majoring in mathematics, and my professors are obsessed with this book. I, however, am not.
First of all, there are no solutions to the exercises at the end of each chapter, so students are left frustrated when they cannot arrive at the next step of a proof.
Second, what the author sees and deems "obvious" as far as steps and recollections are concerned is not necessarily obvious to the reader.
Axler tries to motivate readers for the proofs by offering little exercises for them to "verify." That's overkill, but to many professors and analysts, overkill in the abstract is probably necessary in order to ensure a given student's success in an advanced linear algebra course.
I'm taking one such course to fulfill my requirements for a math major, and must say these abstract/proof courses get very monotonous and, thus, ridiculously boring. The text, itself, for this book does not particularly motivate me, and I expect to consult the chapters to learn and understand concepts, not to verify info from the chaper. Essentially, the flow of the concepts is ruined by the lack of examples; how are we supposed to verify ideas when the author hasn't really even exemplified the components of them yet?
I find myself falling asleep before I even complete one or two pages in this book. The layout is dull and the propositions and theorems seem endless.
My point is the following: That which is good for the instructor is not necessarily good for the student. Students need motivation, and it is difficult to achieve this goal without offering students detailed examples, interest-catchers and solutions to the time-consuming and overwhelming exercises and concepts.
In the realm of the college curriculum, this book is average. I understand the difficulty of making abstract algebra interesting, but this notion is precisely what students need. To the student math geniuses and professors that live and breathe math, this book is a gift from the gods.
To your average math student, however, that lacks patience and the desire to give up their free time to submerge himself/herself into this book, this book, like mine, will just end up sitting on the shelf and collecting dust.