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Linear Algebra: An Introduction to Abstract Mathematics (Undergraduate Texts in Mathematics) Corrected Edition
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Top Customer Reviews
Just a few examples of the truly deep knowledge that this book communicates follows. For instance (this will ring a bell for those who have taken calculus) the "constant of integration" that must be added when doing an antiderivative is actually a property of group homomorphisms. The "absolute value" that must be introduced when taking square roots is structurally THE SAME property of group homomorphisms. Also, we all know that you can't divide by zero; it's just not allowed. But, the reason for that is ultimatley rooted in group theory; namely, the real numbers are NOT a group under multiplication. This type understanding has EVERYTHING to do with matrices and systems of equations!Read more ›
It is targeted to graduate students that need a more theoretical approach to mathematics (instead of the usual calculus courses)
This book is the best introduction to abstract algebra for the following reasons
-its style : good introduction in each chapter, making the reader curious to read further.
-its rigor : everything is well explained in full details with proof.
-its elegance : This book treats the abstract structural aspects of algebra and then suddenly shows how more concrecte applications follow from these abstract results. This is the kind of elegance and style that makes mathematics an art : build a very abstract theory and then see how more concrete stuff follows immediately as special case of this abstract framework. This way, new things can be discovered and most of the time (as in this book), you can explain practical calculation rules in a short and rigorous way.
Definitely the finest there is ....
This is a beautiful book though you have to belong to a certain reader segment to appreciate it.
The readers that will like this book probabely are beginning undergraduate students that want to build a mathematical career and want a first and quick introduction to abstract mathematics. The reader is not overwhelmed by exotic topics that are rarely used, but is introduced to abstract basic principles needed to understand other courses like for instance quantum mechanics,more advanced graduate courses in algebra or functional analysis.
The power of this book is that it covers just enough material to have a solid foundation of algebra for other abstract courses like functional analysis,
When I compare it for instance with the book of Shilov, I strongly prefer this book since it is better organised, covers less topics, but enough to know the basics. This book succeeds in providing shorter proofs compared to Shilov without sacrifying rigor and clarity. How is this possible ?? Ah my friend, this is a reward coming from abstract reasoning as illustrated by this book.
If you read this book, you will not only gain knowledge of abstract algebra, but also understand clearly why mathematics is art. It was a real fun reading this book. The topics are presented in such a way that the author leads you to a climax, making you curious to read further, and help you to explore the beauty in all the ideas of abstract mathematics. This book is the best book I ever read on abstract algebra.
The emphasis in on rigor and abstract structural concepts. It is nice to see that the more practical applications follow as a special result from the abstract structural concepts. This is a very elegant approach !!
Most Recent Customer Reviews
This was the textbook for an honors course in linear algebra I took my second semester in college, and my introduction to real, abstract mathematics-- also one of the reasons I... Read morePublished on April 25, 2013 by Max Wallace
Great book. As a former college math professor who taught linear algebra to both math majors and non-majors, I wish this book had been available for use with the math majors. Read morePublished on December 13, 2011 by Bill Gordon