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Linear Algebra: An Introduction, Second Edition, by Richard Bronson, Gabriel B. Costa
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In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form).
The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students.
- Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
- Gives computational algorithms for finding eigenvalues and eigenvectors
- Provides a balanced approach to computation and theory
- Superb motivation and writing
- Excellent exercise sets, ranging from drill to theoretical/challeging
- Useful and interesting applications not found in other introductory linear algebra texts
- Sales Rank: #1770884 in Books
- Published on: 2007-07-20
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.04" w x 7.52" l, 1.10 pounds
- Binding: Paperback
- 520 pages
Review
"The text is unusually well and carefully written for a textbook and the exposition is very clear."
- George Feldvoss, University of South Alabama
"The quality of the exercises is better than that of Anton. Bronson's exercises seem more original and less trivial. While he does have routine drill problems his non-routine problems require the student to either extend the student's knowledge base or fill in a portion of a proof. The range on these problem sets is quite large, spanning the routine drill problems needed by all students to the theoretical problems for the better students."
-Renee Britt - Louisiana State University
"I appreciate the slow increase in the progression of difficulty with proofs... I regard the exposition as superior. Prof. Bronson's text is the best example I've ever seen of motivating definitions in linear algebra, right from the very first page... Bronson incorporates the application first, thus motivating the definition, going from concrete to abstract, instead of the reverse."
-Michael Ecker, The Pennsylvania State University
From the Back Cover
In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational ( a 3 x 5 matrix describing a store's inventory) and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form).
The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students.
Excerpt. � Reprinted by permission. All rights reserved.
Written by the Recipient of the 1994 Mathematical Association of America-New Jersey Distinguished Teaching Award!An Innovative textbook at an affordable price
Most helpful customer reviews
2 of 2 people found the following review helpful.
great exposition but riddled with substantial typos
By bearieq
This book has just the right coverage of topics, great motivation of concepts, very clear exposition, and loads of useful example problems. However, this book (second edition) also has more substantive typos than any book I have ever read. Incorrect matrix entries, incorrect variable names, incorrect fonts, incorrect drawings, minus signs that incorrectly disappear and then suddenly reappear several steps later in the derivation, symbols thrown seemingly randomly onto the page in a way that makes no syntactic sense whatsoever. The book was apparently typeset by someone who does not know the first thing about math, and then not proofed by the authors. Every copy of this book (second edition) should be recalled and burned, and corrected copies issued in their place. Shame on Academic Press for issuing such a mess. I give it zero stars for all the typos, which is a shame, because without the typos the book is a five.
14 of 14 people found the following review helpful.
Very good and easy introduction
By A Customer
As I started my studies at Uni and we got this horrible Algebra teacher I was looking for some good book to help me pass this course. This book met all my requirements. This book starts with a very easy example of a matrix and builds up from there with easy to follow steps. Even though the book is very easy to read and explains Algebra very comprehensively it still meets the universitiy-level. Everything stated is formally proved or left as an exercise. An excellent book for a guy that thought he'd never understand linear algebra. This book proved me wrong. It may lack some topics, but the ones in the book surely can't be found elsewehre explained as good as in there.
8 of 8 people found the following review helpful.
Easily the best introduction to linear algebra
By Randolph Crawford
I've tried to learn on my own from several other linear algebra books (Anton, Lay, McMahon), but like many college-level math textbooks, the authors too often emphasize elegance at the cost of clarity. This frequently leaves me scratching my head, asking "How did he get here from there"? Bronson is the only linear algebra text I've seen that SKIPS NO STEPS. I wish more mathematicians understood how critical to learning explanation and illustration are, in contrast to adding Yet Another Proof.
This is not to say that Bronson isn't rigorous. But his exposition comes first; only then does he get formal--his proofs do not substitute for discussion. (In fact, his proofs are often quite straightforward and intuitive, IMHO).
Bronson's is a very welcome attitude among math instructors. This is an excellent book.
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