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Charles W. Curtis
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Linear Algebra: An Introductory Approach Hardcover – 2 May 1984

by Charles W. Curtis (Author)
3.9 3.9 out of 5 stars 14 ratings
Edition: 4th ed. 1984
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Linear algebra is the branch of mathematics that has grown from a care­ ful study of the problem of solving systems of linear equations. The ideas that developed in this way have become part of the language of much of higher mathematics. They also provide a framework for appli­ cations of linear algebra to many problems in mathematics, the natural sciences, economics, and computer science. This book is the revised fourth edition of a textbook designed for upper division courses in linear algebra. While it does not presuppose an earlier course, many connections between linear algebra and under­ graduate analysis are worked into the discussion, making it best suited for students who have completed the calculus sequence. For many students, this may be the first course in which proofs of the main results are presented on an equal footing with methods for solving numerical problems. The concepts needed to understand the proofs are shown to emerge naturally from attempts to solve concrete problems. This connection is illustrated by worked examples in almost every section. Many numerical exercises are included, which use all the ideas, and develop important techniques for problem-solving. There are also theoretical exercises, which provide opportunities for students to discover interesting things for themselves, and to write mathematical explanations in a convincing way. Answers and hints for many of the problems are given in the back. Not all answers are given, however, to encourage students to learn how to check their work.
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  1. ISBN-10
    0387909923
  2. ISBN-13
    978-0387909929
  3. Edition
    4th ed. 1984
  4. Publisher
    Springer
  5. Publication date
    2 May 1984
  6. Part of series
    Undergraduate Texts in Mathematics
  7. Language
    English
  8. Dimensions
    15.88 x 1.91 x 24.13 cm
  9. Print length
    360 pages
  10. See all details
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Product description

Review

Fourth Edition

C.W. Curtis

Linear Algebra

An Introductory Approach.

"This book is an important addition to the literature of linear algebra. It would be a pleasure to use it for a one-semester or two-quarter course intended for serious (and talented) students. This book deserves to be as influential with the current generation of mathematics students as was Halmos’ Finite-Dimensional Vector Spaces with this reviewer’s generation, 45 years ago."―MATHEMATICAL REVIEWS

About the Author

Product details

  • Publisher ‏ : ‎ Springer; 4th ed. 1984 edition (2 May 1984)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 360 pages
  • ISBN-10 ‏ : ‎ 0387909923
  • ISBN-13 ‏ : ‎ 978-0387909929
  • Dimensions ‏ : ‎ 15.88 x 1.91 x 24.13 cm
  • Customer Reviews:
    3.9 3.9 out of 5 stars 14 ratings

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Charles W. Curtis

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3.9 out of 5 stars
3.9 out of 5
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George
5.0 out of 5 stars Very thorough digest of theory on Linear Algebra
Reviewed in the United States on 3 July 2014
Verified Purchase
So far the most rigorous textbook on Linear Algebra!
It looks abstract and theoretical at first glance, but it is the only book solving theoretical problems I have ever seen.
For example, the determinant problem. Traditional approach is to list definition first and then list some properties. But this book starts from the very beginning of area, then derive properties, at last the definition and calculation. So you will have a whole structure of the knowledge instead of just a memorization of it. And you will understand Jacobian Determinant too - an important but rarely covered topic in either Calculus or Linear Algebra.

It suits thinkers who really want to understand Linear Algebra. If you are puzzled by traditional textbook, try this one and you won't regret!
5 people found this helpful
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Olusola Bolaniran
5.0 out of 5 stars Very Clean
Reviewed in the United States on 6 February 2019
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The cleanest book I've ever bought here
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Aaron Leclair
3.0 out of 5 stars Terse text but easy exercises
Reviewed in the United States on 10 December 2009
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As other readers have noted, this is your standard, terse, theorem-lemma-proof type math text. If you are approaching this text with your only mathematical background being a popular treatment of the calculus like those of Stewart or Larson, the style takes a lot of getting used to. Though a lot of effort is placed into making the text short and packed with information, it is impossible to sit down with this text (or any other upper-division math text, for that matter) and read passively. Curtis leaves out many details in the proofs and examples, asking the reader to follow the ordinary, though annoying, convention of theorem-lemma-proof texts and provide the details him(yes, him)self.

In my linear algebra class, we covered the equivalent of the first six chapters, though after the determinants chapter, we stopped following the ordering and pace of the text, and therefore, it's hard to tell whether the later chapters make an optimal teaching or self-study device. The first four chapters (up to determinants), however, take a theoretical approach to linear algebra with a few scattershot references to the geometric intuitions that it formalizes.

My biggest complaint is that in some points of the text, Curtis seems unsure of whether to continue in an informal or an abstract manner. Many of the exercises are numerical problems of the type you see in a non-proof linear algebra class focused on applications, and when Curtis gets to systems of linear equations, he seems confused about whether he is writing a book for a proof-based or a numerical class. As long as you are familiar with induction and proof by contradiction, the exercises that require proofs are fairly easy. Our professor constantly supplemented them with problems that were far more difficult than anything in Curtis.
6 people found this helpful
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Chris
2.0 out of 5 stars Very Abstract and user-unfriendly
Reviewed in the United States on 19 May 2020
Verified Purchase
Unless you want to be an algebraist, this is definitely NOT the book you want to have.

I just want a reference book that provides proofs for elementary linear algebra, and a good introduction to advanced topics like Jordan forms/bilinear forms/Quadratic forms/dual spaces, etc with proofs.

There are also way too many theorems in a chapter. Many of them are not so essential and can be simply left as exercises or for students to discover themselves. The writing style is boring and in an extremely abstract way. I don't think anyone can still recognize what a polynomial is after reading the author's introduction...
One person found this helpful
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dc
3.0 out of 5 stars Eh
Reviewed in the United States on 8 December 2013
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Not bad. The examples could use some work and the formatting is a bit dated. The exercises were decent if not a bit easy, and most had solutions in the back. I prefer Axler's Linear Algebra Done RIght, though. I don't see any reason to use this book over that for an introduction to linear algebra.
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