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Linear Algebra with Applications [Hardcover]

Otto Bretscher

Price: 103.99 & FREE Delivery in the UK. Details
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Book Description

30 Sep 2008 0136009263 978-0136009269 4

Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.

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Amazon.com: 2.2 out of 5 stars  46 reviews
14 of 15 people found the following review helpful
2.0 out of 5 stars Much better texts out there... 27 April 2010
By Jeffrey A. Boye - Published on Amazon.com
Format:Hardcover|Verified Purchase
- Bare Bones explanations of theorems
- Usually the example problems are trivial
- Teaches material out of a proper canonical order

- One definitely should have an adequate professor to back the material presented in this text. I didn't. Just had to grind through the material and absorb it bit by bit on my own.

- You most definitely CAN learn linear algebra from this text, just not very efficiently.

Side Note: I highly suggest watching Gilbert Strang's MIT OpenCourseWare to accompany this course as well as using his text as a supplement.

19 of 23 people found the following review helpful
1.0 out of 5 stars Students in my class (including myself) have given up 21 May 2012
By Perfectrancenow - Published on Amazon.com
For the student who is proficient in calculus and algebra but is taking linear algebra for the first time, this book is mostly unreadable. Here is my overall summary of the book: heavy on symbol usage, theorems, and proofs, light on examples. Then after reading the section, you get thrown off into the deep end with tons of complicated word problems. You are left with the task of connecting theorems with the applications. If you ask me, this is just plain lazy on the author's part.

My advice: as a punishment to your instructor for picking this book for your class, be in his or her office every single day and ask them to explain all of the problems past number 30 to you. You will get a good laugh when you realize that THEY struggle with them.
6 of 7 people found the following review helpful
By Joseph - Published on Amazon.com
Format:Loose Leaf
Ditto on most of the bad reviews: bad, if not overly simple examples compared to assignments; bad order (studying supspaces before defining vector spaces). Why didn't we choose Strang's book for this class I'll never know. Thankfully there was a great teacher to teach from this terrible text.
2 of 2 people found the following review helpful
1.0 out of 5 stars Author or Editor fail? Not sure. 23 July 2013
By Kyle Haley - Published on Amazon.com
Format:Loose Leaf|Verified Purchase
I am currently enrolled in a summer semester course for Linear Algebra. It's not a heavy class, nor is it lightweight. We have extensive homework assignments... hence where the reason I hate it comes in.

It actually is not that the book doesn't provide examples for the types of problems it expects you to answer. A student of science and mathematics becomes accustomed to this.

What IS frustrating is that the homework sections are asking you to solve problems where the explanation of how to solve the problem is in a section further along in the chapter. For instance, section 2.1 had many problems related to inverse matrices. There was a very brief (more or less an example story) about inverse matrices earlier in the section, but it provided no theorems. It supplied a more or less example of application. So if you skip ahead to section 2.4, you may be surprised to find it titled "The Inverse of Linear Transformation", which provides detailed examples of matrix inversion and the associated theorems.

The reason I am writing this is review is for those that get stuck with this book. Look in the sections ahead if something seems unfamiliar or if you cannot find enough detailed examples in the current chapter. You will likely find your answers to assist you in answering the questions in a manner that is conducive to Linear Algebra.
12 of 17 people found the following review helpful
5.0 out of 5 stars I really loved this book 5 Aug 2011
By dwu - Published on Amazon.com
Format:Hardcover|Verified Purchase
In sincere disagreement with the negative reviews here, I absolutely loved this book. I took a class on linear algebra my freshman year of college that used Otto Bretscher's book, and I read it pretty much from cover to cover. Now, I wasn't a very studious student at the time, so this says a lot about just how well Bretscher presented the subject -- it was so interesting that I just wanted to keep reading. Unlike more advanced textbooks in math, Bretscher's book is rigorous while remaining friendly. I was always assured that I could understand anything in the text after a few tries and a bit of thinking, because enough detail is included to make sure the engaged reader does not get lost. The result is a highly streamlined presentation that makes you really appreciate the beauty of linear algebra, and takes you through some cool theorems, like the Spectral Theorem.

Other reviewers have remarked that the writing is "terse" or complained that examples are "done in symbols". In response to the former complaint, I don't think the explanations are terse at all. Sure, the text might make you think more and work out more things on your own than any math book you've encountered before reading this one, but it's certainly very doable for those who aren't lazy. In fact, in comparison to an often-used math book (though not linear algebra) like Rudin's Principles of Mathematical Analysis, Bretscher's book helps the reader out way more. So much more. The text is just really clear and unintimidating. I can't emphasize this enough.

In response to the complaint about examples, I found the examples to be very accessible, straightforward and illustrative of the concept at hand. They're well-integrated and, yes, they're done in math symbols, but, well, what else could you expect from a math book? Sure, you could try to explain concepts verbally instead, but usually it's just better to be walked through a "symbolic" example and see how the math is really done. After all, as a learner of the subject, you'll have to do it yourself as well.

And the problems are great. They can definitely be solved using knowledge gained from the relevant section in the text, though not all are completely straightforward, as previous unsatisfied reviewers seem to be expecting. I say this with such confidence because I did many of the problems myself without knowing anything about linear algebra that Bretscher's book did not teach me.

Since taking linear algebra, I've had to recall concepts I'd learned and use them in other science and math courses, and to my surprise I still have a good grasp of the important ideas, no doubt due in large part to the fine teaching of the book being reviewed.
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