Which text? Second course in linear algebra

[Sulphagne]

Hi!

I am signing up to take a second course in linear algebra this upcoming semester at my university. Among the professors with whom I would like to take the class, one is using one book and the rest another. The one is using Linear Algebra & It's Applications 4th edition by Gilbert Strang and the rest are using Linear Algebra by Friedberg, Insel & Spence. Can you comment on these books? Do you recommend one over the other? Why? I have been told that Friedberg's text is very good, but also separately that Strang's text is very good. So, while I know they are both good, I don't know how to compare them. Please let me know what you think of these texts.

Thanks.

 

[mathwonk]

strang is a famous teaching prof at MIT, and many people like his book. i have not taught from either one you mention, so you might look at reviews on amazon.

im going to guess that strang is very comutational oriented, in an advanced sense, and less focused on theoretical discussions for their own sake.

he has a certain philosophy as i recall hearing, emphasizing the "4 funedamental subspaces" for a matrix, row space, column space, kernel, cokernel?

of course these are just row space, column space, and their orthogonal complements.

he also emphasizes certain a trangular decomposition that he thinks is basic, but that i am not myself familiar with.

dr shifrin at uga who is an oiutstanding teacher, seems to have liked strang as i recall, and strang of course is also a well regarded teacher at MIT.

you might look at strangs free videos from MITs open courseware program, for an idea of his own lecture style. and i suggest going to the library and looking the books over yourself.

 

[mathwonk]

here is areview from amazon of strang by one of my favorite reviewers:
13 of 13 people found the following review helpful:
a good impression, September 20, 2004
I wondered how this book could elicit such mixed opinions, so I took a quick look by reading the first few pages, and scanning the first couple chapters. One can already see the writing style resonsible for this.

Strang is trying to clearly explain the ideas behind the various mechanical constructions, such as Gaussian elmination, in terms of their interpretation via matrices, and also explain practical aspects of the constructions such as cost of implementation, efficiency, and tendency to go "wrong" under roundoff.

This is a lot of ideas to put in a few pages, and students used to books which merely display a mechanical operation, then drill it over and over, are likely stunned by the compactness of the presentation. They are not used to mulling a few succint phrases for meaning, and taking their time. One student reviewer even complained that he had to reread after a few paragraphs, as if that were a bad thing.

He does give very clear and simple examples, he just doesn't give a lot of them. When he has made his point, he does not dwell on it, he moves on to enhance and deepen it. Probably you should work every single exercise in this book.

This is obviously an excellent book from which to learn a lot of deep useful insights into linear algebra and its uses. For those who want more drill on the arithmetic involved, any other book will have a lot of that. But those books will not have the clarity and focus of this book, in most cases. I recommend it highly.

 

[Parthalan]

If you're looking for something less computational, you might want to look into Finite-Dimensional Vector Spaces by Paul Halmos, considered by many to be one of the greatest expositors in mathematics of his time. If you're after a reference, then look elsewhere, but it is a beautiful book for a second course in linear algebra.

 

[mathwonk]

here are some student reviews of friedberg, insel, spence, but the book seems to be out of print and unavailable:
Amazing
Between my instructor for this course and the explinations in the book there was nothing in this book that I did not understand by the end of the semester. This is a rigorous book which is very clearly written.
Also recommended: Matrix Theory - Gantmacher

ABrittainB (abbonser@hotmail.com), A reviewer, 03/03/2004
Depends on what you're looking for...
I could see how this might be a good reference book for Linear Algebra, but I'm using this text in my first course on the subject and it's very very frustrating that it doesn't have the answers to over half of the problems it gives you to work. It's difficult to understand a subject well if you can't easily identify and learn from your mistakes. I've had to procure additional Linear Algebra texts to help me out. On the bright side, its narrative style and more abstract approach has forced me to think for myself and figure things out much more than typical math texts have. I hope that the next edition can find a middle ground by including more solutions.

Kaccie Li, an engineering student, 01/09/2003
Pretty Bad
This book presents linear algebra from the theoretical approach. Yes, it is deeper than the usual choice for most college algebra courses but there are many other books at a similar level. One problem: I'm not too impressed with how the authors decide to provide half their theorems with "proof as exercise". Hello... you're writing the book. Prove your proposed theorems instead of giving me a headache. What's the point of this book if it does not prove the theorems but asks the readers to. There are probably many other much better choices out there.

 

[morphism]

I liked Friedberg very much. It has just about everything.

 

[Sulphagne]

Thanks everyone for your inputs. It seems another professor with whom I wouldn't mind taking this course is teaching using Axler. I've heard good things about Axler too. It's supposed to be very revolutionary and notably abstract. Interestingly, it avoids mentioning the idea of a matrix at all until the very last chapters and it insists on providing proofs that do not use the concept of determinants.

Personally, I like a text to present things very generally and abstractly, and build up the theory in a logical manner. So, I like theory and abstract concepts. At the same time, however, my primary major is electrical engineering+computer science, so the computational aspect of math (while less appealing to me than the elegance of the abstract) is important to my studies. Do you think Axler or maybe the other texts cover both aspects well?

Right now I'm leaning toward taking the course taught using Axler because it seems like a very interesting text and the professor seems very good.

 

[morphism]

Actually, Axler uses the concept of a matrix early on. In my copy (of the 2nd edition of Linear Algebra Done Right), he introduces the concept of the matrix of a linear map in the 3rd chapter. I guess you meant to say he leaves determinants for the last chapter, which is true.

Are both courses the same? By that I mean, do they cover the same material? If so, don't choose the course based on the text used, but instead pick the one with the better professor. You could always check out several texts from the library and read them on your time to supplement your studies.

 

[mathwonk]

i like that advice. i remember more that my good professors said, than my books said, in most cases.

 

[mathwonk]

you might read my web notes on the topic. i cover everything in 15 pages.

 

[tronter]

personally I like Hoffman/Kunze for linear algebra. They introduce fields in the first chapter.

 

[robphy]

Possibly of interest:
http://web.mit.edu/18.06/www/#videos

 

[mathwonk]

someday someone will read my 15 page treatment of linear algebra, and realize that everything is there, except determinants. i can wait for my adoring public. at least another 5 years or so, then ill be 3 score and 10 as they say.

 

[dontdisturbmycircles]

I have read it and found it useful mathwonk. (Some (maybe lots) of it was past what I can comprehend at this time though)

 

[mathwonk]

thank you!