A question on linear algebra text

[danny_91]

A question on linear algebra text!

Hello everybody! I'm new to this forum. Actually, this is my first post in here.

I'm currently a sophomore student in college. My major is in mechanical engineering.

Right now, I'm taking the course introductory linear algebra, which is the first course in linear algebra. The book I'm having for my class is the 1st edition of Introduction to Linear Algebra with Apps by James DeFranza, I don't know if any of you know this book or not. My instructor said that this book sucks since it's 1st ed., so I guess no complaint then. I read through it and don't really like it. So I won't spend my money buying it.

Since I don't have much insight into the subject than you guys, can anyone recommend me a good book on the subject? The book Introduction to Linear Algebra by Gilbert Strang, 4th ed., seems to have really good reviews on amazon, what are your opinions on this? Is this a good text 4 LA?

I prefer a visual way of presentations, with logic explanations of what's going on, and worked-out examples. I just get bored when looking at a book that's too wordy, with explanations drag out too long. Since I'm new, I prefer a good thorough introductory text. Oh, and some applications too! So any recommendation?? Thanks in advance!

 

[ZenOne]

Check out the (Howard) Anton text--he's on his 10th Edition or something. Really straightforward text IMO. Concise explanations and multiple examples, and BONUS he actually gives the answers to all the questions unlike the Stewart Calculus books.

 

[Ashuron]

Another straightforward text would be that of David C Lay's.
I just used this as a textbook for an introductory linear algebra course last semester.
It's a decent first book on linear algebra.
The solution manual is also widely available.

 

[Fredrik]

I don't like Anton (mainly because linear operators aren't defined until page 300 (in the 6th edition); I would put that definition on page 2 or 3), but it does fit the description, and it's not bad in other ways. I just think it presents things in the wrong order, and emphasizes the wrong things. For example, I would say that the relationship between linear operators and matrices (how every matrix is the matrix of components of a linear operator with respect to a pair of bases) is the most important thing in all of linear algebra, but people who take a class based on Anton often come out of if not knowing anything about this. They end up thinking that linear algebra is about multiplying matrices, solving systems of linear equations, and applying those things to problems in geometry. (I would say that linear algebra is the mathematics of linear operators between finite-dimensional vector spaces).

There are lots of threads about linear algebra books. I suggest you do a search.

 

[danny_91]

Thanks for your replies! I actually looked in the forum, and there are bunches of different opinions on each book. Most recommended was the book by Axler, but I don't know if that is too advanced for me right now. Others suggest a book by Huffman and Kuzne, a book from quite a long time ago. There are also books from Meyer, and from Spence. Spence, lots ppl say that it' not for engineers and computer scientists. Meyer seems to be fine.

There are not a lot of discussion on Strang's book that I mentioned above. He also have another book which called Linear Algebra and Its Applications. What are your opinions on these?

 

[contramundum]

I have Strang's Intro to Linear Algebra third edition. It's much too wordy in my opinion. I stopped using it.

 

[Fredrik]

Most recommended was the book by Axler, but I don't know if that is too advanced for me right now.

It doesn't assume that you know anything about linear algebra, and starts at the very beginning, so it's almost certainly not too advanced. But there are other reasons why you might prefer another book. For example, I don't recall seeing a lot of stuff about the applications of linear algebra in Axler.

I don't know anything about Strang's book.

 

[danny_91]

Alright, so far I think I have the following choices:

_ Linear Algebra and Its Applications by David C Lay
_ Linear Algebra Done Right by Axler
_ Either Introduction to Linear Algebra or Linear Algebra and Its Applications by Gilbert Strang
_ Matrix Analysis and Applied Linear Algebra by Carl Meyer
_ Hoffman and Kuzne book, it's quite old.
_ There is also this book by David Poole called Linear Algebra: A Modern Introduction

Look like a list of bunches of books on LA. Since I'm not going to buy the Linear Algebra book by DeFranza, which my class is using, I need something that can supplement me for my course.

 

[mathwonk]

go to the library and see which one you can read. good candidates are: hoffman and kunze; lang; friedberg, insel, firedberg and spence; shilov; shields; or any of the free books on my web site, or elsewhere on the web:
http://www.math.uga.edu/~roy/

try linear algebra done wrong, by sergei treil, brown univ.

http://www.math.brown.edu/~treil/

 

[Sankaku]

This is a very solid book for Free:

Linear Algebra by Jim Hefferon
http://joshua.smcvt.edu/linearalgebra/

Try it first and then, if it is too basic, pick up Axler or Hoffman and Kuzne instead. Or, as mathwonk says, try them in the library before buying them...

Just a note: Just because a book is "old" does not mean it has anything wrong with it.

 

[chiro]

danny_91

The recommendation I'm about to give is if you want to go deeper into linear algebra. It is not a first book text at all, but if you want to go deeper and understand things or need the knowledge in say graduate school I would recommend "The Linear Algebra A Graduate Student Ought To Know 2nd Edition" Published by Springer.

Like I said definitely not a first book, but definitely one if you want deeper understanding.

 

[abiyo]

Well it really depends on whether you really want to understand the course for its own sake or just learn the concepts good enough to use it and apply it in other courses. If you really want to understand linear algebra, here is my recommendations(some people have already said it)(sadly vector spaces and operators are never discussed early in some books)

Hoffman and Kunze--my favourite
Axler
Linear Algebra Done Wrong
Shilov
Lang

When it comes to free resources online I choose mathwonk's notes(rigorous) and Paul Dawkins lecture notes.

David Poole and Strang might fit you if you are interested in applications and less rigour. Honestly, Strang's book is too verbose and it does the thinking for you. But as I said it all depends on how far you want to understand the subject.

All the best
Abiyo

.

 

[osnarf]

I don't claim to know much about LA (about to start Shilov myself, hopefully that will change after), but one thing to consider is that if you're using it as a strict replacement for the course book, and not a supplement, and if it goes in a completely different order than your course does it may be frustrating. So I'd compare table of contents, too.

 

[jasonRF]

Hello everybody! I'm new to this forum. Actually, this is my first post in here.

I'm currently a sophomore student in college. My major is in mechanical engineering.

welcome. Sorry I am posting so late. I also took LA as a sophomore engineering major (was required 3rd semester of engr math sequence). I am in the US, where in the world are you?

Right now, I'm taking the course introductory linear algebra, which is the first course in linear algebra. The book I'm having for my class is the 1st edition of Introduction to Linear Algebra with Apps by James DeFranza, I don't know if any of you know this book or not. My instructor said that this book sucks since it's 1st ed., so I guess no complaint then. I read through it and don't really like it. So I won't spend my money buying it.

great - if you can get by without buying it, then you save your money. When I look at the table of contents it looks like the typical soph. level intro. When I took that course we had no text.

I prefer a visual way of presentations, with logic explanations of what's going on, and worked-out examples. I just get bored when looking at a book that's too wordy, with explanations drag out too long. Since I'm new, I prefer a good thorough introductory text. Oh, and some applications too! So any recommendation?? Thanks in advance!

worked out examples ... Axler is out, then. I love Axler, and it is not too wordy, but worked out examples it does not have. No applications either.

Since I don't have much insight into the subject than you guys, can anyone recommend me a good book on the subject? The book Introduction to Linear Algebra by Gilbert Strang, 4th ed., seems to have really good reviews on amazon, what are your opinions on this? Is this a good text 4 LA?

reasonable text - but very wordy. Not what you describe as your goal. Otherwise has examples and applications. A little shy on the abstract side of the topic for my taste, but the MIT grads I work with that took that course seem to have no problems at all (they are smarter than me, though).

If I were you, I would ask the Prof. what he recommends. Since he hates your book, he clearly must have a better book in mind. Perhaps he is basing his lectures on another book anyway.

If that doesn't pan out, start with the free books listed. They may be what you want and are free, after all. However, if they are both too "hard", then Anton is the kind of book you want. Early editions are much more concise than the newer ones yet still clear - I have a 3rd edition that is better than the newer editions for the basic theory, in my opinion, although it may miss a few minor topics here and there. The newer editions do have a lot of nice applications that the old editions do not have, though. Either way an edition of Anton is likely to help. Used copies of any but the newest edition can be found quite inexpensively.

Schaum's outlines may also be worthwhile - your bookstore probably has it on the shelf for you to look through.

I hope you have a successful first brush with LA. Not only can it be a fun subject, you will find it is extremely useful in practice. When I took the course we had no applications and I thought it was a waste of time, but have been proven wrong on hundreds of occasions by now.

Good luck!

jason