Linear Algebra Textbook like George Simmons

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Discussion Overview

The discussion centers around recommendations for a linear algebra textbook that matches the exposition quality of George Simmons' works. Participants express a desire for books that are intuitive, less formal, and suitable for self-study, particularly for someone preparing to study mathematics at the university level.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant praises George Simmons' books for their intuitive approach and historical context, seeking a similar style in a linear algebra textbook.
  • Another participant recommends "Elementary Linear Algebra" by Anton, noting its two versions and practical applications.
  • A different participant mentions a book by Paul Shields, suggesting it may also fit the desired criteria.
  • Concerns are raised about the high cost of textbooks, with suggestions to consider second-hand options or older editions.
  • Some participants express differing opinions on the suitability of "Linear Algebra Done Right" by Sheldon Axler, with one suggesting it may be better for those with more mathematical maturity.
  • Another participant critiques Anton's book for delaying the introduction of linear operators, while expressing a preference for other texts like Axler, Friedberg, Insel & Spence, and Hoffman & Kunze.
  • Participants discuss the potential benefits of visiting a university library to compare textbooks directly.
  • One participant emphasizes that while some recommended texts are rigorous, they may lack the motivation and historical context sought by the original poster.

Areas of Agreement / Disagreement

There is no consensus on a single recommended textbook, as participants express a variety of opinions and preferences regarding different texts. Some participants agree on the merits of certain books, while others challenge those recommendations or suggest alternatives.

Contextual Notes

Participants mention the importance of historical context and intuitive understanding in their textbook choices, indicating that some recommended texts may not align with these preferences. The discussion reflects a range of experiences with different linear algebra textbooks, highlighting the subjective nature of textbook selection.

Who May Find This Useful

Individuals seeking recommendations for linear algebra textbooks that are accessible and less formal, particularly those preparing for university-level mathematics studies.

afrocod
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I know there are suggestions in previous threads and I've searched and read them.

I'm currently working through "Calculus with Analytic Geometry" by George Simmons and I love it. I worked though Simmons' pre-calculus book before that. I learned more from Simmons' books in a few months than I ever did from years of school. I plan to read his topology and differential equations texts as well.

Unfortunately Simmons never wrote a linear algebra textbook. So can anyone recommend a text of similar exposition quality to Simmons'. If you're not familiar with the texts, they cut back on the formalism, have nice historical context meanderings throughout the book and are good for self-study. A general intuitive approach to the subject.

I'll hopefully be going off to university after the summer to get a mathematics degree and I'll get to all the formalism then, but for now I just want to get a good feel for the subject.

I hope some knowledgeable member of the community can shed some light on my problem,

Thank you for any time spent doing so.

Cillian.
 
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Elementary Linear Algebra by Anton is for you.

There are two versions.

The ordinary version and the 'applications version' which has lots of useful well ... applications to make it all real.

go well
 
Studiot said:
Elementary Linear Algebra by Anton is for you.

There are two versions.

The ordinary version and the 'applications version' which has lots of useful well ... applications to make it all real.

go well

Thank you sir, the reviews look good.
 
All right this is good. Thank you for your input.

Anyone else agree or disagree with the previous recommendations or have one of their own?

Hopefully I can get some kind of consensus. Textbooks are so expensive, I need to be really sure before I buy.
 
Textbooks are so expensive

But often much cheaper second hand or even sometimes discounted new. You don't need the latest and (not always) greatest edition for an introduction.
 
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Studiot said:
But often much cheaper second hand or even sometimes discounted new. You don't need the latest and (not always) greatest edition for an introduction.

Some books are so nice, you just have to get the hardback though. But then again if it's just an intro, I know what you mean.

Are you familiar with the Simmons texts? Just wondering is your recommendation based on that knowledge or are you naming a nice, easy, introductory book that you have worked through yourself.

Once again, I appreciate your time.
 
Sorry I don't know Simmons.

There are many good books about Linear Algebra - it is a much written about subject. However I thought Anton was particularly suited to your needs. It provides lots of backup information. I used an early edition (of the basic) when I learned LA to explain all the serious stuff in Nehring, which is the LA Bible, but very formal.
 
Studiot said:
Sorry I don't know Simmons.

There are many good books about Linear Algebra - it is a much written about subject. However I thought Anton was particularly suited to your needs. It provides lots of backup information. I used an early edition (of the basic) when I learned LA to explain all the serious stuff in Nehring, which is the LA Bible, but very formal.

What do you think of "Linear Algebra Done Right" Sheldon Axler? Would that be a bit too much for my first look at the subject?
 
  • #10
  • #11
afrocod said:
What do you think of "Linear Algebra Done Right" Sheldon Axler? Would that be a bit too much for my first look at the subject?

Axler is probably better for a second course unless you have some mathematically maturity already (proofs & abstraction).

I am not familiar with Simmons but, if cost is an issue, there are some very good free textbooks available:

http://joshua.smcvt.edu/linearalgebra/

http://linear.ups.edu/

Try them and see what you think.
 
  • #12
the's why i linked you to a copy costing less than $10 with shipping.
 
  • #13
No money's not an issue. I just want to be sure before I buy because textbooks are often but not always dearer then the average book.

I don't mind paying a lot of money for a great book that I'll keep coming back to over the years.
 
  • #14
I don't like Anton, mainly because one of the most important topics, linear operators, isn't introduced until about 300 pages into the book. If you're OK with that, it's certainly easy enough to read and all that.

There are probably more of these threads then there are linear algebra books. You can search for them and see what people said there. I like Axler. Micromass doesn't like it, but likes Friedberg, Insel & Spence. (I'm not familiar with it). Hoffman & Kunze is often mentioned as a good book with a more complete coverage of linear algebra than any of the others. There are lots of choices, and most of them are at least OK.
 
  • #15
perhaps you could visit a university library and compare them yourself. n the one i recommended is an introduction for students who now nothing of the topic and is restricted to 2 and 3 dimensions to keep the ideas clear in the simplest cases.

books such as axler and halmos and hoffman and kunze are advanced abstract general treatments. hefferon is quite easy as well.

i also am not a fan at least of anton's calculus, but i have not seen his linear algebra book.
 
  • #16
You asked about Axler. It's a great linear algebra text (for a first or second treatment) but based on your first post not at all what you're looking for. The same, I think, is true of Hoffman & Kunze as well as Friedberg; they all emphasize rigor and do not go out of the way to offer motivation or historical context.
 
  • #17
All right, thank you to everyone who replied. I think I have enough different opinions to go on to make an informed decision.

It really is a great community here, everyone is very helpful and generous with their time.
 

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