8
$\begingroup$

We are using Elementary Linear Algebra by Howard Anton in the class and I’m not happy with it. At times there is many pages of writing, yet, there is very little information contained. I really like vector spaces but to find appreciation of them I have to scavenge online sources. What would be a good supplement, maybe substitution? I don’t have knowledge beyond Calculus 3, and I really want to learn how to understand and write proofs. At the same time, I’d like to be able to follow at least half of the time what the author is trying to convey.

$\endgroup$
7
$\begingroup$

Linear Algebra Done Right by Sheldon Axler is a very clear book that takes a proof based approach to linear algebra and works natively with vector spaces with a minimum of algebraic matrix manipulation. I highly recommend it.

$\endgroup$
  • 4
    $\begingroup$ "Linear Algebra Done Wrong" by Sergei Treil is also a nice text, and it is freely available on the WWW. $\endgroup$ – Andreas Rejbrand Apr 2 '18 at 20:24
5
$\begingroup$

The book Linear Algebra by Friedberg, Insel and Spence is a very comprehensive book with lots of examples and exercises. You can find some examples of infinite dimensional vector spaces in the book. It even includes optional topics like dual vector spaces, which serves as a nice initiation to linear .

$\endgroup$
  • $\begingroup$ Thanks! A copy of the book is on the way! $\endgroup$ – mAbel Apr 2 '18 at 18:32
4
$\begingroup$

A completely different option would be to use the materials for the Massive Open Online Course titled "Linear Algebra: Foundations to Frontiers" on edX. It has online exercises, video, and simple programming exercises that links abstraction in mathematics to abstraction in programming. It is meant to be more appealing to students who are more computational science/computer science oriented.

This course does not require calculus and does include proofs of essentially all results.

$\endgroup$
  • $\begingroup$ I should have mentioned: It is free, including an 800 page book. $\endgroup$ – Robert van de Geijn Apr 2 '18 at 16:52
  • $\begingroup$ Another video-based option is the 18.06 MIT course by Gilbert Strang. Excellent. web.mit.edu/18.06/www/videos.shtml I also recommend the textbooks by Poole and by Lay. $\endgroup$ – Randy Apr 2 '18 at 17:01
  • $\begingroup$ Strang does not do proofs. He motivates very nicely with small matrices. $\endgroup$ – Robert van de Geijn Apr 2 '18 at 18:09
3
$\begingroup$

I also recommend "Book of Proof" by Richard Hammack for instruction, examples, and exercises in writing proofs in general.

$\endgroup$
  • $\begingroup$ Thank you, I ordered the book and will work through it diligently. $\endgroup$ – mAbel Apr 2 '18 at 18:30
3
$\begingroup$

If you are a math major or studying to be a mathematician, and have already taken a course on matrix algebra, I recommend "The Linear Algebra a Beginning Graduate Student Ought to Know" by John Golan. Don't let the name fool you; while this book is aimed at a beginning graduate student, it's very accessible to undergraduates with a semester of basic vector-matrix algebra. This text will introduce you to some interesting ideas and notations that would supplement a theoretical linear algebra class well. It's not a tough read, and it will help you bridge the gap later when you move on to modern/abstract algebra courses.

$\endgroup$
  • 1
    $\begingroup$ Thank you for the suggestion. I’m planning to be an Actuary but I really want to do mathematics without computation aspect; at least once. Linear Algebra is the only class that allowed me to think in more abstract terms and I really like it; that’s why I was looking for different text to just dwell on the subject little bit longer. $\endgroup$ – mAbel Apr 2 '18 at 19:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.