A First Course in Linear Algebra

by Robert A. Beezer

This textbook is designed to teach the university mathematics student the basics of linear algebra and the techniques of formal mathematics. There are no prerequisites other than ordinary algebra, but it is probably best used by a student who has the \mathematical maturity” of a sophomore or junior. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully.

Genres: Mathematics, Nonfiction

1034 pages, ebook

First published January 1, 2004

Reviews

[Leo Walsh · Rating 5 out of 5]

Overall, a very well written book. It is every bit as good as the Linear Algebra textbook that I donated to Salvation Army, which was worth over $100 back in the 90's. And the price was right -- free. Plus, I could store this with a sprawling open source textbook collection -- physics, calculus, vector calculus, chemistry, o-chem, biology, statistics, probability -- right on my Kindle. And have backups on Amazon in case I need to look something up at the office.

All for free! Amazing.

Breezer covers nearly every aspect of linear algebra quite well, and in depth. From defining subspaces to vector and matrix operations, it is all there. His style is clear, albeit with a bit too conversational at times. Which works well, but linear algebra is supposed to be where we are getting used to purely abstract proofs. But, I suppose, I am just picking nits here...

Some people may find that the illustrations lack "punch" because they are black-and-white. But to be honest with you, I've always found that modern illustrations in math text books distract. They are often too fancy, with details obscuring an otherwise excellent concept. Breezer's illustrations were simple, elegant and spot-on.

He also does a great job integrating computer algebra systems, illustrating how to use them to solve more complex problems. But, unlike most textbooks, who use the expensive Mathematica or MatLab programs, he focuses on a wonderful freeware SageMath.

My main gripe -- and I almost lowered my rating from 5-stars because of it -- is Breezer's unique naming conventions. He names chapters with odd abbreviations. For instance, instead of saying "System if Linear Equations," his chapter and table of contents reads "SLE." And every other concept gets that treatment. Which makes the text sometimes baffling and difficult to navigate. Which is odd, since I aced linear algebra "back in the day."

So, I'd say "Go for it." I wonder why colleges don't use these free texts. Most are peer reviewed, and the information solid...-

[Sam · Rating 5 out of 5]

I really enjoyed reading this textbook. It is well written, and structured in a very pleasing way.

[prarobinson · Rating 3 out of 5]

This is the first open source (GNU) book I've come across. The whole idea just sort of blows my mind, and the content is really well put together too. I'm trying to learn more Python, and came across SAGE (a Python environment for doing numerical things like linear algebra); this book, while having many examples in straight-up mathematical notation, also has examples using SAGE. This is awesome because nobody's going to solve some system of equations involving more then four or five variables by hand if he or she doesn't have to.

[Lulu]

Linear Algebra - easier