3 ms·
Disclaimer: I am very happy that books like this are written, and look forward to never seeing another $120 doorstop being used as a text for the course anywher
by romwell 10y ago
Disclaimer: I am very happy that books like this are written, and look forward to never seeing another $120 doorstop being used as a text for the course anywhere. What follows is criticism and a question which, if addressed, could help those on the fence about this book.
----------------------
Speaking of Axler, his Linear Algebra Done Right is still the best book on the subject, in my opinion.
For one, it's lean. You can fit the softcover in a purse, and read it in the bathroom. It may be scant on examples, but it's a book that can be read in its entirety.
This book, at 500+ hundred pages, simply means nobody will really read it. No student is going to be reading several dozen pages of hard math EVERY WEEK - the exceptions to that are those who will do well with any other book too.
So we have a book here that, alas, is not meant to be read - in entirety, at least.
Yes, these are two very different books. But then we also have Linear Algebra Done Wrong.
A text by Serge Treil, it was written as a counter to Axler's book (and was named in jest). It covers many of the same topics, and is available as a free (!) PDF.
So, my question is - why this book? Aside from the title, what does it really do in a new way?
There's not enough in the preview for me to conclude that this book did anything Linear Algebra Done Wrong does not, so I ask those who read it (or the author).
- ivan_ah 10y agoThanks for your question, which I will respond to in a second. First let me explain how we got to 550 pages. I wanted to include a review of prerequisites material from high school math, which burned 100pp right off the batt. Then the main material (Ch2-Ch6) is just 220pp which is not bad (especially when you take into account the book is a compact format 5.5" x 8.5"). All of this was done in 2014, when I started to think about the applications of linear algebra. But then the feature creep starts! In the introduction of the book I make the claim about how powerful LA techniques are, and how they serve as the foundation of machine learning, and generally "scientific modelling." To substantiate this claim, I decided to make a kick-ass applications chapter that SHOWS how powerful linear algebra really is (show me, don't tell me). Two years later, the result is a 270-page survey of pretty much everything I've learned over the years from engineering, physics, and computer science that used linear algebra. > why this book? what does it really do in a new way? The main point of this book is to teach all the LA material in an approachable, informal narrative as opposed to formal the theorem-proof approach used in most textbooks. Can serious mathematical topics be introduced using informal language, yet without saying anything outright wrong? Can I trick the reader into learning advanced topics like Fourier transforms and quantum mechanics by making the connections to basic operations explicit? Can I sneakily introduce spaced repetition by covering core ideas several times in the book using different notation and in different contexts?
- deleted 10y ago[deleted]
- romwell 10y agoThanks for the answer! So, the book is really three books. How do you get around actually proving things?
- ivan_ah 10y agoThe book proves most things, just doesn't follow the standard math format of theorem-followed-by-proof. All the definitions are reasonably clear, and most of the proofs that are accessible and educational are given (e.g. the equivalence statements about invertible matrices). The exercises and problems also ask readers to complete several other interesting proofs (with solutions in the back). In a future pass I plan to add more proofs, wherever adding formal structure doesn't interfere with the flow.