Ten years old discussion: https://news.ycombinator.com/item?id=351334
Couple of things to note about this link:
Contains the 3rd edition of the book.
Has extra problems and solutions from when he taught the class in 2014
Linear Algebra by Jim Hefferon – free textbook
31–40 of 62 posts
Re: Linear Algebra by Jim Hefferon – free textbook
#32What is nice about this book is it includes solutions to exercises. I wish more proof-theoretic books included exercises in the back of the book like this one does. Yes, you can prove something in multiple ways, and no that isn't a good excuse to not include at least one version of the proof in the back of the book. It really benefits the self-learner. The math community seems to have a lot of artificial gatekeeping…
> They tell the self-learner that solutions aren't provided because everyone has the ability to know if their solutions are correct without having their work checked. Would you write a complicated program and write no test cases, or could you instantly know your program is bug free the first time you write it? Why is math suddenly any different?
Math is an art of making a specific type of rigorous, formal arguments that are meant to convince, beyond all doubt, another human being that one statement follows from another. If an argument like that fails to convince even the proof author themselves, then you know the argument isn't good even without comparing it to another solution.
In practice, after you've written down your proof, you examine it for weak spots. If any particular step raises doubts or objections then you recursively spell it out in greater detail (or replace with an alternative approach) until eventually all doubt dissipates. At that point you don't need to compare it to another solution.
In fact, as you recognized yourself, your solution is likely to be different from the book author's, so comparison isn't helpful. Similarly, a problem like "write a small application to..." in a coding book or an assignment like "write an essay on..." in a writing book don't include solutions. Code, proofs and essays are all too free-form to subject them to correctness verification by comparison with a standard.
Perhaps what you have in mind are examples. All good math textbooks include worked-out proofs that illustrate the techniques. In fact these are generally the bulk of the book! Perhaps you're asking for more examples. That's fair. Proof problems OTOH should be given without solutions to encourage independent creative thought of the reader and to avoid incorrect implication that there is the single correct solution.
(Disclaimer: Not a mathematician.)
Re: Linear Algebra by Jim Hefferon – free textbook
#33It's nice to have a free book as a supplement. Linear Algebra Done Right by Sheldon Axler is a much better choice and when making an investment in learning, particularly a difficult subject like linear algebra, saving money with a free text is probably the most expensive thing you can do. You might save $40 but end up not really learning and wasting hours you don't have. Above all, find a good teacher.
Why can't a free open source book be equivalent to or better than a more traditional book? First of all the release cycle of the free book should be much faster. Edits and alterations can be incorporated much more rapidly. Giving publishers such control over knowledge can be harmful. Being free does not have to sacrifice quality (this book is written by a mathematician anyway). Also I recall reading Axler, and I thin…
Open source textbooks could theoretically be better than paid but generally speaking the big problem is that there usually isn't enough people to actually "care" for the book so to speak. Eventually the original writers lose interest and move on. For other open source books...they end up only becoming half written....and then turn into abandonware....see wikibooks.
You could solve the problem with something like a wiki but I've seen that usually results in quality problems. It isn't like a wiki article where all the results can basically see what has been written. With a wikibook though...you need all writers to basically know where stuff has already been explained...otherwise you just get a bunch of people explaining x here and then other people explaining the same thing in a later chapter.
Re: Linear Algebra by Jim Hefferon – free textbook
#34What is nice about this book is it includes solutions to exercises. I wish more proof-theoretic books included exercises in the back of the book like this one does. Yes, you can prove something in multiple ways, and no that isn't a good excuse to not include at least one version of the proof in the back of the book. It really benefits the self-learner. The math community seems to have a lot of artificial gatekeeping…
Would you make a book list for other mathematical subjects? I have tried following the "recommended book" route and it really isn't productive. The first person recommends A and then everyone else doesn't want to look at l33t so they concur.
I would highly recommend ASU's College Algebra and Problem Solving [1]. They have a large comprehensive test at the beginning that determines your knowledge. Should you be missing knowledge, they'll use the same platform to teach you all the prerequisites (i.e. they won't let you take the course until you go through ALEKS, their learning platform). After that's done, this course is something like preparation for college math classes.
So far, I like it a lot, thanks to ALEKS. Give it a shot; it's free.
[1] https://www.edx.org/course/college-algebra-problem-solving-a...
Re: Linear Algebra by Jim Hefferon – free textbook
#35Are there any books like this for probability?
Re: Linear Algebra by Jim Hefferon – free textbook
#36Are there any books like this for probability?
First chapter of this book has a similar style and will get you started: http://mbmlbook.com
Re: Linear Algebra by Jim Hefferon – free textbook
#37It's nice to have a free book as a supplement. Linear Algebra Done Right by Sheldon Axler is a much better choice and when making an investment in learning, particularly a difficult subject like linear algebra, saving money with a free text is probably the most expensive thing you can do. You might save $40 but end up not really learning and wasting hours you don't have. Above all, find a good teacher.
This book saved my life during uni. I found the explanations to be clear and well thought out. Math textbooks are expensive and it’s a hard sell when you’re still an undergraduate and not sure what you will end up doing with your life. Furthermore, as I can attest, finding a good teacher is n even harder proposition. It’s very rare to have good teachers when you’re in university. Most lecturers get their jobs based on their research skills and not their teaching skills. In the absence of good teachers, textbooks taught me everything I know and this is one of them. I hear where you are coming from, but this book is an exception and is fantastic. There’s a reason people are still talking about it and using it.
Re: Linear Algebra by Jim Hefferon – free textbook
#38It's nice to have a free book as a supplement. Linear Algebra Done Right by Sheldon Axler is a much better choice and when making an investment in learning, particularly a difficult subject like linear algebra, saving money with a free text is probably the most expensive thing you can do. You might save $40 but end up not really learning and wasting hours you don't have. Above all, find a good teacher.
The videos are free! They are a pretty good introduction by themselves.
Linear Algebra Abridged, a free compactified version of Linear Algebra Done Right, 2016. http://linear.axler.net/LinearAbridged.html
Linear Algebra Done Right videos, free videos to accompany the book, 2017. http://linear.axler.net/LADRvideos.html
Re: Linear Algebra by Jim Hefferon – free textbook
#39Earlier quoted context omitted.
> What makes LADR superior to this book? Axler's approach for determinants.
Are you serious? Axler defines determinant as (up to a sign) the constant term of the characteristic polynomial, and he needs two different definitions for characteristic polynomial, one over R and one over C. Now what if the ground field is something else? Do we need yet another definition of characteristic polynomial in order to define the determinant? What if you are doing linear algebra over a commutative ring? L…
Thanks. I found LADR not that helpful - I use linear algebra constantly but only on a very elementary level. After reading your message I now feel it's ok not to find that book applicable to my pursuits and that I'm not missing some concept I failed to grasp from the book.
Re: Linear Algebra by Jim Hefferon – free textbook
#40How nice to see this link here! I could answer any questions that anyone has. --Jim