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Linear Algebra by Jim Hefferon – free textbook

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Re: Linear Algebra by Jim Hefferon – free textbook

#51

Post by hopler »

The_suffocated wrote: post #29
devereaux wrote: post #9

Earlier 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…

The secret is that math is too big to fit into any one book. It takes many books with many perspectives you learn the generality and applicability of the topic. The average person who couldn't learn a topic read one book on the topic. The average mathematician read 5 or 10.

Re: Linear Algebra by Jim Hefferon – free textbook

#52

Post by sriram_malhar »

roenxi wrote: post #26
skh wrote: post #11

Earlier quoted context omitted.

In my experience (math teacher at a community college for 20 years and former Ph.D. student who quit before finishing the thesis) the overwhelming majority of people can not learn mathematics properly from a textbook. They need a teacher or someone to help with problems. It's very difficult to get to a point of really understanding the definition/motivation behind concepts. Even with a teacher it's hard to understand…

> the overwhelming majority of people can not learn mathematics properly from a textbook. While you are right, a related issue is that most maths textbooks are atrocious at most aspects that aren't writing pages of equations. There is almost nobody sitting at the 3-way intersection of great mathematician, great writer and great educator who can then write great textbooks. I've found books with terms like "History" an…

Did you mean "Statistical Thought" by Chatterjee?

Re: Linear Algebra by Jim Hefferon – free textbook

#53

Post by cs702 »

jimhefferon wrote: post #40

How nice to see this link here! I could answer any questions that anyone has. --Jim

First, let me say THANK YOU for making this a free textbook available online to everyone everywhere. The world owes you a debt of gratitude. I, for one, will do my part and make a donation via the link at the bottom of your textbook's web page. I hope others here will join me.

My question is: What motivated you to create this freely available book?

Re: Linear Algebra by Jim Hefferon – free textbook

#54

Post by romwell »

enriquto wrote: post #45
romwell wrote: post #18

Earlier quoted context omitted.

Axler's Linear Algebra Done Right has always been my favorite linear algebra text (I say this 10+ years after reading it and finishing my math PhD, if that matters). For those who want a free alternative, behold: Treil's Linear Algebra Done Wrong[2] The books is downloadable as a free PDF. The name is an answer to Axler's book (dry mathematician's humor), and offers an opposite approach (getting to determinants first…

> 6. Shears are linear maps that don't change the volume. Just to nitpick, but this sentence might be read ambiguously by some people, who would understand it as the definition of shear. You may want to say "Shears are an example of ...".

Thanks; I'm past the edit time cut-off, but will keep it in mind for the next time I say something like that :)

Re: Linear Algebra by Jim Hefferon – free textbook

#55

Post by jimhefferon »

cs702 wrote: post #53
jimhefferon wrote: post #40

How nice to see this link here! I could answer any questions that anyone has. --Jim

First, let me say THANK YOU for making this a free textbook available online to everyone everywhere. The world owes you a debt of gratitude. I, for one, will do my part and make a donation via the link at the bottom of your textbook's web page. I hope others here will join me. My question is: What motivated you to create this freely available book?

Thank you for the donation. I use the funds to work on revisions of this text, and on developing others.

For motivation: briefly, I was at Union College and was asked to teach Linear. I saw a second edition of Strang's book, thought it was wonderful (still do), and adopted it. But the students, who were perfectly good students, did not get it. They just couldn't solve the problems that a person should solve in that class. I decided after some reflection that the folks I had need to be brought along to where they are ready for a higher level understanding. So I put together a presentation that uses lots of examples, motivation, and naturalness to try and develop maturity in people who do not yet have it.

(Again, I'm not talking Strang's book down, it is very fine indeed. But the students that I have in front of me at this point are just not yet ready.)

Re: Linear Algebra by Jim Hefferon – free textbook

#56

Post by yesenadam »

hopler wrote: post #51
The_suffocated wrote: post #29

Earlier quoted context omitted.

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…

The secret is that math is too big to fit into any one book. It takes many books with many perspectives you learn the generality and applicability of the topic. The average person who couldn't learn a topic read one book on the topic. The average mathematician read 5 or 10.

Good point. Even in maths, "bias" is inevitable. Every mathematician has a point of view. There's no objectively best curriculum or way of doing things, understanding things, solving problems etc.

(I'm more familiar with this phenomenon in philosophy, where the greater the philosopher, the more they have entirely their own way of looking at things, untranslatable into another tongue, which you just have to come to understand on its own terms. A summary of their views leaves out the personal aspect, the style, the way of thinking, and will seem dead.)

Re: Linear Algebra by Jim Hefferon – free textbook

#57

Post by roenxi »

sriram_malhar wrote: post #52
roenxi wrote: post #26

Earlier quoted context omitted.

> the overwhelming majority of people can not learn mathematics properly from a textbook. While you are right, a related issue is that most maths textbooks are atrocious at most aspects that aren't writing pages of equations. There is almost nobody sitting at the 3-way intersection of great mathematician, great writer and great educator who can then write great textbooks. I've found books with terms like "History" an…

Did you mean "Statistical Thought" by Chatterjee?

Oh, sorry, yes I did. "Statistical Thought: A Perspective and History". The first half is basically all the schools of thought on how probability theory and the real world interact; so I keep thinking of it as a philosophy book.

Re: Linear Algebra by Jim Hefferon – free textbook

#59

Post by nelsots »

vasili111 wrote: post #20
nafizh wrote: post #14

If you want to learn linear algebra by coding in python, this is hands down the best book out there. Coding the Matrix - Philip Klein [0] It used to have a Coursera course, but I think it's been taken down. The website has videos of the course taught at Brown I think. The associated website is: http://codingthematrix.com [0] https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co...

The course is available here: http://academictorrents.com/details/54cd86f3038dfd446b037891... It is legal, not a pirated version.

That was a great course! I'm glad it's still accessible. I was not aware of this resource for courses. There was a fantastic course on probability from the University of Pennsylvania that disappeared when Coursera went through a change a few years ago. Maybe I can find that one there too. Thanks for the link.

Re: Linear Algebra by Jim Hefferon – free textbook

#60

Post by romwell »

skh wrote: post #13
devereaux wrote: post #9

Earlier quoted context omitted.

> What makes LADR superior to this book? Axler's approach for determinants.

People who are going to be users of applied linear algebra would probably benefit from a traditional treatment of determinants. Axler's book is excellent for people who plan to go for more pure mathematics in their studies.

>benefit from a traditional treatment of determinants

The only beneficial traditional treatment I can think of is saying "determinant is volume", and that's what Axler does.

From there, one can look into alternating forms, convince oneself that an alternating n-linear form does the same thing, and obtain a formula for it (e.g. summing up signed products of numbers on the diagonals over all permutations of columns).

If by "traditional" you mean: "Here's an insanely complicated formula that does something magical. Learn to compute it. On page 5, we'll prove that it tells something about independence. Oh, and we'll mention volume on page 10 briefly" -- then I not only think this is not useful, I think it's outright harmful.

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