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Linear Algebra by Jim Hefferon – free textbook

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Re: Linear Algebra by Jim Hefferon – free textbook

#41

Post by tejuis »

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…

It is easy to agree with these findings. In general it is important for humans to get answers to WHY. History answers typically to WHY questions and to some extent also examples, i.e. you see by example WHY the theory works.

Re: Linear Algebra by Jim Hefferon – free textbook

#42

Post by thanatropism »

gballan wrote: post #23

Here is another [1]--perhaps not to everyone's taste, but it was influential for me. In particular, the first words of the preface: "The underlying spirit of this treatment of the theory of matrices is that of a concept and its representation." [1] https://archive.org/details/LinearAlgebraAndMatrixTheory

My own take is that the "theory of matrices" (not a standard usage but should be) is worth learning for some (sp if you're going into hardcore numerics like stability of algorithms) but not for everyone. It's like studying calculus as the theory of smooth curves -- it robs you of some potential for growth.

Also: some people just want "math for deep learning" and that's mostly baby calculus: the chain rule and gradient descent.

Re: Linear Algebra by Jim Hefferon – free textbook

#43

Post by citizenkeen »

release_cycle wrote: post #10

What 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…

So, as someone who finagled their way into an MSCS progress with no calculus... What intro calc textbook for a self-disciplined self-learnerv would you recommend?

Re: Linear Algebra by Jim Hefferon – free textbook

#44

Post by devereaux »

bollu wrote: post #12
devereaux wrote: post #9

Earlier quoted context omitted.

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

The determinant story of "distortion of unit volume" only makes sense AFAICT if you're in R^n. What does the determinant mean when you're considering linear functions from 2^n to 3^n? There's no geometric interpretation I'm aware of for this case; indeed, I doubt there is one, due to the inherent nature of finite fields.

Geometric interpretations have a place in learning: until one is ready to understand another interpretation that is more complete, better, yet more complicated.

You don't start kids with complex numbers until they can handle reals. You don't even start negative numbers until they can handle positive numbers.

Re: Linear Algebra by Jim Hefferon – free textbook

#45

Post by enriquto »

romwell wrote: post #18
Mugwort wrote: post #3

It'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.

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 ...".

Re: Linear Algebra by Jim Hefferon – free textbook

#46

Post by release_cycle »

citizenkeen wrote: post #43
release_cycle wrote: post #10

What 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…

So, as someone who finagled their way into an MSCS progress with no calculus... What intro calc textbook for a self-disciplined self-learnerv would you recommend?

I'd recommend "Calculus Made Easy" for intuitive exposure. It was the book Feynman studied from.

Then pick up any calculus textbook and chug through it (Thomas is good from what I've heard). Even if the questions don't have answers in the back of the book you can check your computational steps for free using: https://www.symbolab.com.

I also recommend lots of practice, so khan academy is good for drilling + any problem set book with lots of calculus problems, such as "Schaum's 3,000 Solved Problems in Calculus" or "Essential Calculus Skills Practice Workbook". They don't have to be huge calculus text, doing problems is more important than reading through 1,000s pages of colorful examples. You can find shorter calculus books that focus primarily in drilling calculus techniques. Focus on those to nail the techniques.

Re: Linear Algebra by Jim Hefferon – free textbook

#47

Post by faitswulff »

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…

What other books have you found helpful other than the Chatterjee text?

Re: Linear Algebra by Jim Hefferon – free textbook

#48

Post by neves »

skh wrote: post #11
release_cycle wrote: post #10

What 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…

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…

I have 2 sons, and I saw how difficult is to build a clear explanation to them. I must quickly build a way to explain: 3x + 2x = (x + x + x) + (x + x) = 5x, and it is not easy. If I hesitate, they get bored and don't want to study anymore.

That's why Khan Academy is a so fantastical resource. They really build a very clear explanation of the concepts. Every teacher should watch it before classes.

Re: Linear Algebra by Jim Hefferon – free textbook

#49

Post by hopler »

neves wrote: post #48
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…

I have 2 sons, and I saw how difficult is to build a clear explanation to them. I must quickly build a way to explain: 3x + 2x = (x + x + x) + (x + x) = 5x, and it is not easy. If I hesitate, they get bored and don't want to study anymore. That's why Khan Academy is a so fantastical resource. They really build a very clear explanation of the concepts. Every teacher should watch it before classes.

Try beastacademy.com

It's not free but it's an amazing comic book textboom and fun instersting challenging problems for kids.

Buy the books and share them with your neighbors, and share an online account if you can't afford your own.

Re: Linear Algebra by Jim Hefferon – free textbook

#50

Post by hopler »

romwell wrote: post #18
Mugwort wrote: post #3

It'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.

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…

Thanks. Most everyone thinks the first book they read sucks and the second book they read is better, because they don't realize the right way to learn is to read two or more different combine perspectives and revisit the material.
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