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Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

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Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#11

Post by wheels »

rkowalick wrote: post #5

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one. I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors: Show that question X is false as stated. Give t…

I think it really depends on how comfortable you are with mathematical symbols as a means of conveying something. I, for instance, tend to think of things very geometrically or algorithmically, so usually in understanding mathematics I have to visualize the application and work backwards. As such, the "applications" aren't so much a toolbox a la applied math as much as nice concrete examples that help me understand the underlying theory.

And for the record, another hat in the ring for Strang's Linear Algebra and its Applications.

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#12

Post by charlesju »

I hated math in college, I never thought that any math past basic Algebra would ever be used again in my life. But as I progressed further in Computer Science, I learned that if anything, Linear Algebra is involved in so many cool fields; AI, Graphics, Searching, etc.

My biggest regret in college was not learning linear algebra as well as I should have, thanks for the great link.

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#13

Post by rkowalick »

msie wrote: post #8
rkowalick wrote: post #5

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one. I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors: Show that question X is false as stated. Give t…

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things." You are a special case. I think you can succeed in spite of the book being used. :)

I picked Rudin's book because it is infamously terse. It's an analysis/advanced calculus books with NO pictures at all.

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#14

Post by plinkplonk »

rkowalick wrote: post #5

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one. I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors: Show that question X is false as stated. Give t…

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis"

Can you recommend a similar book for Linear Algebra? (terse comprehensive rigorous).

Thanks in advance,

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#15

Post by dylan »

Always interesting to see if someone can write a great linear algebra book. I like Axler's "Linear Algebra Done Right" [1] because he puts off the determinant until it's clear why you want to define such a map. That the book continually treats the case when your field is the complex numbers slows things down at times, though.

[1] http://linear.axler.net

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#16

Post by carterschonwald »

rkowalick wrote: post #13
msie wrote: post #8

Earlier quoted context omitted.

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things." You are a special case. I think you can succeed in spite of the book being used. :)

I picked Rudin's book because it is infamously terse. It's an analysis/advanced calculus books with NO pictures at all.

its also just a really fun book, though I think his Real & Complex book is much more pretty in terms of exposition and topics

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#17

Post by rkowalick »

plinkplonk wrote: post #14
rkowalick wrote: post #5

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one. I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors: Show that question X is false as stated. Give t…

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis" Can you recommend a similar book for Linear Algebra? (terse comprehensive rigorous). Thanks in advance,

While it certainly isn't terse, Linear Algebra by Friedberg, Insel, and Spence is comprehensive and rigorous. It has everything you would ever want to know about linear algebra with some applications too.

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#18

Post by antigravity »

plinkplonk wrote: post #14
rkowalick wrote: post #5

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one. I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors: Show that question X is false as stated. Give t…

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis" Can you recommend a similar book for Linear Algebra? (terse comprehensive rigorous). Thanks in advance,

(1) Axler's "Linear Algebra Done Right"

...a nice introduction to abstract linear algebra, but not quite abstract or terse enough.

(2) These course notes: http://www.math.mcgill.ca/goren/AlgebraII07-08/AlgebraII.htm

...good, though the duality section is a bit lacking. Riesz Representation Theorem FTW!

Re: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

#19

Post by uuilly »

kqr2 wrote: post #6

My favorite text on Linear Algebra is Gilbert Strang's Linear Algebra and Its Applications although the current edition is ridiculously expensive: http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St...

We used Strang for Linear Algebra. It was the only math class in college I did badly in. I tried multiple times to understand linear algebra and every time I ended up at the picture in the first few pages of the book. Each page built upon the previous page and there were no pictures to anchor on.

A year later I took an OpenGL class then a grad class in Computational Geometry. Once I had pictures and application I was fine. Morphing space and w/ matrix transformations and drawing in it in OpenGL was all I needed to snap the semester of symbol manipulation into focus. Strang to me was like man pages. Great for reference, terrible for learning.

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