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Comment by rkowalick | Hacker News Reader

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 the correct hypothesis and prove the new theorem.

How can we strengthen question Y?

On page ABC, what is the error in the proof of such and such. How can it be fixed?

Honestly, any good professor can make even the worst of books enjoyable.

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"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

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.

"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!

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.

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