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For real analysis, I suggest Bartle's "Introduction...". I had a horrible teacher (well, I loved him, but he never prepped for class), and was able to learn ev

For real analysis, I suggest Bartle's "Introduction...". I had a horrible teacher (well, I loved him, but he never prepped for class), and was able to learn everything by working through the proofs in the text. Bartle has a multi-dimensional version too. For linear algebra, I was suggest Strang's "Linear Algebra with applications", 3rd edition. Then "Linear Algebra Done Right". While you are at it, get Hungerfords "Abstract Algebra: An Introduction"; you will need an easy reference to fields and groups and polynomials. All these books require an hour per page, but they lay it all out for you if you work for it. These are definitely undergrad books, but that is their beauty. Bartle also has "Elements of integration and lebesgue measure" -- I bet it is great, but I haven't used it. And if you find a good probability book, please post the title ;)

btilly 16y ago
Upvoted for suggesting Linear Algebra Done Right. To get a sense of the approach, read his earlier article Down with Determinants at http://www.axler.net/DwD.html http://www.axler.net/DwD.html. That article was the first time I felt I really understood a lot of the material I had already theoretically learned and done well at. On the real analysis side, I learned from Royden and liked it. But my mind definitely heads the analysis way, and what I find easy someone else might not.
- dbfclark 16y ago
  I definitely enjoyed Royden a lot -- I got through my real analysis qual back in grad school using Royden to teach myself essentially all of the material. Readable and excellent. And as to minds heading the analysis way: I'm about as algebraicly-minded as they come and I thought it was highly readable.
leif 16y ago
I learned linear algebra from axler and real analysis from bartle and sherbert too. :) Great books.
znmeb 16y ago
Good probability book? What's wrong with Feller? ;-) Linear algebra: well, there are lots of good theory books but I'm a big fan of the computational approach, and Golub and Van Loan is my pick there hands down!
simplegeek 16y ago
Al Drake's book on probability is pretty good. If you know of any good introductory level Combinatorics books then please enlighten me ;)
ww520 16y ago
Real Analysis! OMG that brings back bad memory. Got a horrible teacher as well. Somehow Complex Analysis was easier. Sadly I have forgot all of them now. :(

btilly 16y ago

Upvoted for suggesting Linear Algebra Done Right. To get a sense of the approach, read his earlier article Down with Determinants at http://www.axler.net/DwD.html http://www.axler.net/DwD.html. That article was the first time I felt I really understood a lot of the material I had already theoretically learned and done well at. On the real analysis side, I learned from Royden and liked it. But my mind definitely heads the analysis way, and what I find easy someone else might not.

dbfclark 16y ago
I definitely enjoyed Royden a lot -- I got through my real analysis qual back in grad school using Royden to teach myself essentially all of the material. Readable and excellent. And as to minds heading the analysis way: I'm about as algebraicly-minded as they come and I thought it was highly readable.

leif 16y ago

I learned linear algebra from axler and real analysis from bartle and sherbert too. :) Great books.

znmeb 16y ago

Good probability book? What's wrong with Feller? ;-) Linear algebra: well, there are lots of good theory books but I'm a big fan of the computational approach, and Golub and Van Loan is my pick there hands down!

simplegeek 16y ago

Al Drake's book on probability is pretty good. If you know of any good introductory level Combinatorics books then please enlighten me ;)

ww520 16y ago

Real Analysis! OMG that brings back bad memory. Got a horrible teacher as well. Somehow Complex Analysis was easier. Sadly I have forgot all of them now. :(