I have the book so I read it before I go to bed sometimes, but I haven't had much serious time to devote to it (sort of). I generally prefer to start a new book when I have a lot of spare time.
I've thought over the problem stating that if an abelian group has subgroups of deg. m and n then...
I'm planning on reading Topics in Algebra; I've read about half of Finite-Dimensional Vector Spaces, and I've skimmed most of Herstein's book, so I think I can finish the first three chapters over break (I'll probably go straight to field theory if I have extra time).
I was thinking of buying...
In "Surely You're Joking Mr. Feynman" he mentions that he still has the notes from the first lectures he gave at Cornell, which were on math methods for physics. Does anyone know if they still exist, or if they were every published?
He wrote an article "Algebra and Topology as Two Roads to Mathematical Comprehension" that you might want to read. It gives some examples of how you can view a problem algebraically and topologically (... you probably got that from the title). I haven't read the whole thing, so I'm not sure if...
Gallian's book is fairly standard (although I've heard it's a little easy), and an older edition might only be $20-30. I forgot the title (probably Abstract Algebra), but the author is Joseph Gallian.
If you aren't used to doing proofs then you might want to find a book on the basics of proofs. "How to Prove It" by Velleman has a good reputation.
If you're studying on your own, access to someone who knows analysis well (e.g. a professor) is great.
Also, MIT uses this book for their real...
I record my results in a notebook, since typing up work in TeX usually takes too long. I like to keep it neat so I do my work out on the board or on scrap. If you write carefully your notes should be legible, but it tends to take a lot less time to write notation than type it (maybe not in...
My desk at home is really small and uncomfortable so i tend to stand up and use my white board when I'm working out problems. If you go to Lowe's, they sell sheets of white board material for $10. The only down side is my feet hurt from this, but I need new shoes. You might want to try to get...
So far, you have:
a(b-c) = a(b + (-c)) = ab + a(-c)
Now you need to show that a(-c) = -ac... what property does -ac have that you suspect a(-c) has? they're both additive inverses of ac, so..
ac - ac = a(c - c) by a.3
and ac + a(-c) = a(c + (-c)) = a(c - c),
so ac - ac = ac + a(-c), and by...
Prove that ac + a(-c) = 0... then a(-c) = -ac.. I suppose you have to prove that additive inverses are unique but you can use the cancellation law for this. Don't stress over this part too much; most proofs aren't like this. If you did most of the set proofs you should be good - generally that...