Linear algebra (abstract) prerequisites I want to understand dynamic programing, so im figuring out the irreducible and minimal path i should take. The secuence is:
1. General topology (Munkres chapters 1-4).
2. Abstract algebra.
3. Linear algebra.
4. Functional analysis.
5. Calculus of variations.
6. Dynamic prigramming.
So, im asking for some books, in specific a book that allow me to jump from 2 to 3 in an eficient maner.
Thanks, and sorry for my english!
 A: I don’t think any of those things are necessary for dynamic programming. AFAIK just understanding proofs by induction and basic algebra are sufficient to prove correctness and complexity of such things. 
But not don’t know a lot of deep dynamic programming. There are probably some things you do need those subjects for.
The most relevant thing you might want to look up ahead of time is what recursion is in computer science. Other than that, just look for introductory material on algorithms. Dynamic programming can be considered an algorithmic paradigm. I took a Coursera course on algorithms for fun, Stanford I think, and it was really well explained. You might try finding that course and see if a trial is available.
Needless to say it would be silly to insist on learning all those five things before studying dynamic programming. Most of them do not seem relevant to me, with  the partial exception being linear algebra. You should just pick up all the basics of linear programming first and then backfill those subjects as necessary.
Also, leaning abstract algebra before linear algebra is silly.  Do that the other way around.
