Recent content by sid_galt

Hey, I'm studying Rudin's Real and Complex Analysis by myself and it would be really nice if I could find a solution manual to all/part of the exercises at the end of the chapters. Does anyone know if such a solution manual exists? Thanks

Suppose we have two finite abelian groups G,G^{\prime} of size n=pq, p,q being primes. G is cyclic. Both G,G^{\prime} have subgroups H,H^{\prime}, both of size q. The factor groups G/H,\ G^{\prime}/H^{\prime} are cyclic and since they are of equal size, they are isomorphic. Are G,G^{\prime}...

Let A, M be a commutative ring and a finitely generated A-module respectively. Let \phi be an A-module endomorphism of M such that \phi (M)\subseteq \alpha\ M where \alpha is an ideal of A. Let x_1,\dots,x_n be the generators of M. Then we know that \displaystyle{\phi(x_i)=\sum_{j=1}^{n}...

Suppose we have a two giant ideal springs very far apart from each other such that each spring can be used to launch a spaceship X to relativistic speeds. So a spaceship is launched using spring A to relativistic speeds, it reaches spring B which it compresses and is thus relaunched when spring...

Is there an easy (by which I mean an algorithm polynomial in size of input) way to know whether in the multiplicative group of integers mod P (P is a prime), whether an element is a generator or not?

I'm not entirely clear on the concept of kolmogorov complexity. Does it mean that the a certain string is complex if there is no combinatorial (not sequential) circuit which outputs that string or does it mean that a certain string is complex if there is no program which can output that string...

Say you have two circuits C1 and C2, a circuit being a directed acyclic graph in which each node is a NAND gate or an input variable. C1 and C2 represent the same boolean function B. The only operations allowed on C1 and C2 are adding a gate node (with edges to some other nodes) or removing...

Simplex is exponential in the worst-case. Although there's Karmarkar's algorithm, it is for optimization of an objective function. Although it can be used for solving systems of linear inequalities, it takes n^3.5*L^2 time. I was wondering if there was a faster algorithm for giving a solution to...

Hi, Is there a polynomial time algorithm (polynomial time in terms of the number of input constraints and variables) to solve a system of linear inequalities or or indicate whether a solution for a system of linear inequalities exists or not? Thanks

How can I load a .py file in the python interactive shell for debugging?

I would also throw in a recommendation for Vim as an editor.

Thanks for the reply. I just need a true and false answer as to whether a path exists or not. Unfortunately the adjacency matrix trick won't work because the adjacency matrix itself is n^2 big (n being the number of nodes in the graph) making the whole operation atleast O(n^2).

Is there an algorithm which is O(1) or O(log n) (basically a very fast algorithm) which can tell whether there is a path from a node A to a node B in a graph? Thanks

Well there's galahad but it's in fortran http://galahad.rl.ac.uk/ You can use it in C/C++ code though I believe.Also there's Ipopt for nonlinear optimization written in C++. https://projects.coin-or.org/Ipopt You might also want to check out Numerical Recipes in C The book is available online...

4 courses per semester. We are allowed to take at most 5 courses per semester but very few do.