## How can i find most frequent number in Series December 1

Suppose we have a Series of numbers. Is there a way to find the most frequent number in that series using only basic operations like: max,min,+,*,\ etc? If not Doe's their is an approximation for this problem? To be accurate i don't seek for algorith

## M is finitely generated but $ker(f)\subset M$ is not. December 1

So I'm searching for an homomorphism of $A$-modules $f:M\mapsto N$ and some A-modules $M$, $N$ such both are finitely generated but Ker $f\subset M$ is not.Thanks.

## linear algebravector (sub)spaces December 1

I have two questions that I am struggling with.. 1) In a space of real functions we have a subspace defined by the set $V = \langle 1,x, cos x, sin x \rangle$ and its subspace defined by the set $W = \{f \in V: f(\pi) = 0\}$Find some basis of $W$.2)