Given these two methods:

METHOD math$1$:

$$ public int math$1($ int n $)\{$

$$ if $($n $<=1)\{$

$$return $1$;

$\}//$ if

else $\{$

$$ return $($ n $*2)+$ math$1($ n$-1)$;

$\}//$ else

$\}//$ math$1$

METHOD math$2$:

$$ public int math$2($ int n $)\{$

$$ if $($n $<=1)\{$

$$ return $1$;

$\}//$ if

$$ else $\{$

$$ return n $+$ math$1($ n $)*$ math$2($ n$/2)$;

$\}//$ else

$\}//$ math$2$

$($a$)$ Set up a recurrence relation for the running time of the method math$1$ as a function of n$.$ Solve your recurrence relation to specify THETA bound of math$1.$

$$

$($b$)$ Now set up a recurrence relation for the running time of the method math$2$ as a function of n$.$ Solve your recurrence relation to specify the Big$-$O bound of math$2.$

HINT: When doing this, the call to math$1$ can be replaced by the equation that you found when solving the recurrence relation for math$1$ in part $($a$)).$