title: Renaming variables to solve recursion method
body: <p><a href="https://i.stack.imgur.com/LrPcJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/LrPcJ.png" alt="enter image description here"></a></p>
  
  <p>I know the idea of renaming the variables that is transforming the recurrence to one that you have seen before.</p>
  
  <p>I'm OK with slide until line 4 .. they renamed T(2^m) with S(m) >> this mean they made 2^m = m</p>
  
  <p>So S(m) should be :
  S(m)= 2T(m^(0.5)) + m </p>
  
  <p>also m i think we shouldn't leave m as it is, because it here mean 2^m but they in real are not </p>
  
  <p>Could any one explain this to me?</p>
  
  <p>And also how can i know which variables I should use to make it easy to me ?</p>