This is for my algorithm analysis class, and I needed help on the explanation of these. Will leave a thumbs up for good explanation.

What is the meaning of floor and ceiling and how to calculate them.

How is the Master Theorem used? What are the boundary conditions of the Master Theorem (b > 1, a >= 1, epsilon and Case III tests).

What are the three cases of the Master Theorem?

Give the definitions and meaning of lower bound, tightly bound and upper bound.

How do you prove for any given f(n) and g(n) that f(n) O(g(n)), f(n) Omega(g(n)),f(n) Theta(g(n)) and how that proof process is done.