1. Asymptotics & Stirling’s Approximation
Mathematics for Computer Science MIT 6.042J/18.062J
Asymptotics & Stirling’s Approximation
Copyright © Albert Meyer, 2002.
Prof. Albert Meyer & Dr. Radhika Nagpal

2. Factorial defines a product:
Stirling’s Formula
Factorial defines a product:
Turn product into a sum taking logs:

3. bound by integral method
Stirling’s Formula
bound by integral method …

4. Integral method to bound ln(n!)
Stirling’s Formula
Integral method to bound ln(n!)

5. Stirling’s Formula
n!  (n/e)n n!
(n/e)n = 0
lim
n

6. Asymptotic Notation
f(n) = O(g(n))
g(x) +c
f(x) n0

7. Defs 7.1,7.2,7.3.7.7 from ln6 on separate slides