# Lecture 10

Asymptotic Analysis (Part III)

## Learning Outcomes

At the end of this lecture, you’ll be able to:

• Express the formal, mathematical definition of Big Oh.
• Use the mathematical definition of Big Oh to prove asymptotic running time of a given program.
• Express the mathematical definition of Big Omega.
• Use the mathematical definition of Big Omega to prove asymptotic running time of a given program.
• Recognize that big Oh and big Omega are not necessarily tight bounds.
• Recognize growth rate type (upper or lower bound) is different from worst case vs. best case analysis.
• Express the mathematical definition of Big Theta.
• Use the definition of Big Theta to show asymptotic running time of a given program.
• Enumerate various asymptotic notation used in this course.
• Explain what is meant by asymptotic complexity analysis of an algorithm.
• Contrast between time vs space complexity.
• Express the space requirements for a given code segment as a function of the input size in the worst case scenario.
• Elaborate on the benefits of using asymptotic notation and worst-case analysis to study computational complexity of algorithms.

## Lecture Plan

In this lecture, we'll cover the following lessons:

Lessons marked with ⚡ contain exercise/activity.