1. The problem: Explain Asymptotic Notation simply and clearly for a beginner in computer science. 2. Imagine you want to know how fast a computer program runs, but different computers have different speeds, so timing the program isn't always reliable. 3. Instead, we look at how the number of instructions that run depends on the size of the input, called $N$. 4. For example, a program might run $5N^2 + 3N + 2$ instructions for input size $N$. 5. To simplify, we drop constants and less important terms as $N$ gets very large, so $5N^2 + 3N + 2$ becomes approximately $N^2 + N$. 6. Since $N^2$ grows much faster than $N$ when $N$ is large (for example, at $N=1000$, $N^2 = 1,000,000$ but $N = 1000$), we focus only on the biggest term. 7. This is the idea behind Asymptotic Notation: describing how the runtime grows as input size grows, by keeping the most significant term and ignoring constants. 8. The common notations are: - Big Theta $\Theta(N^2)$ means the runtime is exactly proportional to $N^2$. - Big O $O(N^2)$ means the runtime grows at most as fast as $N^2$. - Big Omega $\Omega(N^2)$ means the runtime grows at least as fast as $N^2$. 9. For example, an algorithm that counts up to $N$ might execute around $2N$ to $5N+2$ operations, but since this grows proportionally to $N$, we say its runtime is $O(N)$. 10. Big O notation helps us focus on the growth trend of running time without worrying about exact counts or machine speed. Answer: Asymptotic Notation is a way to describe how an algorithm’s runtime grows with input size by focusing on the most important term and ignoring constants and smaller terms, helping us understand the efficiency of an algorithm regardless of hardware differences.