Homeworks should be written up clearly and succinctly; you may lose points if your answers
are unclear or unnecessarily complicated.
This is an example of what we are looking for.
Question: In big-O notation, how many contiguous subsequences are there of a list of $n$ numbers?
Answer: There are $O(n)$ choices for the starting position of the subsequence
and $O(n)$ choices for the ending position.
Therefore, there are $O(n^2)$ possible contiguous subsequences.
Here, using words is precise enough and easy to read.
More Involved Question
Question: Suppose you flip a sequence of independent fair coins until you get heads,
and on each preceding tails flip, you roll a 6-sided fair dice.
What is the expected value of the sum of the die?
- Try to balance mathematical notation and words.
- Introduce notation only if you need to refer back to it later in an exact way and words aren't enough.
- If you introduce your own notation in the problem, define everything up front.
- When you make a statement, it should be clear whether it is assumed from the problem, or derived from a previous step, or something that you're trying to derive.
- Regardless of whether you use mathematical notation of words, be clear and precise.
- You can break down a solution using bullet points to make things more readable.