Step 1: Understanding the Concept:
Mesityl oxide is a common name for the $\alpha, \beta$-unsaturated ketone formed by the aldol condensation of acetone.
Step 2: Formula Application:
Structure: $(CH_3)_2C=CH-COCH_3$.
Step 3: Explanation:
1. Number the chain from the carbonyl end: $C_1(H_3)-C_2(=O)-C_3(H)=C_4(CH_3)-C_5(H_3)$.
2. The double bond starts at $C_3$.
3. The ketone is at $C_2$.
4. A methyl branch is at $C_4$.
Name: 4-methylpent-3-en-2-one.
Step 4: Final Answer:
The IUPAC name is 4-methylpent-3-en-2-one.