Introduction:
In Act 3, Scene 1 of William Shakespeare's play "The Tempest," Miranda expresses her desire to serve Ferdinand even if he does not marry her. This scene takes place on the island where Miranda and her father, Prospero, have been living in exile. Ferdinand, the Prince of Naples, has been separated from his father's ship and has been brought to the island by Prospero's magic. Miranda and Ferdinand have fallen in love at first sight and are engaged in a conversation about their feelings for each other.

Reasons why Miranda wants to serve Ferdinand:

1. Love and attraction:
Miranda is deeply attracted to Ferdinand, and their encounter has sparked an instant connection between them. She is captivated by his appearance and noble demeanor, which is evident when she refers to him as "the best of men." Miranda's love for Ferdinand is genuine and she desires to be in his presence, even if it means serving him in a non-marital capacity.

2. Desire to be useful:
Miranda has spent most of her life on the isolated island with only her father and the spirit Ariel for company. Meeting Ferdinand presents an opportunity for her to interact with someone new and engage in a different kind of relationship. By offering to serve Ferdinand, Miranda demonstrates her willingness to contribute and be of value to him, showcasing her selfless nature and desire to be useful.

3. Cultural and societal expectations:
As a young woman living in the 17th century, Miranda would have been raised with certain cultural and societal expectations. Serving others, especially those of higher social standing, was considered a duty for women of her time. Miranda's offer to serve Ferdinand may stem from her understanding of these expectations and a desire to fulfill her role as a woman in society.

4. Self-sacrifice:
Miranda's offer to serve Ferdinand even if he does not marry her can be seen as an act of self-sacrifice. She is willing to put aside her own desires and personal happiness for the sake of Ferdinand's well-being. This selflessness reflects Miranda's compassionate and caring nature, as she prioritizes the needs of others above her own.

Conclusion:
Miranda's desire to serve Ferdinand, even if he does not marry her, can be attributed to her love and attraction towards him, her desire to be useful, cultural and societal expectations, and her willingness to make self-sacrifices for the well-being of others. This scene showcases Miranda's strong character and her willingness to go against societal norms in order to express her feelings and contribute to the happiness of the man she loves.