Gatsby presents the best example of determination in the novel. He is set on his course and refuses to deviate from it regardless of what may stand in his way.
Gatsby intends to marry Daisy and fulfill his romantic vision with her as his wife. He plots and plans and agonizes over this goal, not dissuaded by the fact that Daisy is married and has a child. His vision of attaining Daisy drives his whole life and becomes his obsession.
He had thrown himself into it with a creative passion...
Gatsby's determination is also seen in the degree of his success. He achieved wealth after starting with nothing.
His boldness and determination are the qualities that got him rich. It is his determination that, in fact, gives him his name.
Perhaps the best example of Gatsby's determination comes in his decision to stand outside Daisy's house the night Myrtle is killed. At this point, Nick sees clearly that Gatsby cannot convince Daisy to leave Tom. Gatsby, however, refuses to acknowledge this.
Even after what happened, he insists on standing vigil outside her window because he will not give up on his dream.