Put the woman at the center of “The Yellow Wallpaper” in gothic context. Consider, also, how this story, like those of other gothic writers, deals with the intricacies and the deterioration of the human mind.

There are two major parts to the question you have been asked. The first is:
1. How does "The Yellow Wallpaper" fit into the context of gothic literature, and what gothic tropes does it utilize?
The second is:
2. How does this story deal with mental deterioration on the part of this heroine, and how does this fit into the gothic genre?
Let us, then, begin with the first part of the question.
"The Yellow Wallpaper"was written in 1892. This puts it firmly into the category of the Gothic Revival, a group of fin de siecle gothic works which include novels like Wilde's The Picture of Dorian Gray and Stephenson's Dr. Jekyll and Mr. Hyde. Gothic works of this period drew upon many of the tropes of early nineteenth century gothic but had an increased fascination with the duality of human nature and, particularly, the fragility of the psyche.
Gothic elements which are used in The Yellow Wallpaper include:
- The house as a character, contributing to the tone and thrust of the story itself. The "colonial" house in which the protagonist of this story finds herself is essential to the plot: the house itself is what entraps our heroine and drives her mental deterioration;
- The tragic heroine, an archetype of early Gothic;
- The gothic hinterland, as conveyed in this story through the medium of the wallpaper itself. Gothic texts often use something to represent an in-between space, a place between what is real and what is not. Sometimes, this is conveyed through natural phenomena, such as fog, moors, or marshes. In this story, the wallpaper itself is the hinterland between the protagonist and what she fears, its patterns containing "things nobody knows."
- Gothic duality is a strong presence in this narrative. This idea of the dualism within ourselves is more particular to late gothic than to early gothic—see Jekyll and Hyde—but we can also see it in, for example, Mary Shelley's Frankenstein, with its tension between the doctor and his creation. In this story, the duality exists between the protagonist in the story and the many "creeping women" she imagines within the wallpaper; it is the difference between the confined life she must live and the many unfettered lives she imagines.
This leads us on to question 2: how this story deals with the intricacies of the deterioration of the human mind and how this can be set in gothic context. Our psychology has long been a fascination for gothic writers. In Frankenstein, Frankenstein's narcissism and desire to innovate drive him to create a being he cannot love or handle; in Dorian Gray, a young man's innocence is corrupted, which leads him down a path of vice to his ultimate doom; in Jekyll and Hyde, a man's base desires are sublimated so fiercely that they emerge as an entirely separate personality. In this story, the protagonist's desire to be free, so pushed against by her husband/doctor, drives her slowly mad. Her imprisonment in the house, which they see as for her own benefit, seems to her a punishment which cannot be escaped. Eventually, she seems to trespass into a madness which is, in itself, a form of freedom—the woman trapped behind the wallpaper is a manifestation of herself but, in her own way, is freer than the protagonist. In moving beyond the hinterland boundary presented by the wallpaper, the protagonist steps over the encumbrance her husband presents and enters an upside-down world of her own, on the other side of reality.