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A problem domain is the area of expertise or application that needs to be examined to solve a problem. A problem domain is simply looking at only the topics you are interested in, and excluding everything else. For example, if you were developing a system trying to measure good practice in medicine, you wouldn't include carpet drawings at hospitals in your problem domain. In this example the domain refers to relevant topics solely within your interest: medicine.
This points to a limitation of an overly specific, or overly bounded, problem domain. An individual may think they are interested in medicine and not interior design, but a better solution exists outside of the problem domain as it was initially conceived. For example, when IDEO researchers noticed that patients in hospitals spent huge amount of time staring at acoustic ceiling tiles, which "became a symbol of the overall ambiance: a mix of boredom and anxiety from feeling lost, uninformed, and out of control." The research team then "started a series of deliberate discussions about the findings, and those led us to talk about improving the overall approach to ER logistics, so patients were treated less like objects to be positioned and allocated, and more like people in stress and pain." Although not originally within the bounded problem domain of measuring good practices in medicine, this non-intuitive finding could then be added to the domain space. Arational, problem seeking and non-linear approaches to research such as art, design, creative work and post-normal science may help internalize previously excluded areas of interest within a problem domain.
In mathematics, the term defines a domain where the parameters defining the boundaries of the domain and sufficient mappings into a set of ranges including itself are not well enough understood to provide a systematic description of the domain.
Alternatively, a domain specifically defined by some extrinsic problem-system to differentiate it from the set of all domains.
See: domain theory for the mathematical discipline related to these issues.
Having defined a specific problem domain with sufficient parameters and mappings for consultation, a systematic approach to the solution can be developed in accordance with the Parker Rule. Using this rule, it is implied that any topics not directly associated with the initial problem domain, and its immediate mappings should not be included within the problem domain, but should be considered as parameters of the secondary mappings of any associated domains.