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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.
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.
This would be a target space of meta-tools designed to explore a search space.
Alternately, 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.
In this context see information theory as the idea behind a domain as a minimal set of sources for mappings relative to the problem a specific instance of applying Occam's Razor.
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.
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