MMP.Preface:1 - Problem frame - Make a mathematical question useful

You may know the relevant formulas and still be unable to build a model for the question in front of you. The candidate objects may be unclear. A recorded value may hide part of the observing procedure. A proposed decision may use information that arrives too late. A detailed model may become affordable only after removing something its answer depends on.

Mathematical Modeling develops methods for constructing and revising such mathematical questions. Its subject can be a physical situation, a working method, a computational process or another mathematical construction. The useful result may be a prediction, an explanation, an admissible arrangement, an instruction, a bound or a question that directs further inquiry. Start with what that result would let you understand or do.

This language belongs to the Foundational Thinking DPF Suite alongside Mathematical Thinking, Physical Thinking, Computational Thinking and Notational Engineering. Its three parts address formulation, inference and model revision, and changes that preserve a needed use. The Table of Contents identifies the methods available here; obtaining a contribution outside them still needs another source or collaborator.

The mathematical account and the subject supply different parts of the reasoning. A relation describing a material, an observing procedure or a permitted action needs its corresponding subject knowledge. A mathematical construction then helps express the relation and derive consequences. The answer returns to the original question with the conditions under which that interpretation holds. The First Principles Framework (FPF) develops this connection in B.5.FM and the C.29 family; the bodies here develop particular model-forming operations within it. Find a named FPF pattern by its full code in FPF-Spec.md and open its Problem frame and Solution. If GitHub cannot display the large file, use its View raw or Download raw file action, then search that copy.

The needed preparation depends on the operation. Finite arrangements can use sets, functions and elementary counting. Probabilistic recording needs conditional probability and sums or integrals. Evolution and reduction can require differential equations. Each body states its prerequisites and works small cases. When a collaborator or assisting agent supplies the mathematics, ask for the meaning of its inputs, its conditions and the result the next part of your work can use. You can ask for that explanation in the language of your work.

Begin with the Readme when the useful entry is unclear. Enter a body directly when its Problem frame matches the difficulty.