Foundational Thinking DPF Suite

The Suite Readme introduces available members and connected examples. The Reference explains their architecture and how to move between mathematical constructions, modeling and other contributions. Notational Engineering adds methods for making those contributions expressible, interpretable and usable together.

Larger questions need several patterns. Changing a combining rule connects a counterexample, retained information, an operation and a proof. Answering with incomplete model detail connects reduction, bounds, interpretation and further work. Developing a physical prediction links assumptions about an unknown physical law to a prediction, an observation that distinguishes alternatives, and revision when those assumptions change. Constructing an algorithm within available resources connects decomposition, reused subcomputations, search bounds and recovery of the requested answers. Carrying meaning through several expressions connects interpretation, transformation, translation loss and the intended change. These sequences and worked explanations show how the pattern contributions depend on one another.

Mathematical Thinking

The Mathematical Thinking publication contains twenty patterns and worked connections between their methods. Start with MP-FRAME when you have a working question but do not yet know which mathematics it needs. The Preface shows how to choose a representation, obtain and interpret a result, and revise the representation when the question changes. The individual bodies develop the mathematical constructions used along the way. This independently usable publication belongs to the Foundational Thinking DPF Suite. The Suite Reference gives working combinations and explains how these methods connect with FPF and Method Engineering.

Mathematical Modeling

The Mathematical Modeling publication contains fourteen general modeling methods and worked connections between them. Begin with the Readme introduction when the working question has no mathematical formulation. The methods cover formulation, inference, prediction repair, intervention effects, counterfactual comparisons, observation design, sequential decisions, reduction, surrogates and model coupling. Readme and Preface show how one result supplies the next operation, how a changed question returns to its affected construction, and when an adequate answer permits stopping.

Physical Thinking

The Physical Thinking publication contains ten patterns and worked connections between their methods. Start with a physical question for which you need an account, a prediction, an observation or a revised assumption. The methods help constrain unknown laws, choose the effects to retain, derive how a system changes, relate possible microscopic states to collective behavior, use physical similarity and analogues, establish physical limits, and construct measurements and tests. The Preface shows how physical, mathematical and computational contributions work together, and which contribution to revisit when the physical situation changes.

Computational Thinking

The Computational Thinking publication contains fourteen patterns for algorithmics within computer science. Its Readme follows connections for translating programs, obtaining answers within resource limits, and sharing calculations while keeping request effects correct. The methods help construct and revise algorithms, control computation cost and error, preserve meaning when translating a program, and make interacting computations produce the required result. The Preface’s worked example changes from finding one optimal solution to enumerating all of them. It shows which earlier pruning and reconstruction choices must change. Numerical computation is one application of these methods.

Notational Engineering

The Notational Engineering publication contains eight patterns for designing expressions and their use. Use the connected examples to follow a changed request through several representations, or keep a sequence usable when its reader or reference frame changes. The methods cover grouping and binding, interpretation, meaning-preserving transformation, translation losses, complementary representations, difficult reading operations, and temporal or embodied notation. The Preface follows a formula, graph and table through a changed request without overwriting independent observations.