6.5 Recursion and Induction
Defining objects step by step and proving properties by following the same construction.
Tag
Patterns
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6.4 Decomposition and Composition
Breaking complex objects into simpler parts and building larger structures from controlled combinations.
6.3 Local-to-Global Principles
How mathematics studies small pieces first and then assembles them into statements about the whole.
6.2 Symmetry and Invariance
How transformations preserve structure and how invariants record what remains unchanged.
6.1 Duality
Understanding how reversing structure reveals parallel theories and results.
Chapter 6. Patterns Across Mathematics
Overview of recurring patterns such as duality, symmetry, local-to-global reasoning, decomposition, recursion, and induction.