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Mathematical Thinking DPF

20 patterns · 486 sections · 0.5 MB

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Table of contents

Patterns · All sections
  1. MATH.16MATH.16 - Choose a Mathematical Construction from Its Required Maps (Universal Property)
  2. MATH.17MATH.17 - Construct Mathematical Spaces of Operations and Operations on Them
  3. MATH.1MATH.1 - Build a Mathematical Structure of Composable Paths
  4. MATH.2MATH.2 - Treat Objects as the Same While Preserving Operations (Quotient)
  5. MATH.5MATH.5 - Extend a Generator Assignment While Preserving Operations (Homomorphism)
  6. MATH.7MATH.7 - Transport a Mathematical Structure Through a Bijection
  7. MATH.18MATH.18 - Compare Mathematical Accounts through Interpretations
  8. MATH.19MATH.19 - Construct a Proof through Intermediate Claims
  9. MATH.4MATH.4 - Construct a Witness by Induction
  10. MATH.12MATH.12 - Extract a Construction from a Proof
  11. MATH.6MATH.6 - Refute a Mathematical Claim with a Countermodel
  12. MATH.20MATH.20 - Bound a Mathematical Unknown by Comparable Constructions
  13. MATH.11MATH.11 - Construct an Invariant from Transformation Rules
  14. MATH.13MATH.13 - Derive a Consequence from a Symmetry
  15. MATH.8MATH.8 - Generate a Solution Family by Symmetry
  16. MATH.9MATH.9 - Determine Whether and How a Choice Rule Can Respect Symmetry
  17. MATH.10MATH.10 - Improve a Mathematical Candidate or Derive a Necessary Condition by Admissible Variation
  18. MATH.21MATH.21 - Construct an Object through Convergent Approximations
  19. MATH.22MATH.22 - Change Axioms and Trace Their Consequences
  20. MATH.23MATH.23 - Develop a Conjecture by Changing a Construction

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