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Mathematical Thinking DPF

20 patterns · 486 sections · 0.5 MB

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Patterns · All sections
  1. Mathematical Thinking DPF
  2. Table of Contents
  3. Public units
  4. Part A - Choose and relate constructions
  5. Part B - Construct and criticize arguments
  6. Part C - Change a construction and develop its theory
  7. Mathematical Thinking - Readme
  8. Practical entries
  9. MP-FRAME - Find the mathematical contribution in an unfamiliar problem
  10. MP-COMBINE-RESULTS - Change a rule so that separately obtained results can be combined
  11. Worked connection for MP-COMBINE-RESULTS
  12. Mathematical Thinking - Preface
  13. MATH.Preface:1 - Problem frame - Construct mathematics for the question
  14. MATH.Preface:2 - Problem and forces - Make a usable construction
  15. MATH.Preface:3 - Solution - Connect constructions through what they supply
  16. MATH.Preface:3.1 - Form objects, operations and representations
  17. MATH.Preface:3.2 - Obtain an argument and the object it supports
  18. MATH.Preface:3.3 - Change a construction and develop its theory
  19. MATH.Preface:3.4 - Return a construction to further work
  20. MATH.Preface:3.5 - Use this contribution within the wider repertoire
  21. MATH.Preface:3.6 - Constituent actions in ongoing work
  22. MATH.Preface:4 - Worked use - Choose a representation after the question changes
  23. MATH.Preface:5 - Worked use - Construct a choice after finding an obstruction
  24. MATH.Preface:6 - Checks and common failures - Preserve what the next construction needs
  25. MATH.Preface:7 - Consequences, biases and limits
  26. MATH.Preface:8 - Architectural Rationale - Organize by reusable constructions
  27. MATH.Preface:9 - Source use and currentness
  28. MATH.Preface:10 - Relations to further reasoning and work
  29. MATH.Preface:End
  30. Part A - Choose and relate constructions
  31. MATH.16MATH.16 - Choose a Mathematical Construction from Its Required Maps (Universal Property)
  32. MATH.16:1 - Problem frame
  33. MATH.16:2 - Problem
  34. MATH.16:3 - Forces
  35. MATH.16:4 - Solution
  36. MATH.16:4.1 - Express the needed use as maps and equations
  37. MATH.16:4.2 - State the universal property before choosing an encoding
  38. MATH.16:4.3 - Construct an object and establish the property
  39. MATH.16:4.4 - Derive the next map, comparison or operation
  40. MATH.16:4.5 - Use the result and return to a changed requirement
  41. MATH.16:5 - Archetypal Grounding
  42. MATH.16:5.1 - Two classifications, then one shared integer
  43. MATH.16:5.2 - Process both results or either result
  44. MATH.16:5.3 - Two views of one quantity
  45. MATH.16:5.4 - Construct an object that can itself be applied
  46. MATH.16:6 - Bias-Annotation
  47. MATH.16:7 - Conformance Checklist
  48. MATH.16:8 - Common Anti-Patterns and How to Avoid Them
  49. MATH.16:9 - Consequences
  50. MATH.16:10 - Architectural Rationale
  51. MATH.16:11 - SoTA-Echoing
  52. MATH.16:12 - Relations
  53. MATH.16:End
  54. MATH.17MATH.17 - Construct Mathematical Spaces of Operations and Operations on Them
  55. MATH.17:1 - Problem frame
  56. MATH.17:2 - Problem
  57. MATH.17:3 - Forces
  58. MATH.17:4 - Solution
  59. MATH.17:4.1 - Specify the operations and the question about them
  60. MATH.17:4.2 - Construct the admissible collections
  61. MATH.17:4.3 - Establish the composition that the work needs
  62. MATH.17:4.4 - Construct an operation on operations and its law
  63. MATH.17:4.5 - Use the construction to change or compare rules
  64. MATH.17:5 - Archetypal Grounding
  65. MATH.17:5.1 - Individually permitted changes and a permitted whole
  66. MATH.17:5.2 - Lift a rule, then change how repetition is distributed
  67. MATH.17:5.3 - An operator whose useful law has another form
  68. MATH.17:5.4 - Change a function while preserving its increments
  69. MATH.17:6 - Bias-Annotation
  70. MATH.17:7 - Conformance Checklist
  71. MATH.17:8 - Common Anti-Patterns and How to Avoid Them
  72. MATH.17:9 - Consequences
  73. MATH.17:10 - Architectural Rationale
  74. MATH.17:11 - SoTA-Echoing
  75. MATH.17:12 - Relations
  76. MATH.17:End
  77. MATH.1MATH.1 - Build a Mathematical Structure of Composable Paths
  78. MATH.1:1 - Problem frame
  79. MATH.1:2 - Problem
  80. MATH.1:3 - Forces
  81. MATH.1:4 - Solution
  82. MATH.1:4.1 - Choose objects and generating arrows
  83. MATH.1:4.2 - Form finite paths
  84. MATH.1:4.3 - Define composition by concatenation
  85. MATH.1:4.4 - Use the path at the needed level
  86. MATH.1:5 - Archetypal Grounding
  87. MATH.1:5.1 - A continuation that needs a permission
  88. MATH.1:5.2 - Natural numbers from repetition
  89. MATH.1:5.3 - Order matters under interpretation
  90. MATH.1:5.4 - Keep the intermediate states of interacting updates
  91. MATH.1:6 - Bias-Annotation
  92. MATH.1:7 - Conformance Checklist
  93. MATH.1:8 - Common Anti-Patterns and How to Avoid Them
  94. MATH.1:9 - Consequences
  95. MATH.1:10 - Architectural Rationale
  96. MATH.1:11 - SoTA-Echoing
  97. MATH.1:12 - Relations
  98. MATH.1:End
  99. MATH.2MATH.2 - Treat Objects as the Same While Preserving Operations (Quotient)
  100. MATH.2:1 - Problem frame

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