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Please read this

April 26, 2012

We all begin gathering mathematical ideas in early childhood, when we discover that our two hands match, and later when we learn that other children also have grandmothers, so that this is an abstract relationship that a child might bear to an older person, and then that ‘uncle’ and ‘cousin’ are of this type also…

As the reader goes through it, this book [Conceptual Mathematics] may add some treasures to the collection, but that is not its goal. Rather we hope to show how to put the vast storehouse in order, and to find the appropriate tool when it is needed, so that the new ideas and methods collected and developed as one goes through life can find their appropriate places as well. There are in these pages general concepts that cut across the artificial boundaries dividing arithmetic, logic, algebra, geometry, calculus, etc. There will be little discussion about how to do specialized calculations, but much about the analysis that goes into deciding what calculations need to be done, and in what order. Anyone who has struggled with a genuine problem without having been taught an explicit method knows that this is the hardest part.

This book could not have been written fifty years ago; the precise language of concepts it uses was just being developed. True, the ideas we’ll study have been employed for thousands of years, but they first appeared only as dimly perceived analogies between subjects. Since 1945, when the notion of ‘category’ was first precisely formulated, these analogies have been sharpened and have become explicit ways in which one subject is transformed into another. It has been the good fortune of the authors to live in these interesting times, to see how the fundamental insight of categories has led to clearer understanding, thereby better organizing, and sometimes directing the growth of mathematical knowledge and its applications.

Preliminary versions of this book have been used by high school students and university classes, graduate seminars, and individual professionals in several countries. The response has reinforced our conviction that people of widely varying backgrounds can master these important ideas.

F. W. Lawvere & S. H. Schanuel (1997). Conceptual Mathematics: A First Introduction to Categories. Cambridge University Press, p. xiii.

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89 Comments
  1. Hi Raduyu,

    I´m glad to hear from you.

    Yours,

    Klaus Gauger

Trackbacks & Pingbacks

  1. Conceptual Mathematics informs cognitive science. « Conceptual Mathematics
  2. If kids taught « Conceptual Mathematics
  3. Exercises in Conceptual Mathematics (Prof. F. William Lawvere) « Conceptual Mathematics
  4. 1 apple + 1 apple = 2 apples « Conceptual Mathematics
  5. 3rd letter of SUM « Conceptual Mathematics
  6. Learning-with-students « Conceptual Mathematics
  7. Visualizing 1 x 2 « Conceptual Mathematics
  8. Words: General, Particular « Conceptual Mathematics
  9. Unbreak my world « Conceptual Mathematics
  10. A simple story (Math) « Conceptual Mathematics
  11. PART « Conceptual Mathematics
  12. Primal couple (+1) « Conceptual Mathematics
  13. Objects and Maps « Conceptual Mathematics
  14. EMPTY CATEGORY « Conceptual Mathematics
  15. Ideal India « Conceptual Mathematics
  16. Reflections of Reality « Conceptual Mathematics
  17. Exercising licentia poetica « Conceptual Mathematics
  18. Grazie così tanto Mme. Fatima Fenaroli! « Conceptual Mathematics
  19. The Cat in the Hat « Conceptual Mathematics
  20. The Way: Philosophical Algebra « Conceptual Mathematics
  21. Capitalism is for DUMMIES! « Conceptual Mathematics
  22. SUM « Conceptual Mathematics
  23. On choosing from a menu « Conceptual Mathematics
  24. Evil incarnate « Conceptual Mathematics
  25. A debilitating desire to describe « Conceptual Mathematics
  26. Place-value notation « Conceptual Mathematics
  27. Resisting representation :-) « Conceptual Mathematics
  28. Ménage à trois « Conceptual Mathematics
  29. Voices-sans-volume control « Conceptual Mathematics
  30. Is a diagram a map? « Conceptual Mathematics
  31. Tearing pictures « Conceptual Mathematics
  32. Science of Knowing (Cognitive Science) « Conceptual Mathematics
  33. Reinventing the wheel « Conceptual Mathematics
  34. Dr. No & Yes Boss « Conceptual Mathematics
  35. second coming « Conceptual Mathematics
  36. co-trivial ancient concepts « Conceptual Mathematics
  37. somniloquism « Conceptual Mathematics
  38. Please read this | Simply Simplistic Complexities
  39. Kids’ stuff « Conceptual Mathematics
  40. Born again truther « Conceptual Mathematics
  41. Parenting and Geometry-given laws « Conceptual Mathematics
  42. Defining INTERPRETATION « Conceptual Mathematics
  43. How to copy « Conceptual Mathematics
  44. Step dance « Conceptual Mathematics
  45. Method Mathematics: I. Describing IDEMPOTENCE « Conceptual Mathematics
  46. Children and [their] learning « Conceptual Mathematics
  47. A, B, C of math « Conceptual Mathematics
  48. TRANSLATION and MEANING « Conceptual Mathematics
  49. Climbing a ladder called « Conceptual Mathematics
  50. Initial property (aka left identity law) « Conceptual Mathematics
  51. Happy Birthday Professor F. William Lawvere « Conceptual Mathematics
  52. Disturbingly delightful « Conceptual Mathematics
  53. 1, 2, 3… « Conceptual Mathematics
  54. Prove 1 + 1 = 2 | Conceptual Mathematics
  55. Truth about 1 | Conceptual Mathematics
  56. Parts of a map | Conceptual Mathematics
  57. Pathological Liars’ Paradise (no TRUTH to tell ;) | Conceptual Mathematics
  58. Unscripted love life (2 after 1 :D | Conceptual Mathematics
  59. Schrödinger’s ant | Conceptual Mathematics
  60. same abstract form | Conceptual Mathematics
  61. A machine with two switches | Conceptual Mathematics
  62. How to model a calculator? | Conceptual Mathematics
  63. How to catch Snowdens (on finding equalizers) | Conceptual Mathematics
  64. CONSCIOUS: A sense for seeing the visible | Conceptual Mathematics
  65. Get the heavens into your head ;) | Conceptual Mathematics
  66. Generic and archetypal objects (abstract nonsense?) | Conceptual Mathematics
  67. Defining Test-Objects | Conceptual Mathematics
  68. INTERPRETATION and Conscious Interpretations | Conceptual Mathematics
  69. Submit AND Face the Wrath | Conceptual Mathematics
  70. 1 + 2 + 3 (along with everything else!) | Conceptual Mathematics
  71. What’s so NATURAL (about Natural Transformation?) | Conceptual Mathematics
  72. — — are everywhere! | Conceptual Mathematics
  73. Forgetful functors | Conceptual Mathematics
  74. Life after death | Conceptual Mathematics
  75. Structure and Natural transformations | Conceptual Mathematics
  76. Structure and Structure-Preserving Maps | Conceptual Mathematics
  77. HOW MINDS THEORIZE: I. Opposites | Conceptual Mathematics
  78. 2 ways of Knowing | Conceptual Mathematics
  79. Adjoint functor (left or right?) | Conceptual Mathematics
  80. Take 1: ACTION | Conceptual Mathematics
  81. Category of Citizens | Conceptual Mathematics
  82. Parenting and Geometry-given laws | Conceptual Mathematics
  83. Pieces (coequalizer) | Conceptual Mathematics
  84. Ramayana in Arrow Language ;) | Conceptual Mathematics
  85. Antidote to racism (Codiscrete functor) | Conceptual Mathematics

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