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70 questions · full solutions

Math Foundations

The toolbox underneath everything: limits, series, linear algebra, and quick Taylor estimates, each tied to the trading context where it earns its keep.

  1. 01Price the PerpetuityEasy
  2. 02Where e Comes FromEasy
  3. 03Eigenvectors as Risk AxesMedium · Private
  4. 04The Collapsing SumEasy
  5. 05Trend Regression BookkeepingEasy
  6. 06A Million Days of RecordsHard · Private
  7. 07The Series That Almost DivergesHard · Private
  8. 08Weight Each Coin Flip by Its DateMedium · Private
  9. 09Curvature in DisguiseMedium · Private
  10. 10Zero to the Zero, CarefullyMedium · Private
  11. 11A Coin-Flip Limit Hiding the CLTMedium · Private
  12. 12The Riskiest CoinEasy
  13. 13Trade Fast, Trade SlowEasy
  14. 14An Improper Integral with a Clean AnswerMedium · Private
  15. 15The Square That Becomes a CircleHard · Private
  16. 16Three Estimates, With Error Bars in Your HeadMedium · Private
  17. 17One Newton Step Toward Root TwoMedium · Private
  18. 18Two Baskets, Two UnknownsMedium · Private
  19. 19What a Determinant MeasuresEasy
  20. 20When Is It a Real Covariance Matrix?Medium · Private
  21. 21The Tenth Fibonacci, Three WaysHard · Private
  22. 22Regression Is a ShadowHard · Private
  23. 23The Missing EigenvalueMedium · Private
  24. 24The Oldest Algorithm Still in ProductionEasy
  25. 25The Last Digit of a MonsterEasy
  26. 26Fermat's ShortcutMedium · Private
  27. 27Fifty Odd Numbers, One SquareEasy
  28. 28Why the Square of the Average LosesMedium · Private
  29. 29Where the Recursion SettlesMedium · Private
  30. 30Exactly How Long to DoubleMedium · Private
  31. 31The Base That FitsEasy
  32. 32Roots You Never Solve ForEasy
  33. 33Cut the CircleMedium · Private
  34. 34The Self-Root ContestMedium · Private
  35. 35L'Hopital Refuses to AnswerMedium · Private
  36. 36The Biggest Box in the CornerMedium · Private
  37. 37Integrate the Geometric, Win a LogMedium · Private
  38. 38The Product That CollapsesMedium · Private
  39. 39Two Series, One Letter ApartMedium · Private
  40. 40An Arithmetic Ladder on a Geometric SlideMedium · Private
  41. 41Ten Steps of the Same MapHard · Private
  42. 42The Shadow on a PlaneHard · Private
  43. 43The Spread ChainHard · Private
  44. 44Factor the RiskHard · Private
  45. 45A Determinant You Don't ExpandHard · Private
  46. 46The Correlation You Don't Get to ChooseHard · Private
  47. 47The Determinant Sees the BlocksHard · Private
  48. 48Closest Point, Shadow Price IncludedHard · Private
  49. 49Slice the NotionalHard · Private
  50. 50Four Decimal Places of eHard · Private
  51. 51Nearest Point on the CurveHard · Private
  52. 52The Gaussian's Second Moment, From ScratchHard · Private
  53. 53The Substitution That Pays TwiceHard · Private
  54. 54Two Decays, One LogarithmHard · Private
  55. 55Square Weights on Halving CoinsHard · Private
  56. 56Two Edges, Two VerdictsMedium · Private
  57. 57The S-Curve ClockMedium · Private
  58. 58Collapse by FactorialMedium · Private
  59. 59Three Roots You Never MeetMedium · Private
  60. 60Eight Turns Close the CircleHard · Private
  61. 61Discs Before DeterminantsHard · Private
  62. 62Sum Every EchoHard · Private
  63. 63The Cheapest Split of a BudgetHard · Private
  64. 64The Law That Forces the ExponentialHard · Private
  65. 65A Thousand Doublings, Two DigitsHard · Private
  66. 66Climbing Toward ThreeHard · Private
  67. 67Two Solvers, One Golden TargetHard · Private
  68. 68Double the Index, Not the WorkHard · Private
  69. 69How Wide Is One Hundred Factorial?Hard · Private
  70. 70Basel, Odds OnlyHard · Private