Arithmetic and Geometry Math Foundations

Arithmetic and Geometry Math Foundations

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The problem with `functions' | Arithmetic and Geometry Math Foundations 42b | N J Wildberger

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The problem with `functions' | Arithmetic and Geometry Math Foundations 42b | N J Wildberger

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Arithmetic and Geometry Math Foundations

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  1. 1 What is a number? | Arithmetic and Geometry Math Foundations 1 | N J Wildberger
  2. 2 Arithmetic with numbers | Arithmetic and Geometry Math Foundations 2 | N J Wildberger
  3. 3 Laws of Arithmetic | Arithmetic and Geometry Math Foundations 3 | N J Wildberger
  4. 4 Subtraction and Division | Arithmetic and Geometry Math Foundations 4 | N J Wildberger
  5. 5 Arithmetic and maths education | Arithmetic and Geometry Math Foundations 5 | N J Wildberger
  6. 6 The Hindu-Arabic number system | Arithmetic and Geometry Math Foundations 6 | N J Wildberger
  7. 7 Arithmetic with Hindu-Arabic numbers | Arithmetic and Geometry Math Foundations 7 | N J Wildberger
  8. 8 Division | Arithmetic and Geometry Math Foundations 8 | N J Wildberger
  9. 9 Fractions | Arithmetic and Geometry Math Foundations 9 | N J Wildberger
  10. 10 Arithmetic with fractions | Arithmetic and Geometry Math Foundations 10 | N J Wildberger
  11. 11 Laws of arithmetic for fractions | Arithmetic and Geometry Math Foundations 11 | N J Wildberger
  12. 12 Introducing the integers | Arithmetic and Geometry Math Foundations 12 | N J Wildberger
  13. 13 Rational numbers | Arithmetic and Geometry Math Foundations 13 | N J Wildberger
  14. 14 Rational numbers and Ford Circles | Arithmetic and Geometry Math Foundations 14 | N J Wildberger
  15. 15 Why infinite sets don't exist | Arithmetic and Geometry Math Foundations 16 | N J Wildberger
  16. 16 Extremely big numbers | Arithmetic and Geometry Math Foundations 17 | N J Wildberger
  17. 17 Primary school maths education | Arithmetic and Geometry Math Foundations 15 | N J Wildberger
  18. 18 Geometry | Arithmetic and Geometry Math Foundations 18 | N J Wildberger
  19. 19 Euclid's Elements | Arithmetic and Geometry Math Foundations 19 | N J Wildberger
  20. 20 Euclid's Books VI--XIII | Arithmetic and Geometry Math Foundations 21 | N J Wildberger
  21. 21 Euclid and proportions | Arithmetic and Geometry Math Foundations 20 | N J Wildberger
  22. 22 Difficulties with Euclid | Arithmetic and Geometry Math Foundations 22 | N J Wildberger
  23. 23 The basic framework for geometry (I) | Arithmetic and Geometry Math Foundations 23 | N J Wildberger
  24. 24 The basic framework for geometry (II) | Arithmetic and Geometry Math Foundations 24 | N J Wildberger
  25. 25 The basic framework for geometry (III) | Arithmetic + Geometry Math Foundations 25 | N J Wildberger
  26. 26 The basic framework for geometry (IV) | Arithmetic and Geometry Math Foundations 26 | N J Wildberger
  27. 27 Trigonometry with rational numbers | Arithmetic and Geometry Math Foundations 27 | N J Wildberger
  28. 28 What exactly is a circle? | Arithmetic and Geometry Math Foundations 28 | N J Wildberger
  29. 29 Parametrizing circles | Arithmetic and Geometry Math Foundations 29 | N J Wildberger
  30. 30 What exactly is a vector? | Arithmetic and Geometry Math Foundations 30 | N J Wildberger
  31. 31 Parallelograms and affine combinations | Arithmetic + Geometry Math Foundations 31 | N J Wildberger
  32. 32 Geometry in primary school | Arithmetic and Geometry Math Foundations 32 | N J Wildberger
  33. 33 What exactly is an area? | Arithmetic and Geometry Math Foundations 33 | N J Wildberger
  34. 34 Areas of polygons | Arithmetic and Geometry Math Foundations 34 | N J Wildberger
  35. 35 Translations, rotations and reflections (I) | Arithmetic and Geometry Math Foundations 35
  36. 36 Translations, rotations and reflections (II) | Arithmetic and Geometry Math Foundations 36
  37. 37 Translations, rotations and reflections (III) | Arithmetic and Geometry Math Foundations 37
  38. 38 Why angles don't really work (I) | Arithmetic and Geometry Math Foundations 38 | N J Wildberger
  39. 39 Why angles don't really work (II) | Arithmetic and Geometry Math Foundations 39 | N J Wildberger
  40. 40 Correctness in geometrical problem solving | Arithmetic and Geometry Math Foundations 40
  41. 41 Why angles don't really work (III) | Arithmetic and Geometry Math Foundations 41 | N J Wildberger
  42. 42 The problem with `functions' | Arithmetic and Geometry Math Foundations 42b | N J Wildberger
  43. 43 Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43
  44. 44 Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
  45. 45 Quadrilaterals, quadrangles and n-gons | Arithmetic + Geometry Math Foundations 45 | N J Wildberger
  46. 46 Introduction to Algebra | Arithmetic and Geometry Math Foundations 46 | N J Wildberger
  47. 47 Baby Algebra | Arithmetic and Geometry Math Foundations 47 | N J Wildberger
  48. 48 Solving a quadratic equation | Arithmetic and Geometry Math Foundations 48a | N J Wildberger
  49. 49 Solving a quadratic equation 48b | Arithmetic and Geometry Math Foundations | N J Wildberger
  50. 50 How to find a square root | Arithmetic and Geometry Math Foundations 49 | N J Wildberger
  51. 51 Algebra and number patterns | Arithmetic and Geometry Math Foundations 50 | N J Wildberger
  52. 52 More patterns with algebra | Arithmetic and Geometry Math Foundations 51 | N J Wildberger
  53. 53 Leonhard Euler and Pentagonal numbers | Arithmetic and Geometry Math Foundations 52 | N J Wildberger
  54. 54 Algebraic identities | Arithmetic and Geometry Math Foundations 53 | N J Wildberger
  55. 55 The Binomial theorem | Arithmetic and Geometry Math Foundations 54 | N J Wildberger
  56. 56 Binomial coefficients and related functions | Arithmetic and Geometry Math Foundations 55
  57. 57 The Trinomial theorem | Arithmetic and Geometry Math Foundations 56 | N J Wildberger
  58. 58 Polynomials and polynumbers | Arithmetic and Geometry Math Foundations 57 | N J Wildberger
  59. 59 Arithmetic with positive polynumbers | Arithmetic and Geometry Math Foundations 58 | N J Wildberger
  60. 60 More arithmetic with polynumbers | Arithmetic and Geometry Math Foundations 59 | N J Wildberger
  61. 61 What exactly is a polynomial? | Arithmetic and Geometry Math Foundations 60 | N J Wildberger
  62. 62 Factoring polynomials and polynumbers | Arithmetic and Geometry Math Foundations 61 | N J Wildberger
  63. 63 Arithmetic with integral polynumbers | Arithmetic and Geometry Math Foundations 62 | N J Wildberger
  64. 64 The Factor theorem and polynumber evaluation 63 | Arithmetic and Geometry Math Foundations
  65. 65 The Division algorithm for polynumbers | Arithmetic + Geometry Math Foundations 64 | N J Wildberger
  66. 66 Decimal numbers | Arithmetic and Geometry Math Foundations 66 | N J Wildberger
  67. 67 Row and column polynumbers | Arithmetic and Geometry Math Foundations 65 | N J Wildberger
  68. 68 Laurent polynumbers (the New Years Day lecture) | Arithmetic and Geometry Math Foundations 68
  69. 69 Visualizing decimal numbers and their arithmetic 67 | Arithmetic and Geometry Math Foundations
  70. 70 Translating polynumbers and the Derivative | Arithmetic and Geometry Math Foundations 69
  71. 71 Calculus with integral polynumbers | Arithmetic and Geometry Math Foundations 70 | N J Wildberger
  72. 72 Tangent lines and conics of polynumbers | Arithmetic + Geometry Math Foundations 71 | N J Wildberger
  73. 73 Graphing polynomials | Arithmetic and Geometry Math Foundations 72 | N J Wildberger
  74. 74 Lines and parabolas I | Arithmetic and Geometry Math Foundations 73 | N J Wildberger
  75. 75 Lines and parabolas II | Arithmetic and Geometry Math Foundations 74 | N J Wildberger
  76. 76 Cubics and the prettiest theorem in calculus | Arithmetic and Geometry Math Foundations 75
  77. 77 Object-oriented versus expression-oriented mathematics | Arithmetic and Geometry Math Foundations 77
  78. 78 An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger
  79. 79 Inconvenient truths about sqrt(2) | Real numbers and limits Math Foundations 80 | N J Wildberger
  80. 80 Measurement, approximation and interval arithmetic (I) | Real numbers and limits Math Foundations 81
  81. 81 Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82
  82. 82 Newton's method for finding zeroes | Real numbers and limits Math Foundations 83 | N J Wildberger
  83. 83 Newton's method for approximating cube roots | Real numbers and limits Math Foundations 84
  84. 84 Solving quadratics and cubics approximately | Real numbers and limits Math Foundations 85
  85. 85 Newton's method and algebraic curves | Real numbers and limits Math Foundations 86 | N J Wildberger
  86. 86 Logical weakness in modern pure mathematics | Real numbers and limits Math Foundations 87
  87. 87 The decline of rigour in modern mathematics | Real numbers and limits Math Foundations 88
  88. 88 Fractions and repeating decimals | Real numbers and limits Math Foundations 89 | N J Wildberger
  89. 89 Fractions and p-adic numbers | Real numbers and limits Math Foundations 90 | N J Wildberger
  90. 90 Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
  91. 91 Difficulties with real numbers as infinite decimals (II) | Real numbers + limits Math Foundations 92
  92. 92 The magic and mystery of "pi" | Real numbers and limits Math Foundations 93 | N J Wildberger
  93. 93 Problems with limits and Cauchy sequences | Real numbers and limits Math Foundations 94
  94. 94 The deep structure of the rational numbers | Real numbers and limits Math Foundations 95
  95. 95 Fractions and the Stern-Brocot tree | Real numbers and limits Math Foundations 96 | N J Wildberger
  96. 96 The Stern-Brocot tree, matrices and wedges | Real numbers and limits Math Foundations 97
  97. 97 What exactly is a sequence? | Real numbers and limits Math Foundations 98 | N J Wildberger
  98. 98 "Infinite sequences": what are they? | Real numbers and limits Math Foundations 99 | N J Wildberger
  99. 99 Slouching towards infinity: building up on-sequences | Real numbers and limits Math Foundations 100
  100. 100 Challenges with higher on-sequences | Real numbers and limits Math Foundations 101 | N J Wildberger
  101. 101 Limits and rational poly on-sequences | Real numbers + limits Math Foundations 102 | N J Wildberger
  102. 102 Extending arithmetic to infinity! | Real numbers and limits Math Foundations 103 | N J Wildberger
  103. 103 Rational number arithmetic with infinity and more | Real numbers and limits Math Foundations 104
  104. 104 The extended rational numbers in practice | Real numbers and limits Math Foundations 105
  105. 105 What exactly is a limit?? | Real numbers and limits Math Foundations 106 | N J Wildberger
  106. 106 Inequalities and more limits | Real numbers and limits Math Foundations 107 | N J Wildberger
  107. 107 Limits to Infinity | Real numbers and limits Math Foundations 108 | N J Wildberger
  108. 108 Logical difficulties with the modern theory of limits (I)|Real numbers + limits Math Foundations 109
  109. 109 Logical difficulties with the modern theory of limits(II)|Real numbers + limits Math Foundations 110
  110. 110 Real numbers and Cauchy sequences of rationals(I) | Real numbers and limits Math Foundations 111
  111. 111 Real numbers and Cauchy sequences of rationals (II) | Real numbers and limits Math Foundations 112
  112. 112 Real numbers and Cauchy sequences of rationals (III) | Real numbers and limits Math Foundations 113
  113. 113 Real numbers as Cauchy sequences don't work! | Real numbers and limits Math Foundations 114
  114. 114 The mostly absent theory of real numbers|Real numbers + limits Math Foundations 115 | N J Wildberger
  115. 115 Difficulties with Dedekind cuts | Real numbers and limits Math Foundations 116 | N J Wildberger
  116. 116 The continuum, Zeno's paradox and the price we pay for coordinates 117 | Math Foundations
  117. 117 Real fish, real numbers, real jobs | Real numbers and limits Math Foundations 118 | N J Wildberger
  118. 118 Mathematics without real numbers | Real numbers and limits Math Foundations 119 | N J Wildberger
  119. 119 Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120
  120. 120 Axiomatics and the least upper bound property (I1) | Real numbers and limits Math Foundations 121
  121. 121 Mathematical space and a basic duality in geometry | Rational Geometry Math Foundations 122
  122. 122 Affine one-dimensional geometry and the Triple Quad Formula | Rational Geometry Math Foundations 123
  123. 123 Heron's formula, Archimedes' function, and the TQF | Rational Geometry Math Foundations 124
  124. 124 Brahmagupta's formula and the Quadruple Quad Formula (I) | Rational Geometry Math Foundations 125
  125. 125 Brahmagupta's formula and the Quadruple Quad Formula (II) | Rational Geometry Math Foundations 126
  126. 126 The Cyclic quadrilateral quadrea theorem | Rational Geometry Math Foundations 127a | NJ Wildberger
  127. 127 The Cyclic quadrilateral quadrea theorem (cont.) | Rational Geometry Math Foundations 127b
  128. 128 Robbins' formulas, the Bellows conjecture + polyhedra volumes|Rational Geometry Math Foundations 128
  129. 129 The projective line, circles + a proof of the CQQ theorem| Rational Geometry Math Foundations 129
  130. 130 The projective line, circles and the CQQ theorem (II) | Rational Geometry Math Foundations 130
  131. 131 Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
  132. 132 The Bretschneider von Staudt formula for a quadrilateral | Rational Geometry Math Foundations 132
  133. 133 Higher dimensions and the roles of length, area and volume | Rational Geometry Math Foundations 133
  134. 134 Absolute versus relative measurements in geometry | Rational Geometry Math Foundations 134
  135. 135 NJ's pizza model for organizing geometry | Rational Geometry Math Foundations 135 | NJ Wildberger
  136. 136 The projective Triple Quad Formula | Rational Geometry Math Foundations 136 | NJ Wildberger
  137. 137 Algebraic structure on the Euclidean projective line | Rational Geometry Math Foundations 137
  138. 138 Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
  139. 139 Isometry groups of the projective line (II) | Rational Geometry Math Foundations 139 | NJ Wildberger
  140. 140 Isometry groups of the projective line III | Rational Geometry Math Foundations 140 | NJ Wildberger
  141. 141 The three-fold symmetry of chromogeometry | Rational Geometry Math Foundations 141 | NJ Wildberger
  142. 142 Relativistic velocity, core circles and Paul Miller's protractor (I) | Rational Geometry MF142
  143. 143 Relativistic velocity, core circles, and Paul Miller's protractor (II) | Rational Geometry MF143
  144. 144 Relativistic velocity, core circles and Paul Miller's protractor (III) | Rational Geometry MF144
  145. 145 Relativistic velocity, core circles and Paul Miller's protractor IV | Rational Geometry MF145
  146. 146 The Triple spread formula, circumcircles and curvature | Rational Geometry Math Foundations 146
  147. 147 The curvature of a parabola, without calculus | Rational Geometry Math Foundations 147
  148. 148 The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger
  149. 149 The circumquadrance of a cyclic quadrilateral|Rational Geometry Math Foundations 149 | NJ Wildberger
  150. 150 MF150: What exactly is a set? | Data Structures in Mathematics Math Foundations | NJ Wildberger
  151. 151 Sets and other data structures | Data Structures in Mathematics Math Foundations 151
  152. 152 Fun with lists, ordered sets, multisets I Data Structures in Mathematics Math Foundations 152
  153. 153 Fun with lists, multisets + sets II | Data structures in Mathematics Math Foundations 153
  154. 154 Fun with lists, multisets and sets III | Data Structures in Mathematics Math Foundations 154
  155. 155 The realm of natural numbers | Data structures in Mathematics Math Foundations 155
  156. 156 The realm of natural number multisets | Data structures in Mathematics Math Foundations 156
  157. 157 The algebra of natural number multisets | Data structures in Mathematics Math Foundation 157
  158. 158 An introduction to the Tropical calculus | Data Structures in Mathematics Math Foundations 158
  159. 159 Inclusion/Exclusion via multisets | Data structures in Mathematics Math Foundations 159
  160. 160 Unique factorization, primes and msets | Data Structures in Mathematics Math Foundations 160
  161. 161 Fun with lists, multisets and sets IV | Data structures in Mathematics Math Foundations 161
  162. 162 Four basic combinatorial counting problems | Data structures in Mathematics Math Foundations 162
  163. 163 Higher data structures | Data structures in Mathematics Math Foundations 163
  164. 164 Arrays and matrices I Data structures in Mathematics Math Foundations 164 | NJ Wildberger
  165. 165 Arrays and matrices II | Data structures in Mathematics Math Foundations 165
  166. 166 Maxel theory: new thinking about matrices II | Data Structures Math Foundations 167
  167. 167 Maxel theory: new thinking about matrices I Data Structures in Mathematics Math Foundations 166
  168. 168 Maxel theory: new thinking about matrices III | Data structures Math Foundations 168
  169. 169 Maxel algebra! I | Data structures in Mathematics Math Foundations 169 | NJ Wildberger
  170. 170 Maxel algebra! II | Data structures in Mathematics Math Foundations | NJ Wildberger 170
  171. 171 Singletons, vexels, and the rank of a maxel I Data structures in Mathematics Math Foundations 171
  172. 172 Singletons, vexels, and the rank of a maxel II | Data structures Math Foundations 172
  173. 173 A disruptive view of big number arithmetic | Data structures in Mathematics Math Foundations 173
  174. 174 Complexity and hyperoperations | Data Structures Math Foundations 174
  175. 175 The chaotic complexity of natural numbers | Data structures in Mathematics Math Foundations 175
  176. 176 The sporadic nature of big numbers | Data Structures in Mathematics Math Foundations 176
  177. 177 Numbers, the universe and complexity beyond us | Data structures Math Foundations 177
  178. 178 The law of logical honesty and the end of infinity | Data structures in Math Foundations 178
  179. 179 Hyperoperations and even bigger numbers | Data structures in Mathematics Math Foundations 179
  180. 180 The successor - limit hierarchy | Data Structures in Mathematics Math Foundations 180
  181. 181 The successor-limit hierarchy and ordinals I Data structures in Mathematics Math Foundations 181
  182. 182 The successor-limit hierarchy and ordinals II | Data structures Math Foundations 182
  183. 183 Limit levels + self-similarity in successor-limit hierarchy | Data structures Math Foundations 183
  184. 184 Reconsidering natural numbers and arithmetical expressions | Data structures Math Foundations 184
  185. 185 The essential dichotomy underlying mathematics | Data Structures Math Foundations 185
  186. 186 The curious role of "nothing" in mathematics | Data Structures Math Foundations 186
  187. 187 Multisets and a new framework for arithmetic | Data Structures Math Foundations 187
  188. 188 Naming and ordering numbers for students | Data structures in Mathematics Math Foundations 188
  189. 189 The Hindu Arabic number system revisited | Data Structures in Mathematics Math Foundations 189
  190. 190 Numbers, polynumbers and arithmetic with vexels I | Data Structures Math Foundations 190
  191. 191 Numbers, polynumbers, and arithmetic with vexels II | Data Structures in Math Foundations 191
  192. 192 Arithmetic with base 2 vexels | Data Structures in Mathematics Math Foundations 192
  193. 193 A new look at Hindu Arabic numbers and their arithmetic | Data structures in Math Foundations 193
  194. 194 Arithmetical expressions as natural numbers | Data structures in Mathematics Math Foundations 194
  195. 195 Divisibility of big numbers | Data Structures in Mathematics Math Foundations 195 | NJ Wildberger
  196. 196 Back to Gauss and modular arithmetic | Data Structures in Mathematics Math Foundations 196
  197. 197 Modular arithmetic with Fermat and Euler | Data Structures in Mathematics Math Foundations 197
  198. 198 Unique factorization and its difficulties I Data Structures in Mathematics Math Foundations 198
  199. 199 Unique factorization and its difficulties II | Data Structures Math Foundations 199
  200. 200 MF200: Mission impossible: factorize the number z | Data Structures in Mathematics Math Foundations
  201. 201 A celebration of 200 videos of MathFoundations | Data Structures Math Foundations 201
  202. 202 Reciprocals, powers of 10, and Euler's totient function I | Data Structures Math Foundations 202
  203. 203 Reciprocals, powers of 10, and Euler's totient function II | Data Structures Math Foundations 203
  204. 204 Euclid + the failure of prime factorization for z | Data Structures Math Foundations 204
  205. 205 Negative numbers, msets, and modern physics | Data Structures in Mathematics Math Foundations 205
  206. 206 A new trichotomy to set up integers | Data structures in Mathematics Math Foundations 206
  207. 207 Integral vectors and matrices via vexels and maxels I | Data structures Math Foundations 207
  208. 208 Integral vectors and matrices via vexels and maxels II | Data structures Math Foundations 208
  209. 209 A broad canvas: algebra with maxels from integers | Data Structures Math Foundations 209
  210. 210 Numbers as multipliers + particle/antiparticle duality I | Data Structures Math Foundations 210
  211. 211 Numbers as multipliers + particle/antiparticle duality II | Data Structures Math Foundations 211
  212. 212 The anti operation in mathematics | Data structures in Mathematics Math Foundations 212
  213. 213 An introduction to abstract algebra | Abstract Algebra Math Foundations 213 | NJ Wildberger
  214. 214 Logical challenges with abstract algebra I | Abstract Algebra Math Foundations 214 | NJ Wildberger
  215. 215 Logical challenges with abstract algebra II | Abstract Algebra Math Foundations 215 | NJ Wildberger
  216. 216 The fundamental dream of algebra | Abstract Algebra Math Foundations 216 | NJ Wildberger
  217. 217 What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
  218. 218 Why roots of unity need to be rethought | Abstract Algebra Math Foundations 218 | NJ Wildberger
  219. 219 Linear spaces and spans I | Abstract Algebra Math Foundations 219 | NJ Wildberger
  220. 220 Linear spaces and spans II | Math Foundations 220 | N J Wildberger
  221. 221 Bases + dimension for integral linear spaces I|Abstract Algebra Math Foundations 221 | NJ Wildberger
  222. 222 Lattice relations + Hermite normal form|Abstract Algebra Math Foundations 224 | NJ Wildberger
  223. 223 Bases and dimension for integral linear spaces II | Abstract Algebra Math Foundations 222
  224. 224 Integral row reduction + Hermite normal form|Abstract Algebra Math Foundations 223 | NJ Wildberger
  225. 225 Relations between msets | Abstract Algebra Math Foundations 225 | NJ Wildberger

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