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Lecture |
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1 |
What is a number? (9:55) |
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2 |
Arithmetic with numbers (10:07) |
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3 |
Laws of Arithmetic (9:36) |
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4 |
Subtraction and Division (10:07) |
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5 |
Arithmetic and Math education (9:23) |
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6 |
The Hindu-Arabic number system (8:16) |
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7 |
Arithmetic with Hindu-Arabic numbers (10:03) |
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8 |
Division (9:56) |
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9 |
Fractions (6:29) |
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10 |
Arithmetic with fractions (9:42) |
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11 |
Laws of arithmetic for fractions (6:30) |
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12 |
Introducing the integers (9:22) |
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13 |
Rational numbers (9:15) |
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14 |
Rational numbers and Ford Circles (9:43) |
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15 |
Primary school maths education (10:01) |
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16 |
Why infinite sets don't exist (7:38) |
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17 |
Extremely big numbers (9:58) |
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18 |
Geometry (8:14) |
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19 |
Euclid's Elements (9:05) |
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20 |
Euclid and proportions (9:39) |
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21 |
Euclid's Books VI--XIII (7:33) |
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22 |
Difficulties with Euclid (8:01) |
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23 |
The Basic Framework for Geometry I (8:49) |
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24 |
The Basic Framework for Geometry II (9:39) |
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25 |
The Basic Framework for Geometry III (9:41) |
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26 |
The Basic Framework for Geometry IV (6:52) |
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27 |
Trigonometry with rational numbers (9:34) |
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28 |
What exactly is a circle? (9:14) |
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29 |
Parametrizing circles (8:43) |
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30 |
What exactly is a vector? (9:53) |
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31 |
Parallelograms and affine combinations (9:23) |
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32 |
Geometry in primary school (9:25) |
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33 |
What exactly is an area? (7:55) |
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34 |
Areas of polygons (9:45) |
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35 |
Translations, rotations and reflections I (10:09) |
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36 |
Translations, rotations and reflections II (9:51) |
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37 |
Translations, rotations and reflections III (9:58) |
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38 |
Why angles don't really work I (9:20) |
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39 |
Why angles don't really work II (9:52) |
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40 |
Correctness in geometrical problem solving (9:50) |
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41 |
Why angles don't really work III (8:11) |
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42 |
Deflating Modern Mathematics: the problem with 'functions' - Part 1 (9:43) |
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43 |
Deflating Modern Mathematics: the problem with 'functions' - Part 2 (6:27) |
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44 |
Reconsidering `functions' in modern mathematics (9:52) |
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45 |
Definitions, specification and interpretation (9:54) |
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46 |
Quadrilaterals, quadrangles and n-gons (9:59) |
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47 |
Introduction to Algebra (9:46) |
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48 |
Baby Algebra (9:16) |
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49 |
Solving a quadratic equation (8:11) |
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50 |
Solving a quadratic equation (7:08) |
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51 |
How to find a square root (10:06) |
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52 |
Algebra and number patterns (9:32) |
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53 |
More patterns with algebra (9:54) |
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54 |
Leonhard Euler and Pentagonal numbers (10:05) |
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55 |
Algebraic identities (8:48) |
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56 |
The Binomial theorem (9:58) |
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57 |
Binomial coefficients and related functions (10:04) |
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58 |
The Trinomial theorem (10:08) |
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59 |
Polynomials and polynumbers (9:47) |
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60 |
Arithmetic with positive polynumbers (9:52) |
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61 |
More arithmetic with polynumbers (9:20) |
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62 |
What exactly is a polynomial? (9:39) |
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63 |
Factoring polynomials and polynumbers (9:53) |
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64 |
Arithmetic with integral polynumbers (7:58) |
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65 |
The Factor theorem and polynumber evaluation (10:10) |
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66 |
The Division algorithm for polynumbers (45:17) |
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67 |
Row and column polynumbers (49:53) |
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68 |
Decimal numbers (28:20) |
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69 |
Visualizing decimal numbers and their arithmetic (44:23) |
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70 |
Laurent polynumbers (the New Years Day lecture) (39:52) |
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71 |
Translating polynumbers and the Derivative (37:15) |
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72 |
Calculus with integral polynumbers (36:00) |
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73 |
Tangent lines and conics of polynumbers (36:29) |
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74 |
Graphing polynomials (37:50) |
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75 |
Lines and Parabolas I (39:52) |
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76 |
Lines and Parabolas II (38:19) |
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77 |
Cubics and the prettiest theorem in calculus (28:09) |
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78 |
An introduction to algebraic curves (34:33) |
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79 |
Object-oriented versus expression-oriented mathematics (45:50) |
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80 |
Calculus on the unit circles (35:20) |
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81 |
Calculus on a cubic: the Folium of Descartes (31:56) |
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82 |
Inconvenient truths about Square Root of 2 (42:03) |
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83 |
Measurement, approximation and interval arithmetic I (45:38) |
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84 |
Measurement, approximation and interval arithmetic II (41:49) |
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85 |
Newton's method for finding zeroes (25:50) |
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86 |
Newton's method for approximating cube roots (29:31) |
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87 |
Solving quadratics and cubics approximately (36:18) |
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88 |
Newton's method and algebraic curves (30:28) |
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89 |
Logical weakness in modern pure mathematics (27:10) |
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90 |
The decline of rigour in modern mathematics (27:20) |
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91 |
Fractions and repeating decimals (48:44) |
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92 |
Fractions and p-adic numbers (53:29) |
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93 |
Difficulties with real numbers as infinite decimals I (51:01) |
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94 |
Difficulties with real numbers as infinite decimals II (52:06) |
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95 |
The magic and mystery of π (41:33) |
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96 |
Problems with limits and Cauchy sequences (28:42) |
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97 |
The deep structure of the rational numbers (35:42) |
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98 |
Fractions and the Stern-Brocot tree (36:07) |
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99 |
The Stern-Brocot tree, matrices and wedges (34:14) |
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100 |
What exactly is a sequence? (26:32) |
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101 |
"Infinite sequences": what are they? (36:41) |
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102 |
Slouching towards infinity: building up on-sequences (26:02) |
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103 |
Challenges with higher on-sequences (35:32) |
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104 |
Limits and rational poly on-sequences (48:28) |
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105 |
MF103: Extending arithmetic to infinity! (32:11) |
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106 |
Rational number arithmetic with infinity and more (36:56) |
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107 |
The extended rational numbers in practice (39:20) |
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108 |
What exactly is a limit? (35:03) |
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109 |
Inequalities and more limits (34:33) |
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110 |
Limits to Infinity (38:29) |
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111 |
Logical difficulties with the modern theory of limits I (36:17) |
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112 |
Logical difficulties with the modern theory of limits II (36:50) |
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113 |
Real numbers and Cauchy sequences of rationals I (21:06) |
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114 |
Real numbers and Cauchy sequences of rationals II (35:54) |
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115 |
Real numbers and Cauchy sequences of rationals III (30:24) |
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116 |
Real numbers as Cauchy sequences don't work! (52:19) |
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117 |
The mostly absent theory of real numbers (52:07) |
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118 |
Difficulties with Dedekind cuts (40:20) |
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119 |
The continuum, Zeno's paradox and the price we pay for coordinates (34:38) |
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120 |
Real fish, real numbers, real jobs (21:23) |
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121 |
Mathematics without real numbers (33:07) |
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122 |
Axiomatics and the least upper bound property I (29:11) |
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123 |
Axiomatics and the least upper bound property II (28:27) |
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124 |
Mathematical space and a basic duality in geometry (33:19) |
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125 |
Affine one-dimensional geometry and the Triple Quad Formula (26:56) |
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126 |
Heron's formula, Archimedes' function, and the TQF (46:04) |
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127 |
Brahmagupta's formula and the Quadruple Quad Formula I (41:29) |
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