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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 HinduArabic number system (8:16) 
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7 
Arithmetic with HinduArabic 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 VIXIII (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 ngons (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 
Objectoriented versus expressionoriented 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 padic 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 SternBrocot tree (36:07) 
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99 
The SternBrocot 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 onsequences (26:02) 
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103 
Challenges with higher onsequences (35:32) 
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104 
Limits and rational poly onsequences (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 onedimensional 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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