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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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