Math Foundations B (80-149) by Norman J Wildberger

source: njwildberger     2017年12月20日
Math Foundations B deals quite a lot with the problems involved with real numbers, measurement and alternative ways of thinking about geometry. We really need to address the logical weakness of our thinking about the continuum. A better more solid mathematics is around the corner!

42:03 80: Inconvenient truths about sqrt(2)
45:38 81: Measurement, approximation and interval arithmetic I
41:49 82: Measurement, approximation and interval arithmetic II
25:50 83: Newton's method for finding zeroes
29:31 84: Newton's method for approximating cube roots
36:18 85: Solving quadratics and cubics approximately
30:28 86: Newton's method and algebraic curves
27:10 87: Logical weakness in modern pure mathematics
27:20 88: The decline of rigour in modern mathematics
48:44 89: Fractions and repeating decimals
53:29 90: Fractions and p-adic numbers
51:01 91: Difficulties with real numbers as infinite decimals I
52:06 92: Difficulties with real numbers as infinite decimals II
41:33 93: The magic and mystery of "pi"
28:42 94: Problems with limits and Cauchy sequences
35:42 95: The deep structure of the rational numbers
36:07 96: Fractions and the Stern-Brocot tree
34:14 97: The Stern-Brocot tree, matrices and wedges
26:32 98: What exactly is a sequence?
36:41 99: "Infinite sequences": what are they?
26:02 100: Slouching towards infinity: building up on-sequences
35:32 101: Challenges with higher on-sequences
48:28 102: Limits and rational poly on-sequences
32:11 103: Extending arithmetic to infinity!
36:56 104: Rational number arithmetic with infinity and more
39:20 105: The extended rational numbers in practice
35:03 106: What exactly is a limit??
34:33 107: Inequalities and more limits
38:29 108: Limits to Infinity
36:17 109: Logical difficulties with the modern theory of limits I
36:50 110: Logical difficulties with the modern theory of limits II
21:06 111: Real numbers and Cauchy sequences of rationals I
35:54 112: Real numbers and Cauchy sequences of rationals II
30:24 113: Real numbers and Cauchy sequences of rationals III
52:19 114: Real numbers as Cauchy sequences don't work!
52:07 115: The mostly absent theory of real numbers
40:20 116: Difficulties with Dedekind cuts
34:38 117: The continuum, Zeno's paradox and the price we pay for coordinates
21:23 118: Real fish, real numbers, real jobs
33:07 119: Mathematics without real numbers
29:11 120: Axiomatics and the least upper bound property I
28:27 121: Axiomatics and the least upper bound property II
33:19 122: Mathematical space and a basic duality in geometry
26:56 123: Affine one-dimensional geometry and the Triple Quad Formula
46:04 124: Heron's formula, Archimedes' function, and the TQF
41:29 125: Brahmagupta's formula and the Quadruple Quad Formula I
41:01 126: Brahmagupta's formula and the Quadruple Quad Formula II
29:19 127a: The Cyclic quadrilateral quadrea theorem
22:09 127b: The Cyclic quadrilateral quadrea theorem (cont.)
34:25 128: Robbins' formulas, the Bellows conjecture, and volumes of polyhedra
45:28 129: The projective line, circles, and a proof of the CQQ theorem
37:01 130: The projective line, circles and a proof of the CQQ theorem II
45:48 131: Ptolemy's theorem and generalizations
30:50 132: The Bretschneider von Staudt formula for the quadrea of a quadrilateral
29:05 133: Higher dimensions and the roles of length, area and volume
30:53 134: Absolute versus relative measurements in geometry
38:46 135: NJ's pizza model for organizing geometry
25:46 136: The projective Triple Quad Formula
40:41 137: Algebraic structure on the Euclidean projective line
34:26 138: Isometry groups of the projective line I
35:04 139: Isometry groups of the projective line II
30:45 140: Isometry groups of the projective line III
23:38 141: The three-fold symmetry of chromogeometry
33:01 142: Relativistic velocity addition, core circles and Paul Miller's protractor I
39:15 143: Relativistic velocity addition, core circles, and Paul Miller's protractor II
39:03 144: Relativistic velocity addition, core circles and Paul Miller's protractor III
48:41 145: Relativistic velocity, core circles and Paul Miller's protractor IV
23:58 146: The Triple spread formula, circumcircles and curvature
23:50 147: The curvature of a parabola, without calculus
31:27 148: The projective Quadruple quad formula
36:03 149: The circumquadrance of a cyclic quadrilateral