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| Audichya A. — Mathematics: Marvels and milestones |
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| Предметный указатель |
Abel 80
Acceleration 145
Achilles and the tortoise 135
Algebra, abstract 55 56 93
Algebra, as generalized arithmetic 54
Algebra, as study of algebraic systems 56 93
Algebra, as theory of equations 69
Algebra, boolean 105 107
Algebra, Cayley’s 108
Algebra, classical 93
Algebra, fundamental theorem of 35 73
Algebra, generalized 55
Algebra, linear 105
Algebra, number of algebras 109
Algebra, of schools 50
Algebraic structures 93 104
Analysis 123 124 137
Analysis, and probability 177
Analysis, as study of functions 123
Analysis, basic concepts of 126
Analysis, domain of 124
Analysis, main branches of 166
Analytic function (s) 171
Analytic function (s), related to fluid flow 172
Analytic function (s), uniqueness property of 172
Analytical geometry 17
Anecdote 71 121
Applications of mathematics 111
Applied mathematics 182 183
Approximation methods 81
Approximation of functions, where needed 180
Arithmetic, as abstraction 52
Arithmetic, as theory of numbers 56
Arithmetic, fundamental theorem of 62
Arithmetic, meaning of 52
Arithmetic, modular 102
Arithmetic, progression 132
Axiom systems, formation of 51
Axiomatic algebra 56
Axiomatic algebra, limitations of 46
Axiomatic algebra, method 43 46 49
Banach space 104 105
Benjamin Pierce 112
Bhaskaracharya 86 87 91
Bhaskar’s broken bamboo problem 86
Bhaskar’s peacock-and-the-snake problem 87
Boolean algebra 105 106
Calculus 171
Calculus of variations 175—176
Calculus, differential 23 137 138 175
Calculus, Fundamental Theorem of 155
Calculus, integral 137 155
Cantor 115 116 118
Cardan 77
Cauchy’s integral formula 172
Cayley 16 24
Chebychev 60
circle 18 19
Class, concept of 114
Classical analysis 178 183
Closed curve of infinite length 150
Complex variable 171
Congruent to 103
Conic sections 19
Consistency, problem of 44
Continuity, implications of 181
Continuity, in physical sciences 164
Continuous curve, nowhere differentiable 148 152
Continuous curve, ordinarily differentiable 147
Continuous function 148 149 157
Continuous function, examples of 157
Continuum Hypothesis 118
Continuum Hypothesis, space continuum 119
Continuum Hypothesis, time continuum 119
Conundrum 89
Convergent Series 131
Coordinate geometry 17 18
Coordinate geometry, of 3 dimensions 23 24
Coordinate geometry, of 4 dimensions 25
Coordinate geometry, of n dimensions 24 25
Counting 114
Cretan, Cretans 120
Critical strip 174
Curvature 11 13 23 150 152
Curve, length of 150
Curve, space-filling 151—152
Cycloid, as "Helen of Geometers 176
Cycloid, Inverted Cycloid 176
De La Valle’e Poussin 61
De Morgan’s Conudrum 89
Derivative 129 138
Derivative does not exist, meaning of 147
Derivative, higher partial derivatives 153
Derivative, partial 153
Derivative, second derivative 141 144
Derivative, second derivative, and forces 145
Derivative, second derivative, in mechanics 144
Derivative, second derivative, sign of 142 140
Derivative, second derivative, vanishing of 140
Des Cartes, Rene 17 3 8 79 179
Differential calculus 23 137 138 175
Differential equation(s) 35 155 166 167 168
Differential Equation(s), how formed? 166
Differential Equation(s), ordinary 167
Differential equation(s), partial 167
Differential Equation(s), theory of 168
Differential Equation(s), where used 168
Differential geometry 23
Differentiation 129
Diophantus 85
Dirichlet 61
Discrete 180 181
Discrete, as different from continuous 181
Discrete, mathematics 180
Distribution of primes 60
Divergent series 132
Divisors of composite numbers 63
Einstein 14
Elements of a set 94
ellipse 19 20 22
Ellipse, accoustical property of 22
Ellipse, reflection property of 21
Equation, as mathematical model 70
Equation, biquadratic 78 79
Equation, cubic 76 77
Equation, Diophantine 85
Equation, indeterminate 84 85
Equation, integral 171
Equation, Laplace’s 168
Equation, Location of the roots of an 82
Equation, non-algebraic, solution of 92
Equation, of fifth degree 80
Equation, of first degree 71
Equation, of fourth degree 78
Equation, of second degree 91
Equation, quadratic 71
Equation, wave 170
Equations, Maxwell’s 169—170
Equations, simultaneous 83—84
Equations, Simultaneous ldeterminate 89
Error in Koenig’s calculation 147
Euclid 1 4 42 49
Euclidean geometry 1 3 4 7 8 9 10 12 14 16 43
Euclidean geometry, axioms of 4
Euclidean geometry, basic concepts of 3
Euclidean geometry, postulates of 3 45 187
Euclidean model 9
Euler 38 40 92
Euler’s formula for solids 37
Everywhere dense 118
| Existence theorem 74
Factorial 135
Fermat 92
Fermats’ Last Theorem 67
Fermat’s theorem 64
Ferrari 79
Field (s) 51 94 103
Finite geometry 30
Fluid flow 172
Fluid flow, around bodies of arbitrary shape 173
Foundations of mathematics 50 168
Four colour problem 41
Four dimensional space 28
FOURIER 161—164
Fourier, integrals 161
Fourier’s theorem 161 164
Fourth dimension 28
Frenicle 92
Friedmann 14
Function 126
Function, as different from function of a real variable 171
Function, continuous 148 149
Function, integrable 157 158
Function, of a complex variable 171
Function, of a real variable 171 178
Function, of two or more variables 153
Function, periodic 161—163
Function, regular 171
Functional analysis 178 179
Fundamental theorem of algebra 35 73
Fundamental Theorem of Arithmatic 62
Fundamental theorem of calculus 155
G del 46 47 48
Gdel Numbering 48
Gdel’s discovery 47
Gdel’s discovery, implications of 47
Galileo 22
Galois 81
Gauss 6 13 61 73
Gelfond 54
Generalized functions 177
Geodesic 10
Geometric progression 133
Geometry of colour space 29
Geometry, applied to Algebra 28
Geometry, Euclidean 1—43
Geometry, finite 30
Geometry, Lobachewskian 5 6
Geometry, of elementary particles 14
Geometry, of the Earth 12
Geometry, of the space 13
Geometry, of the universe 14
Geometry, projective 15
Geometry, Riemannian 6
Geometry, true geometry 8
Goldbach’s conjecture regrading even numbers 46 62
Goldbach’s conjecture regrading large numbers 69
Grassmann 24 75
Great circle 10
Group 95 96
Group, abelian 96
groups 94 97
Groups, isomorphic 97
hadamard 61
Hailstones—why spherical 146
Hamilton, William, R 75
Hardy, GH 174
Harmonic 134
Harmonic, progression 133 134
Heisenberg 47
Heron’s problem of the light ray 145
Heron’s problem of the light ray, how solved? 146
Hertz 170
hilbert 43 45 75
Hilbert, curve 152
Hilbert, space 104
Hilbert’s Formalism 47
Hilbert’s program 45
Homeomorphic 32
Honeycomb 146
Honeycomb, minimum surface and maximum volume 146
Honeycomb, mistake of the mathematician or the bees 147
Huntington, E.V. 43
Hyperbola 19 27
Hypergeometric series 137
Infinite convergent series 131
Infinite divisibility 181
Infinite geometric series 136
Infinite geometric series, sequence 131
Infinite geometric series, series 131 134 135 136
Infinite series, application of 134
Inside and Outside- as topological properties 31
Integer as sum of four squares 68
Integers modulo 6 103
Integral domain(s) 94 102 103 104
Integral equation 171
Integral solutions 28
Integral, Lebesgue 160
Integral, Riemann 159
Integration 130
Intersection 105
Is “2+3=5” always true? 53
Isomorphism 97
Joseph Bertrand 60
Kenneth Appel 41
Kepler 22
Koenig 147
Koenig’s berg bridges problem 39
Kurt Godel 45
Lagrange 80
Laplace’s equation 168
Lebesgue 160 161 178
Length of a curve 150
Liebnitz, Gottfried 138 155
Lifting force 173
LIMIT 126 127
Limit of a fiinction, Heine’s definition of 128
Limit of a quotient 127 129
Limit of a sum 127 129
Limit of an infinite sequence 127 131
Line 3
Lobachewskian geometry 1 5 6 7
Lobachewsky 6 8
Logical structure 1
Manifold 26 27
Maraldi 146
Marconi 170
Mathematical existence 50
Mathematical induction 66
Mathematical model 70
Mathematics- basic fields of 123
Mathematics- currently defined 111
Mathematics- modem view 111
Mathematics- traditional conception of 111
Matrix 101
Matrix product not commutative 101
Maximum and minimum 140—144
Maximum and minimum, everyday applications of 143
Maxwell’s equations 169
Measure of a set 160
mobius 36 41
Mobius strip 36 37
Modem Analysis 184
Multiple integrals 165
Newton, Isaac 123 138 155 181
No-nextness 181
Non — Euclidean geometries 9
Number 1, whether prime 57
Number definition of 114
Number of fractions 115
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