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Audichya A. — Mathematics: Marvels and milestones
Audichya A. — Mathematics: Marvels and milestones

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Название: Mathematics: Marvels and milestones

Автор: Audichya A.

Аннотация:

To transport the reader to the highest level of mathematical awareness and to acquaint him with outstanding mathematical achievements. The foremost of them all is the pluralization of mathematics, i.e.,where we had geometry, we now have geometries, and algebras rather than algebra, and number systems rather than number system. It is intended for the intelligent layman who is in search of short and pointed answers to his queries but is little inclined to undertake detai led study of mathematical ideas and concepts.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 192

Добавлена в каталог: 22.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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$\ddot{o}$del      46 47 48
G$\ddot{o}$del Numbering      48
G$\ddot{o}$del’s discovery      47
G$\ddot{o}$del’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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