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Klein F. — Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis
Klein F. — Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis

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Название: Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis

Автор: Klein F.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1945

Количество страниц: 283

Добавлена в каталог: 05.05.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      84 138 154
Abridged reckoning      10
Actually infinitely small quantities      214 218 219
Algorithmic method      see "Processes of growth plan
Analysis situs      267
Applicability and logical consistency in infinitesimal calculus      221
Applicability and logical consistency in infinitesimal calculus, in the theory of fractions      29
Applicability and logical consistency in infinitesimal calculus, in the theory of fractions, complex numbers      56—58
Applicability and logical consistency in infinitesimal calculus, in the theory of fractions, irrational numbers      33
Applicability and logical consistency in infinitesimal calculus, in the theory of fractions, natural numbers      14
Applicability and logical consistency in infinitesimal calculus, in the theory of fractions, negative numbers      23—25
Applied mathematics      4 15
Approximation, mathematics of      36
Archimedes      80 209 219 222 237
Archimedes, axiom of      218
Arithmetization      266
Arrangement within an assemblage      262
Assemblage of algebraic and transcendental numbers      250 254—256
Assemblage of continuous and real functions      206 259—261
Bachmann      39 48
Ball      74
Baltzer      72
Bauer      86
Baumann      220
Berkeley      219
Bernoulli, Daniel      205
Bernoulli, Jacob      200
Bernoulli, Johann      200 205 216
Bernstein      261
bessel      191
Branch points      107 109
Braunmuehl      175
Briggs      172 173
Brouwer      265
Budan      94
Buergi      147
Burkhardt      23 29 191 205
Calculating machines      17—21
Calculating machines and formal rules of operation      21 22
Cantor, Georg      12 32 35 204 221 250 266 267
Cardanus      55 80 134
cardinal number      251
Cartesius      see "Descartes"
Casus irreducibilis of the cubic equation      135
Cauchy      84 154 202 213 219 228 231 235
Cavalieri      210 214
Cayley      68 73 74
Chernac      40
Chisholm      179
Circular functions      see also "Trigonometric functions"
Circular functions, analogy with hyperbolic functions      166
Clebsch      84
Closed fundamental series      264
Coble      143
Complex numbers, higher      58—75
Consistency, and applicability, of infinitesimal calculus      221
Consistency, and applicability, of the theory of fractions      30
Consistency, and applicability, of the theory of fractions, complex numbers      55—58
Consistency, and applicability, of the theory of fractions, irrational numbers      34
Consistency, and applicability, of the theory of fractions, natural numbers      14
Consistency, and applicability, of the theory of fractions, negative numbers      23
Consistency, proofs of      13 25 57
Constructions with ruler and compasses      49
Continued fractions      42—44
Continuity, analysis of, based on theory of assemblages      263—266
Copernicus      81 171
Coradi      198
Curriculum proposals, the Meran      16
Cut, after Dedekind      33
Cyclometric functions, definition of, by means of quadrature of the circle      163—168
Cyclotomic numbers      47
D'Alembert      103 212
De Moivre      153 168
Decimal system      6 9 20
Dedekind      13 33
Dehn      267
Delambre      180 181
Dense      31 249 263 264
Denumerability of a denumerable infinity of de-numerable assemblages      254
Denumerability of algebraic numbers      253
Denumerability of rational numbers      252
Derivative calculus      220 234
Descartes      81 94
Development of infinitesimal calculus      208—220
Diagonal process      254 259 261
Differences, calculus of      228 230—232
Differentials, calculation with, direction of mathematics of approximation      215 216
Differentials, calculation with, formal direction      215
Differentials, calculation with, naive intuitional direction      208—210
Differentials, calculation with, speculative direction      214 216 217
Dimension, invariance of the dimension of a continuum by reversibly unique mapping      264 265
Dirichlet      42 199 202 203 204 206
Discriminant curve of the quadratic and cubic equation      92
Discriminant surface of the biquadratic equation      98—101
Dyck      94
Enriques      55 267
Equations, cyclotomic      50
Equations, of fifth degree      141—142
Equations, pure      110—115 131—134
Equations, reciprocal      51
Equations, the dihedral Equations      115—120 126
Equations, the icosahedral Equations      120—130
Equations, the octahedral Equations      120—130
Equations, the tetrahedral Equations      120—130
Equivalence, of assemblages      251—262
Equivalence, theorem of      260
Eratosthenes      40
Eudoxus      219
Euklid      32 80 219
Euler      50 56 77 82 155 166 200 202 212 234 237
Exhaustion, method of      209
Exponential function, definition by quadrature of hyperbola      149 156—157
Exponential function, function-theoretic discussion of      156
Exponential function, general Exponential function, and $e^{\omega}$      158—159 160—161
Exponential function, series for $e^{x}$      152
Fejer      200
Fermat      39 48 58
Fermat, great theorem of      46—49
Formal mathematics      24 26 29 56
Foundations of arithmetic, by means of intuition      11
Foundations of arithmetic, formalism      13
Foundations of arithmetic, logic      11
Foundations of arithmetic, theory of point sets      12
FOURIER      91 201 204 206 207 222 236
Fourier's series      see "Trigonometric series"
Fourier's series, integral      207
Fractions, changing common into decimal      40
Function, notion of, analytic function      200—201
Function, notion of, arbitrary function      200
Function, notion of, discontinuous real functions      204
Function, notion of, relation of the two in complex region      202—203
Functions, assemblage of continuous and real      206 261—262
Fundamental laws of addition and multiplication      8—10
Fundamental laws of addition and multiplication, consistency      13
Fundamental laws of addition and multiplication, logical foundation      10—16
Fundamental regions on the sphere      111—114 117—120
Fundamental series, Cantor's      264
Fundamental theorem of algebra      101—104
Galle      17
Gamma function      239
Gauss      39 42 50 58 76 102 154 181
Gibbs      199 200
Gordan      143
Goursat      235
Graphical methods for determining the real solutions of equations      87—101
Graphical methods for equations in the complex field      102—133
Grassmann      12 58 64
Gutzmer      2
Hahn      268
Hamilton      11 58 62 73 74
Hammer      175
hankel      26 56
Harnack      235
Hartenstein      99
Heegard      267
Hegel      217
Heiberg      80 209
hermite      238 239 245
hilbert      13 14 48 218 238 243
Historical excursus on, exponential function and logarithm      146—155
Historical excursus on, imaginary numbers      55 75—76
Historical excursus on, infinitesimal calculus      207—223
Historical excursus on, irrational numbers      31—34
Historical excursus on, negative numbers      25—27
Historical excursus on, relations between differential calculus and the calculus of finite differences      232—235
Historical excursus on, Taylor's theorem      233—234
Historical excursus on, the modern development and the general structure of mathematics      77—85
Historical excursus on, the notion of function      200—207
Historical excursus on, transcendence of e and $\pi$      237—238
Historical excursus on, trigonometric series      205—207
Historical excursus on, trigonometric tables and logarithmic tables      170—174
Homogeneous variables in function theory      106—108
Hyperbolic functions      164—166
Hyperbolic functions, analogy with circular functions      166
Hyperbolic functions, fundamental function for      166
Impossibility, proofs of, construction of regular heptagon with ruler and compasses      51—55
Impossibility, proofs of, general      51
Impossibility, proofs of, trisection of an angle      114
Induction, mathematical      11
Infinitesimal calculus, invention and development of      207
Instruction, reform in      5
Interpolation parabolas      229
Interpolation, by means of polynomials after Lagrange      229
Interpolation, by means of polynomials after Newton      229—232
Interpolation, by means of trigonometric      190—193
Investigation, mathematical      208
Irreducibility, function-theoretic      113—114
Irreducibility, number-theoretic      52
jacobi      84
Kaestner      76 210 212
Kant      10
Kepler      208 210
Kimura      74
Koenig, J.      258
Kowalewski      215 216
Kummer      48
L'Hospital      216
Lacroix      235
Lagrange      66 82 83 153 200 220 222 234
Lagrange's interpolation formula      229
Leibniz      13 20 56 82 200 211 214 215 220 222
Lie      84
Limit, method of      211—214
Lindemann      238 243 249
Liouville      256
Logarithm, base of the natural      150—151
Logarithm, calculation of      148 172
Logarithm, definition of the natural Logarithm by means of quadrature of the hyperbola      149 156
Logarithm, difference equation for the Logarithm      148
Logarithm, function-theoretic discussion of Logarithm      156—162
Logarithm, uniformization by means of Logarithm      133 159
Luebsen      216
Lueroth      17
Maclaurin      210 212 234
Maennchen      49
Mangold      267
Markoff      236
Mean-value theorem of differential calculus      213—214
Mean-value theorem of differential calculus, extension of same      231
Mehmke      95 170
Mercator, N.      81 150 168
Michelson      198 199
Minkowski      11 39
Moebius      176 177 182
Molk, J.      8
Mollweide      181
Monge      84
Napier      see "Neper"
Neper      81 147 150 172 173
Netto      86
Newton      81 82 151 168 210 212 222 230 233 237
Newton's interpolation formula      229—232
NOERLUND      236
Nomographic scales for class curves      90 95
Nomographic scales for order curves      89 94
Non-Archimedean number system      218
Non-denumerability of the continuum      256
Normal class curve of biquadratic equation      96—98
Normal curves as, class curves      90—93 95 97
Normal curves as, order curves      89—90 94
Normal equations of radicals      138—141
Normal equations of the regular bodies, solution by separation and series      130—133
Normal equations of uniformization      133—138
Normal reduction of general equations to normal equations      141—143
Number pair      28 56
Number scale      23 26 31
Number, assemblage of continuous and real numbers      250 251—253
Number, notion of      10
Number, transition from, to measure      28
Odhner      17
Ohm      76
Order, types of      263
Osculating parabolas      224—226
Osculating parabolas, limiting form of      227
Ostrowski      103
Peano      12 265
Peano curve      265
Perception, and logic      11
Perception, inner      11
Peurbach      171
Philologists, relation to      2
Picard      84 160
Picard's theorem      160
Pitiscus      172 174
Plato      80 120
Poincare      11
Point lattice      43
Point, the infinitely distant Point of the complex plane      105
poisson      216
Power of a finite number of dimensions      257—258
Power of an assemblage      251—262
Power of an assemblage, the assemblage of all continuous functions      260
Power of an assemblage, the assemblage of all real functions      261
Power of the continuum of a de-numerable infinity of dimensions      258
Precision, mathematics of      36
Prime numbers, existence of infinitely many      40
Prime numbers, factor tables      40
Principle of permanence      26
Pringsheim, A.      233
Process of growth of mathematics, Plan A Separating methods and disciplines, logical direction      75
Process of growth of mathematics, Plan B Fusing methods and disciplines, intuitive direction      77
Process of growth of mathematics, Plan C Algorithmic process, formal direction      79
Psychologic moments in teaching      4 10 16 28 30 34 268
Ptolemy      170
Pythagoras      31 250
Pythagorean numbers      44
Quaternion      60—75
Quaternion, scalar part of Quaternion      60
Quaternion, tensor of Quaternion      63 66 72
Quaternion, vector part of Quaternion      60
Quaternion, versor of Quaternion      72
Rational, in the sense of mathematics of approximation      36
Reform, movement, the beginnings of infinitesimal calculus in school instruction      223 see "Reform
Reform, proposals, Dresden proposal reform for training teachers      2
Reform, the Basel aims toward      2
Regiomontanus      171
Regular bodies, groups of      120—124
Rhaeticus      171
Rieman sphere      105—110
Rieman surfaces      105—110
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