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| Ivanov O.A. — Easy as Pi?: An Introduction to Higher Mathematics |
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| Предметный указатель |
Abelian group 83
Acceleration 130
Acceleration components 135
Acceleration, centripetal 135
Addition 4 6 155 164 167 169
Air resistance 152
Alexander the Great 10
Algebra with an identity element 121 123
Algebra without zero-divisors 121
Algebraic curve 69 79
Algebraic element 121
Algebraic extension 81
Algebraic number 81
Analysis 153
Analysis, foundations of 155
Analytic geometry 63
Arc, polygonal 66 96 137
Arithmetic-geometric mean inequality 46 51
Associative algebra 121 124
Associative law 5 119
Automorphism of an algebra 125
Autonomous system 108
Axiom of Archimedes 156 175
Axiom of Choice 170
Axiom of continuity 156
Axioms 5 156 158
Banach's fixed-point theorem 140
Basis of vector space 42 56 116 118 125
Bernoulli's inequality 15 50
Bernstein — Cantor — Schroeder theorem 99
Bezout's theorem 78
Bilinear map 113 121
Binomial coefficients 18 21 24
Binomial theorem 18 21
Bounded set 35 109 163
Bucephalus 11
Calculus 29 52 128 155
Cantor's theorem 145 163
Cantor's version of axiom of continuity 156
Cardinality 9 100
Cartesian coordinates 37 63 129
Cartesian product 5 10 13 119 121 124
Cauchy sequence 140 167
Cauchy's inequality 50 52
Cauchy's initial value problem 108
Cauchy's version of axiom of continuity 156
Cayley, theorem of 20
Celestial mechanics 135
Cell of a lattice 110
Central symmetry 33 40 56 111
Chain in a graph 89 99 100
Chain in a poset 170
Chain, rule 108 129
Characteristic of a field 82
Characteristic polynomial 23
Circular helix 134
Coefficient field 81
Combinations 16
Combinatorics 13
Commutative algebra 122
Commutative law 5
Complete space 140 156 166 168
Completion 166 173
complex numbers 75 76 81 118 122 124
Complex numbers in trigonometry 19
Components of acceleration 135
Composition of transformations 35
Congruence 110 113 114
Congruence, modulo  25
Conjugate quaternion 120
Conjugate-transpose matrix 125
Connected component 66 89 94
Connected graph 89 90 92
Connected set 91
Conservative system 147
Continuity continuous curve 34
contour 147
Contracting map 140 141
Coordinate functions 128
Countable additivity 105
Critical edge of a graph 89 92
Critical point 144
Cross product 125 134 135 136
cube 34 119
Cubic curve 69
Curvature 136
Cycle in a graph 89
Cyclic group 82 114
Dangling edge 102
De Moivre's theorem 19
Dedekind cut 163
Dedekind's version of axiom of continuity 156 159 175
Degree of a point 35
Degree of a vertex 87
Derivative 18 59 68 128 134
Derivative, partial 108 141
Determinant 74 76 80 107 110 116 119
Diameter of a set 129
Difference between cuts 165
Differentiability 133 142
Differential equations 107 133 136
Dilation 111 135
Dimension of a vector space 81 82 122
Dirichlet 103
Discriminant 75
Division algebra 121
Division algorithm 77 81 82
dodecahedron 94
Dot product 125 129
Edge of a graph 87
Edge, critical 89
Eigenvalues 23
Elimination 80
ellipse 61 65 80 135 145
Energy 147
Equation Diophantine 66 113
Equation of a set 34 64
Equilibrium, stable 149
Equilibrium, unstable 152
EQUIVALENCE 3 155 167 168
Equivalence class 3 155 167 168
Equivalent norms 56 173
Euclidean metric 56
Euclidean motion 37 125
Euclidean motion, discrete 43
Euclidean space 37 55 118 121 125 128
Euler 114
Euler characteristic 94
Euler's formula for a planar graph 92
Euler's identity 26 116 120
Euler's method of approximate solution of a d.e. 137
Eulerian graph 100
Extreme-value theorem 52 56 163
Factor of a polynomial 24 48
Factor Theorem 68 70
Fermat — Euler theorem 113
Fermat's great theorem 67
Fermat's last theorem 67
Fermat's little theorem 113
Fermat's principle 131
Fermat's theorem 129
Fibonacci numbers 21 105
Field 122
Field extension 80 83 122
Field of complex numbers 81
Field of fractions 155
Field of real numbers 156
Field, finite 82
Field, ordered, Archimedean 156 168
Filter 169
| Finite field 82
Finite graph 87
Finite hyperreal number 159
Finite set 9
Finite-dimensional algebra 121 124
Fixed point 140
Formal logic 160
Fourier coefficients 60
Fractional part of a real number 64
Friction 152
Frieze pattern 39
Frobenius' Theorem 123
Fubini's theorem 29 115
Full order 156
Function, concave down 53
Function, continuous 53 66 107 134
Function, smooth 142
Function, vector-valued 128
Functional equation 133
Fundamental region 110
Fundamental theorem of algebra 122
Gamma function 29
General lattice 43
Generating function 18 21
Generators of a group 38 41
Geometric series 140
Geometric transformation 32
Graph 87
Graph of an equation 64
Graph, bipartite 98
Graph, connected 89
Graph, planar 92
Graph, simple unoriented 87
Gravitational field 135 148
Green's theorem 61
Group 38 40 43 82 83 107 113
Group of rigid motions 38 125
Group, multiplicative 82
Hall's theorem 98
Hamilton 120
hilbert 95
Hoelder's inequality 54
Homogeneous function 57
Homogeneous linear system 70 119
Homothety 135
Hyperbola 151
Hyperreal field 159
icosahedron 94
Implicit function theorem 154
Inclusion-exclusion formula 13
Incommensurable numbers 35 106
Index of a point 96
Index of a ray 35
Inequality 46
Inequality between the arithmetic and geometric means 46
Infinite decimal 166
Infinitely close elements 159
Infinitely large element 158
Infinitesimal element 157 171
Inner product 59
Integers 3
Integral domain 82 155
Integral equation 138
Integral of a differential equation 147
Integration by parts 29
Interior of a subset 56
Intermediate-value theorem 66 139 163
Intersection 63 161
Interval method 65
Intrinsic subset 161
Intuitionist 170
Inverse-function theorem 143
Irrational numbers 106 107
Irreducible polynomial 81
Isometry 125
Isoperimetric problem 61
Isoperimetric property of circle 62
Jacobian 109 116
Jacobian matrix 108 143 145
Jensen's inequality 57
Jordan curve theorem 94
Jordan form of a matrix 23
Kepler's laws of motion 135
Klein xiii
Koenigsberg bridge problem 100
Lagrange's four-squares theorem 113
Lagrange's theorem in group theory 113
Latin rectangle 99
Lattice of points 43 110 114
Law of conservation of energy 147
Least upper bound property 157
Lebesgue integral 59
Lebesgue measure 106 144
Leibniz' rule 150
Level curve 147 148
LIMIT 28 52 107 128 133 134 138 140 142 151 156 162 167 174
Linear equations 68 70 75 76 119
Linear independence 82 121 122
Linear transformation 37 121 124
Linearization 142
Liouville's theorem 109
Locally volume-preserving map 110
Lower number of a cut 164
Marriage problem 98
Mathematical induction 1 8
Mathematical logic 160 171
Matrix algebra 123
Matrix multiplication 118
Matrix of a linear transformation 124
Mean-value theorem 52 129 141
Means of three numbers 48
Means of two numbers 47
Measure 58 105
Measure-preserving map 105 109
Method of elimination 80
Method of mathematical induction 8
Metric space 139
Minimal polynomial 81
Minkowski's inequality 54
Minkowski's Lemma 111
Minkowski's norm 56
Morse — Sard theorem 144
Motion in a gravitational field 135
Motion of a point-particle 134
Motion of a rigid rod 130
Multilinear map 119
Multiple integral 29 115
Multiple root 68 75 144
Multiplicative group of a field 113
Natural numbers 6
Newton's Second Law of Motion 136 148
Newton's universal law of gravitation 135
Nonarchimedean field 158
NonArchimedean norm 173
Nondegenerate critical point 149
Nonstandard analogue 159
Nonstandard line 158
Nonstandard line, model of 168
Nonstandard proof 163
Nonstandard sequence 161
Nonstandard statement 163
Norm of a quaternion 120
Norm on a vector space 50 55
Norm on the rationals 172
Number of elements of a set 9
Number of partitions of a positive integer 24
Number,  28 29 115
Number, e 28 137
Number, n! (n-factorial) 14 28
octahedron 94
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