دانلود کتاب Fundamental concepts of mathematics

عنوان فارسی :

دانلود کتاب مفاهیم اساسی ریاضیات

عنوان انگلیسی :

Fundamental concepts of mathematics

زبان : English

موضوع : Mathematics

نویسندگان : Kam-Tim Leung P.H. Cheung

ناشر : HKU

ISBN (شابک) : 9789622091818, 9622091814

تعداد صفحات : 264\264

سال نشر : 1988     ویرایش :

حجم : 1 MB       فرمت : djvu

قیمت : 50000 تومان

فهرست :



Table of contents :
Title Page......Page 4
verso......Page 5
Table of Contents......Page 6
Preface......Page 8
Objects......Page 10
Sets......Page 11
Subsets......Page 13
Rule of specification......Page 17
Exercise......Page 19
Complements......Page 21
Intersection......Page 23
Union......Page 27
Exercise......Page 30
Ordered pairs and Cartesian product......Page 33
Exercise......Page 36
One-to-one correspondence......Page 37
Mappings......Page 40
Exercise......Page 42
A proof by induction......Page 46
The well-ordering principle......Page 48
The principle of mathematical induction......Page 50
Exercise......Page 54
Miscellaneous remarks......Page 55
Another version of the principle of mathematical induction......Page 57
Exercise......Page 60
Recursive formulae......Page 63
Exercise......Page 67
Boxes and balls......Page 70
Exercise......Page 72
Permutations......Page 73
Permutations in which repetitions are allowed......Page 76
Exercise......Page 78
Permutations of objects some of which are alike......Page 79
Circular permutations......Page 83
Exercise......Page 85
Combinations......Page 86
Exercise......Page 87
Combinations with repetitions......Page 90
Exercise......Page 92
Binomial theorem......Page 93
Exercise......Page 98
Absolute value......Page 103
Divisibility......Page 104
Euclidean algorithm......Page 106
Exercise......Page 108
The greatest common divisor......Page 109
Exercise......Page 111
An effective division algorithm for the evaluation of gcd......Page 113
Exercise......Page 118
Prime numbers......Page 120
The fundamental theorem of arithmetic......Page 122
The infinity of prime numbers......Page 123
Exercise......Page 126
Congruence......Page 129
Chinese remainder theorem......Page 131
Exercise......Page 132
The number line......Page 134
Exercise......Page 136
Some basic assumptions......Page 137
Exercise......Page 141
Some well-known inequalities......Page 142
Exercise......Page 145
Denseness of the rational numbers......Page 149
Postulate of continuity......Page 151
Exercise......Page 155
Powers and roots......Page 157
Existence of roots......Page 160
Powers and logarithm......Page 162
Exercise......Page 164
Null sequence......Page 166
Convergent sequence......Page 171
Divergent sequence......Page 175
Exercise......Page 176
Sum, product and quotient of convergent sequences......Page 177
The sandwich theorem......Page 179
Exercise......Page 182
Monotone sequence......Page 183
Cauchy's convergence test......Page 188
Exercise......Page 191
Series......Page 192
Geometric series and harmonic series......Page 193
Some useful rules......Page 195
Test of convergence......Page 196
Exercise......Page 197
Appendix......Page 199
Equations and number systems......Page 202
One-dimensional number system......Page 203
Two-dimensional number system......Page 206
Complex numbers......Page 209
Standard notations......Page 214
Exercise......Page 216
Complex conjugate......Page 218
Equations with real coefficients......Page 220
Exercise......Page 223
De Moivre's theorem......Page 224
Exercise......Page 229
The n-th roots......Page 231
Exercise......Page 236
Geometry of complex numbers......Page 237
Circles......Page 240
Straight lines......Page 242
Exercise......Page 246
Appendix......Page 249
Answers to exercises......Page 252
Index......Page 262





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