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Childs L. — A concrete introduction to higher algebra
Childs L. — A concrete introduction to higher algebra



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Название: A concrete introduction to higher algebra

Автор: Childs L.

Аннотация:

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications — to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 341

Добавлена в каталог: 05.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$GF(p^n)$      281
$\mathbb{Z}_m$      58
$\phi(m)$ = Euler’s phi function      94 115 221 276
Abelian group      92
Abel’s theorem      138
Abstract Fermat theorem      92
algebraic      238
Algebraic number      309
Argument of complex number      4
Arithmetic progression      47
Artin’s conjecture      210
Associates      133 183 320
Associativity      63
Automorphism      261 315
Base      37 146
Base a expansion      44 101 148 212
Basis      81
BCH code      242
Berlekamp’s factoring algorithm      187 198 295
Bertrand’s postulate      36
Bezout’s identity      22 133
Bezout’s lemma      22 133
Binomial theorem      14 176 195 214
Board      302
Bound on roots of polynomial      141 161 194 196 197
Brute force technique      170
Cancellation in congruences      49 51 66 173
Casting out nines      50 60 105
Characteristic p      176 258
Characteristic zero      175 258
Chinese remainder theorem      112 216 291
Chinese remainder theorem for polynomials      180
Closed      63
Common divisor      20
Commutativity      63
Complete set of representatives      61
Complex conjugation      143 261 262
complex numbers      4 136 237 260 312
Complex numbers mod p      223
Congruence classes      56 57 234
Congruent modulo n      47
Congruent modulo p(x)      173
Constant polynomial      129
Cube root      41
Cubic polynomial      137 143 290
Cyclic group      210
Decimal expansion      44
Degree      126 129
Derivative      161 182 283
Determinant      75
Differentiation      157
Dimension of null space      82 189
Dirichlet’s Theorem      33
Discriminant      283
Distributive law      63
divides      20 130
Division algorithm = division theorem division theorem, in Z      13 19
Division algorithm = division theorem division theorem, in Z for Gaussian integers      318
Division algorithm = division theorem division theorem, in Z for polynomials      129
Domain of function      255
Echelon form      76
Efficient code      107
Eisenstein’s irreducibility criterion      169 230
Equivalence class      6 99
Equivalence relation      6 52 99
Error-correcting code      105 242
Euclid’s algorithm      21 161 221 318
Euclid’s algorithm for polynomials      132
Euler’s lemma      192 295 298
Euler’s phi function      94 115 221 276
Euler’s theorem      94 117 177
Eventually repeating expansion      46
Expansion in base a      44 101 148 212
Factoring cubic polynomial      137 143
Factorization into primes      120
Fermat number      220 298
Fermatian      219
Fermat’s Last Theorem      216 321 322
Fermat’s theorem      90 116 121 177 207
Fibonacci sequence      12 22
Field      5 57 64 312
Finite field      97 264 281
Formal power series      128
Fundamental theorem of algebra      138 143
Fundamental Theorem of Arithmetic      26
Galois theory      262 314
Game of Euclid      22
Gaussian integers      316
Gauss’s Lemma      167 316
GCD      20
Generalized associativity      93
Generalized commutativity      93
Generator      210
Geometric series      9 32 103 154
GF(16)      245
GF(32)      253
GF(8)      242
GF(9)      66 97
Golden mean      12
Greatest common divisor      20 132 318
Group      92 210 268
Hadamard matrix      299
Hamming code      107 242 251
Head-to-head      302
Homogeneous system      73
Ideal      322
Identity homomorphism      256
IFF      5
Image      255
Imaginary part      4
Inclusion map      257
Indeterminant      127
Induction (1)      7
Induction (2)      11
Infinitude of primes      31 32 223 298
Integers      3
Inverse      61 64 235
Inverse of matrix      75
Irreducible      133 320
Irreducible in $\mathbb{Z}[x]$      168
Irreducible polynomials mod p      274 288
Irreducible polynomials over C      138
Irreducible polynomials over R      142
Irreducible polynomials, number of      141 148 276 279
Isomorphic      256 314
Isomorphism      256
Lagrange interpolator      182
Latin square      268
Leading coefficient      129
Least common multiple (LCM)      29
Least non-negative residue      61
Left coset      99
Legendre symbol      293 300
Length of complex number      4 317
Linearly independent      81
Long division      19 41 130
Matrix      68
Mersenne number      220
Minimal polynomial      239 311
Mobius function      275
Mobius inversion formula      277
MOD      47 173
Monic      129
Multinomial theorem      18
Multiple factor      135 158 178
Multiple root      135
Multiplicative function      276
n!      14
Natural numbers      3
Negative      63
Nonhomogeneous      73
Norm of complex number      317
Null space      81 189
One-to-one      256
Onto      256
Order      96 103 207 212 228
Orthogonal Latin squares      269
Partial fractions      145 216
Pascal’s triangle      15
Period      101 212
Polynomial      126
Prime      11 26 318
Prime number theorem      35 279
Primeness, testing for      218 298
Primes, infinitude of      31 223 298
Primitive element      207 210 295 298
Primitive element mod n      215
Primitive polynomial      167
Principal ideal      322
Pseudoprime      219
Quadratic formula      137
Quadratic reciprocity      54 289 291 296
Quadratic residue      293
Quotient      14
RADIX      37
Range of function      255
Rank      83 249
Rational function      144
Rational numbers      3 6
Real numbers      3
Real part of complex number      4
Reflexivity      6
Relatively prime      20 133
Relatively prime mod q      198
Remainder      14
Repeating decimal expansion      46
Representation in base a      37
Representative of congruence class      58
Residue      61 174
Resultant      283
Right congruent      99
Ring      62 316
Ring homomorphism      255 310 312 322
Ring of integers      316
Root theorem      131 181
round      304
Round robin tournament      54 302
Row operations      76
Row reduced echelon form      76
Row space      82
Russian peasant arithmetic      12 39 96
scalar      129
Scalar multiplication      72
Sieve of Eratosthenes      28
Simple field extension      235
Spacing number      226
span      81
Splitting field      238 281 315
Square root algorithm      40
Squarefree      116
Stickelberger’s theorem      282 284 288 297
Strictly repeating      101
Sturm’s Theorem      161 290
subspace      81
Symmetry      6
Taylor series      4 128 148
Terminating decimal expansion      46
Thirty-six officers      271
Tower of Hanoi      10
Transcendental number      309
Transitivity      6
Triangle inequality      139 195
Unique factorization      26 135 319 320
UNIT      64 133 317 320
Vector      68
Vector space      81
Well-ordering principle      13
Wilson’s theorem word      105
Zero divisor      63
Zero element      63
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