A Computational Introduction to Number Theory and Algebra

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Cambridge University Press, 2009 - Computers - 580 pages
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This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
 

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Contents

III
1
IV
5
V
10
VI
15
VIII
16
IX
19
X
22
XI
25
LXXIV
340
LXXV
342
LXXVI
346
LXXVII
348
LXXVIII
349
LXXIX
350
LXXX
355
LXXXI
357

XII
31
XIII
32
XIV
35
XV
45
XVI
50
XVIII
53
XIX
55
XX
64
XXI
69
XXII
71
XXIII
74
XXIV
77
XXV
82
XXVI
84
XXVII
86
XXVIII
89
XXIX
99
XXX
102
XXXI
104
XXXII
108
XXXIII
110
XXXIV
115
XXXV
116
XXXVI
126
XXXVII
132
XXXVIII
137
XXXIX
142
XL
153
XLI
163
XLII
166
XLIV
176
XLV
185
XLVI
192
XLVII
203
XLVIII
207
XLIX
213
L
221
LI
233
LII
241
LIII
245
LIV
252
LV
260
LVI
266
LVII
270
LVIII
275
LIX
277
LX
285
LXI
287
LXII
292
LXIII
295
LXIV
298
LXV
302
LXVI
304
LXVII
306
LXVIII
311
LXIX
320
LXX
324
LXXI
327
LXXII
329
LXXIII
334
LXXXII
358
LXXXIII
360
LXXXIV
363
LXXXV
367
LXXXVI
370
LXXXVII
377
LXXXVIII
381
LXXXIX
386
XC
388
XCI
392
XCII
398
XCIII
399
XCIV
400
XCV
407
XCVI
414
XCVII
418
XCVIII
421
XCIX
427
C
430
CI
435
CII
438
CIII
440
CIV
444
CV
446
CVI
451
CVII
464
CVIII
465
CIX
468
CX
469
CXI
472
CXII
474
CXIII
478
CXIV
484
CXV
486
CXVI
490
CXVII
492
CXVIII
497
CXIX
500
CXX
501
CXXI
508
CXXII
509
CXXIII
511
CXXIV
515
CXXV
516
CXXVI
522
CXXVII
525
CXXVIII
526
CXXIX
530
CXXX
538
CXXXI
544
CXXXII
546
CXXXIII
548
CXXXIV
549
CXXXV
558
CXXXVI
561
CXXXVII
566
CXXXVIII
572
CXXXIX
574
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About the author (2009)

Victor Shoup is a Professor in the Department of Computer Science at the Courant Institute of Mathematical Sciences, New York University.

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