Applied mathematics for database professionals

Lex de Haan, Toon Koppelaars1590597451, 9781590597453

Relational databases hold data, right? They indeed do, but to think of a database as nothing more than a container for data is to miss out on the profound power that underlies relational technology. A far more powerful way of thinking lies in relational technologys foundation in the mathematical disciplines of logic and set theory.

Databases contain truths or propositions describing some area of interest such as a business. Those truths are organized into sets. Operations from logic and set theory can be applied to existing sets of truths to derive new sets of truths. Applied Mathematics for Database Professionals introduces you to this way of thinking, to the logic and set theory that underlies relational database technology. All this may sound abstract now, but there are profound benefits from the deeper understanding youll gain from this book. Youll learn to
Become a better database designer. Youll make fewer mistakes, and your designs will be more flexible in response to changing data needs. Use the expressive power of mathematics to precisely specify designs and business rules. Communicate effectively about design using the universal language of mathematics. Develop and write complex SQL statements with confidence. Avoid pitfalls and problems from common relational bugaboos such as null values and duplicate rows.
The math that you learn in this book will put you above the level of understanding of most database professionals today. Youll better understand the technology and be able to apply it more effectively. Youll avoid data anomalies like redundancy and inconsistency. Understanding whats in this book will take your mastery of relational technology to heights you may not have thought possible.

This book is reviewed and endorsed by C. J. Date and features a foreword by the same.

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Table of contents :
Cover Page……Page 1
Title: Applied Mathematics for Database Professionals……Page 2
Contents at a Glance (with page links)……Page 5
PART 1 The Mathematics……Page 8
PART 2 The Application……Page 11
PART 3 The Implementation……Page 13
䄀瀀瀀攀渀搀椀砀攀猀……Page 14
Foreword……Page 16
䄀戀漀甀琀 琀栀攀 䄀甀琀栀漀爀猀……Page 18
䄀戀漀甀琀 琀栀攀 吀攀挀栀渀椀挀愀氀 刀攀瘀椀攀眀攀爀猀……Page 20
Acknowledgments……Page 22
Preface……Page 24
䴀愀琀栀攀洀愀琀椀挀椀愀渀猀……Page 26
䠀椀最栀ⴀ䰀攀瘀攀氀 䈀漀漀欀 伀瘀攀爀瘀椀攀眀……Page 27
䐀愀琀愀戀愀猀攀 䐀攀猀椀最渀 䤀洀瀀氀攀洀攀渀琀愀琀椀漀渀 䤀猀猀甀攀猀……Page 28
PART 1 The Mathematics……Page 30
1 Logic: Introduction……Page 32
吀栀攀 䠀椀猀琀漀爀礀 漀昀 䰀漀最椀挀……Page 33
倀爀漀瀀漀猀椀琀椀漀渀猀 愀渀搀 倀爀攀搀椀挀愀琀攀猀……Page 34
䰀漀最椀挀愀氀 䌀漀渀渀攀挀琀椀瘀攀猀……Page 37
吀爀甀琀栀 吀愀戀氀攀猀……Page 40
䘀甀渀挀琀椀漀渀愀氀 䌀漀洀瀀氀攀琀攀渀攀猀猀……Page 45
匀瀀攀挀椀愀氀 倀爀攀搀椀挀愀琀攀 䌀愀琀攀最漀爀椀攀猀……Page 46
䰀漀最椀挀愀氀 䔀焀甀椀瘀愀氀攀渀挀攀猀 愀渀搀 刀攀眀爀椀琀攀 刀甀氀攀猀……Page 47
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 50
䔀砀攀爀挀椀猀攀猀……Page 51
2 Set Theory: Introduction……Page 52
匀攀琀猀 愀渀搀 䔀氀攀洀攀渀琀猀……Page 53
䴀攀琀栀漀搀猀 琀漀 匀瀀攀挀椀昀礀 匀攀琀猀……Page 55
嘀攀渀渀 䐀椀愀最爀愀洀猀……Page 57
䌀愀爀搀椀渀愀氀椀琀礀 愀渀搀 匀椀渀最氀攀琀漀渀 匀攀琀猀……Page 58
匀甀戀猀攀琀猀……Page 59
唀渀椀漀渀Ⰰ 䤀渀琀攀爀猀攀挀琀椀漀渀Ⰰ 愀渀搀 䐀椀昀昀攀爀攀渀挀攀……Page 60
倀漀眀攀爀猀攀琀猀 愀渀搀 倀愀爀琀椀琀椀漀渀猀……Page 64
伀爀搀攀爀攀搀 倀愀椀爀猀 愀渀搀 䌀愀爀琀攀猀椀愀渀 倀爀漀搀甀挀琀……Page 67
匀甀洀 伀瀀攀爀愀琀漀爀……Page 69
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 70
䔀砀攀爀挀椀猀攀猀……Page 71
䄀氀最攀戀爀愀椀挀 倀爀漀瀀攀爀琀椀攀猀……Page 76
儀甀愀渀琀椀昀椀攀爀猀……Page 80
一漀爀洀愀氀 䘀漀爀洀猀……Page 88
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 92
䔀砀攀爀挀椀猀攀猀……Page 93
4 Relations and Functions……Page 96
䈀椀渀愀爀礀 刀攀氀愀琀椀漀渀猀……Page 97
䘀甀渀挀琀椀漀渀猀……Page 99
伀瀀攀爀愀琀椀漀渀猀 漀渀 䘀甀渀挀琀椀漀渀猀……Page 104
匀攀琀 䘀甀渀挀琀椀漀渀猀……Page 106
䘀甀渀挀琀椀漀渀 䌀漀洀瀀漀猀椀琀椀漀渀……Page 111
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 113
䔀砀攀爀挀椀猀攀猀……Page 114
PART 2 The Application……Page 118
吀攀爀洀椀渀漀氀漀最礀……Page 120
吀愀戀氀攀猀……Page 123
䐀愀琀愀戀愀猀攀 匀琀愀琀攀猀……Page 127
伀瀀攀爀愀琀椀漀渀猀 漀渀 吀愀戀氀攀猀……Page 130
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 142
䔀砀攀爀挀椀猀攀猀……Page 143
6 Tuple, Table, and Database Predicates……Page 146
吀甀瀀氀攀 倀爀攀搀椀挀愀琀攀猀……Page 147
吀愀戀氀攀 倀爀攀搀椀挀愀琀攀猀……Page 149
䐀愀琀愀戀愀猀攀 倀爀攀搀椀挀愀琀攀猀……Page 153
䌀漀洀洀漀渀 倀愀琀琀攀爀渀猀 漀昀 吀愀戀氀攀 愀渀搀 䐀愀琀愀戀愀猀攀 倀爀攀搀椀挀愀琀攀猀……Page 156
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 166
䔀砀攀爀挀椀猀攀猀……Page 167
7 Specifying Database Designs……Page 168
䐀漀挀甀洀攀渀琀椀渀最 䐀愀琀愀戀愀猀攀猀 愀渀搀 䌀漀渀猀琀爀愀椀渀琀猀……Page 169
吀栀攀 䰀愀礀攀爀猀 䤀渀猀椀搀攀 愀 䐀愀琀愀戀愀猀攀 䐀攀猀椀最渀……Page 170
匀瀀攀挀椀昀礀椀渀最 琀栀攀 䔀砀愀洀瀀氀攀 䐀愀琀愀戀愀猀攀 䐀攀猀椀最渀……Page 172
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 211
䔀砀攀爀挀椀猀攀猀……Page 212
䴀漀爀攀 䐀愀琀愀 䤀渀琀攀最爀椀琀礀 倀爀攀搀椀挀愀琀攀猀……Page 214
匀琀愀琀攀 吀爀愀渀猀椀琀椀漀渀 䌀漀渀猀琀爀愀椀渀琀猀……Page 219
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 225
䔀砀攀爀挀椀猀攀猀……Page 226
䘀漀爀洀愀氀氀礀 匀瀀攀挀椀昀礀椀渀最 儀甀攀爀椀攀猀……Page 228
䔀砀愀洀瀀氀攀 儀甀攀爀椀攀猀 伀瘀攀爀 䐀䈀开唀䔀堀……Page 230
䄀 刀攀洀愀爀欀 漀渀 一攀最愀琀椀漀渀猀……Page 245
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 247
䔀砀攀爀挀椀猀攀猀……Page 248
䘀漀爀洀愀氀氀礀 匀瀀攀挀椀昀礀椀渀最 吀爀愀渀猀愀挀琀椀漀渀猀……Page 250
䔀砀愀洀瀀氀攀 吀爀愀渀猀愀挀琀椀漀渀猀 伀瘀攀爀 䐀䈀开唀䔀堀……Page 255
䔀砀攀爀挀椀猀攀猀……Page 265
PART 3 The Implementation……Page 268
11 Implementing Database Designs in Oracle……Page 270
䤀渀琀爀漀搀甀挀琀椀漀渀……Page 271
圀椀渀搀漀眀ⴀ漀渀ⴀ䐀愀琀愀 䄀瀀瀀氀椀挀愀琀椀漀渀猀……Page 272
䤀洀瀀氀攀洀攀渀琀椀渀最 䐀愀琀愀 䤀渀琀攀最爀椀琀礀 䌀漀搀攀……Page 276
䤀洀瀀氀攀洀攀渀琀椀渀最 吀愀戀氀攀 匀琀爀甀挀琀甀爀攀猀……Page 284
䤀洀瀀氀攀洀攀渀琀椀渀最 䄀琀琀爀椀戀甀琀攀 䌀漀渀猀琀爀愀椀渀琀猀……Page 288
䤀洀瀀氀攀洀攀渀琀椀渀最 吀甀瀀氀攀 䌀漀渀猀琀爀愀椀渀琀猀……Page 291
吀愀戀氀攀 䌀漀渀猀琀爀愀椀渀琀 䤀洀瀀氀攀洀攀渀琀愀琀椀漀渀 䤀猀猀甀攀猀……Page 294
䤀洀瀀氀攀洀攀渀琀椀渀最 吀愀戀氀攀 䌀漀渀猀琀爀愀椀渀琀猀……Page 319
䤀洀瀀氀攀洀攀渀琀椀渀最 䐀愀琀愀戀愀猀攀 䌀漀渀猀琀爀愀椀渀琀猀……Page 320
䤀洀瀀氀攀洀攀渀琀椀渀最 吀爀愀渀猀椀琀椀漀渀 䌀漀渀猀琀爀愀椀渀琀猀……Page 325
䈀爀椀渀最椀渀最 䐀攀昀攀爀爀攀搀 䌀栀攀挀欀椀渀最 椀渀琀漀 琀栀攀 倀椀挀琀甀爀攀……Page 328
吀栀攀 刀甀氀攀䜀攀渀 䘀爀愀洀攀眀漀爀欀……Page 332
䌀栀愀瀀琀攀爀 匀甀洀洀愀爀礀……Page 333
匀甀洀洀愀爀礀……Page 334
䌀漀渀挀氀甀猀椀漀渀猀……Page 335
PART 4 Appendixes……Page 338
A: Formal Definition of Example Database I……Page 340
䈀椀爀搀ᤠ猀 䔀礀攀 伀瘀攀爀瘀椀攀眀……Page 341
䐀愀琀愀戀愀猀攀 匀欀攀氀攀琀漀渀 䐀䈀开匀……Page 342
吀愀戀氀攀 唀渀椀瘀攀爀猀攀 䐀攀昀椀渀椀琀椀漀渀猀……Page 343
䐀愀琀愀戀愀猀攀 䌀栀愀爀愀挀琀攀爀椀稀愀琀椀漀渀 䐀䈀䌀䠀……Page 353
䐀愀琀愀戀愀猀攀 唀渀椀瘀攀爀猀攀 䐀䈀开唀䔀堀……Page 354
匀琀愀琀攀 吀爀愀渀猀椀琀椀漀渀 唀渀椀瘀攀爀猀攀 吀堀开唀䔀堀……Page 359
B: Symbols……Page 362
C: Bibliography……Page 364
吀漀 䈀攀 䄀瀀瀀氀椀挀愀戀氀攀 漀爀 一漀琀……Page 366
吀栀爀攀攀 ⠀漀爀 䴀漀爀攀⤀ 嘀愀氀甀攀搀 䰀漀最椀挀……Page 369
䌀栀愀瀀琀攀爀 ㄀ 䄀渀猀眀攀爀猀……Page 376
䌀栀愀瀀琀攀爀 ㈀ 䄀渀猀眀攀爀猀……Page 381
䌀栀愀瀀琀攀爀 ㌀ 䄀渀猀眀攀爀猀……Page 382
䌀栀愀瀀琀攀爀 㐀 䄀渀猀眀攀爀猀……Page 384
䌀栀愀瀀琀攀爀 㔀 䄀渀猀眀攀爀猀……Page 385
䌀栀愀瀀琀攀爀 㘀 䄀渀猀眀攀爀猀……Page 386
䌀栀愀瀀琀攀爀 㜀 䄀渀猀眀攀爀猀……Page 387
䌀栀愀瀀琀攀爀 㠀 䄀渀猀眀攀爀猀……Page 389
䌀栀愀瀀琀攀爀 㤀 䄀渀猀眀攀爀猀……Page 390
䌀栀愀瀀琀攀爀 ㄀　 䄀渀猀眀攀爀猀……Page 393
A,B,C……Page 396
D……Page 397
F……Page 399
L……Page 400
P……Page 401
S……Page 402
T……Page 403
U……Page 404
W……Page 405