Mathematics A Discrete Introduction

Name: Mathematics A Discrete Introduction
Price: 128.21 USD
Availability: InStock
ISBN: 9780534356385

ISBN-10: 0534356389

ISBN-13: 9780534356385

Edition: 2000

Authors: Edward A. Scheinerman

List price: $160.95

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This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics. There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics.

Book details

List price: $160.95
Copyright year: 2000
Publisher: Brooks/Cole
Publication date: 1/12/2000
Binding: Hardcover
Pages: 512
Size: 7.50" wide x 9.50" long x 1.00" tall
Weight: 2.046
Language: English

Fundamentals	p. 1
Definition	p. 1
Recap	p. 4
Exercises	p. 4
Theorem	p. 7
The Nature of Truth	p. 7
If-Then	p. 9
If and Only If	p. 11
And, Or, and Not	p. 12
What Theorems Are Called	p. 13
Vacuous Truth	p. 13
Recap	p. 14
Exercises	p. 14
Proof	p. 15
Proving If-and-Only-If Theorems	p. 19
Recap	p. 22
Exercises	p. 22
Counterexample	p. 22
Recap	p. 24
Exercises	p. 24
Boolean Algebra	p. 25
More Operations	p. 28
Recap	p. 29
Exercises	p. 29
Collections	p. 33
Lists	p. 33
Counting Two-Element Lists	p. 34
Longer Lists	p. 36
Recap	p. 40
Exercises	p. 40
Factorial	p. 41
Much Ado about 0!	p. 42
Product Notation	p. 43
Recap	p. 44
Exercises	p. 44
Sets I: Introduction, Subsets	p. 46
Relationships Between Sets	p. 47
Counting Subsets	p. 49
Power Set	p. 50
Recap	p. 51
Exercises	p. 51
Quantifiers	p. 52
There Is	p. 52
For All	p. 53
Negating Quantified Statements	p. 54
Combining Quantifiers	p. 55
Recap	p. 56
Exercises	p. 56
Sets II: Operations	p. 58
Union and Intersection	p. 58
The Size of a Union	p. 60
Difference and Symmetric Difference	p. 63
Cartesian Product	p. 67
Recap	p. 68
Exercises	p. 68
Counting and Relations	p. 72
Relations	p. 72
Properties of Relations	p. 75
Recap	p. 76
Exercises	p. 76
Equivalence Relations	p. 78
Equivalence Classes	p. 82
Recap	p. 85
Exercises	p. 85
Partitions	p. 87
Counting Classes/Parts	p. 90
Recap	p. 93
Exercises	p. 93
Binomial Coefficients	p. 94
Calculating (n k)	p. 98
Pascal's Triangle	p. 100
A Formula for (n k)	p. 102
Recap	p. 104
Exercises	p. 104
Counting Multisets	p. 108
Multisets	p. 109
Formulas for ((n k))	p. 110
Recap	p. 114
Exercises	p. 114
Inclusion-Exclusion	p. 116
How to Use Inclusion-Exclusion	p. 119
Derangements	p. 121
A Ghastly Formula	p. 124
Recap	p. 124
Exercises	p. 124
More Proof	p. 126
Contradiction	p. 126
Proof by Contrapositive	p. 126
Reductio ad Absurdum	p. 128
A Matter of Style	p. 132
Recap	p. 132
Exercises	p. 132
Smallest Counterexample	p. 133
Well-Ordering	p. 139
Recap	p. 145
Exercises	p. 145
And Finally	p. 146
Induction	p. 146
Strong Induction	p. 149
A More Complicated Example	p. 151
Recap	p. 154
Exercises	p. 154
A Matter of Style	p. 157
Functions	p. 158
Functions	p. 158
Domain and Image	p. 160
Pictures of Functions	p. 161
Counting Functions	p. 162
Inverse Functions	p. 163
Counting Functions, Again	p. 167
Recap	p. 169
Exercises	p. 169
The Pigeonhole Principle	p. 171
Cantor's Theorem	p. 174
Recap	p. 176
Exercises	p. 176
Composition	p. 177
Identity Function	p. 180
Recap	p. 181
Exercises	p. 181
Permutations	p. 183
Cycle Notation	p. 184
Calculations with Permutations	p. 187
Transpositions	p. 188
Recap	p. 193
Exercises	p. 194
Symmetry	p. 196
Symmetries of a Square	p. 196
Symmetries as Permutations	p. 198
Combining Symmetries	p. 198
Formal Definition of Symmetry	p. 200
Recap	p. 201
Exercises	p. 201
Assorted Notation	p. 202
Big Oh	p. 202
[Omega] and [Theta]	p. 205
Little Oh	p. 206
Floor and Ceiling	p. 207
Recap	p. 208
Exercises	p. 208
Probability	p. 209
Sample Space	p. 209
Recap	p. 212
Exercises	p. 212
Events	p. 213
Combining Events	p. 216
The Birthday Problem	p. 218
Recap	p. 219
Exercises	p. 219
Conditional Probability and Independence	p. 221
Independence	p. 223
Independent Repeated Trials	p. 226
The Monty Hall Problem	p. 227
Recap	p. 228
Exercises	p. 228
Random Variables	p. 231
Random Variables as Events	p. 232
Independent Random Variables	p. 234
Recap	p. 235
Exercises	p. 235
Expectation	p. 236
Linearity of Expectation	p. 241
Product of Random Variables	p. 245
Expected Value as a Measure of Centrality	p. 248
Variance	p. 249
Recap	p. 252
Exercises	p. 253
Number Theory	p. 255
Dividing	p. 255
Div and Mod	p. 258
Recap	p. 259
Exercises	p. 259
Greatest Common Divisor	p. 260
Calculating the gcd	p. 261
Correctness	p. 263
How Fast?	p. 264
An Important Theorem	p. 266
Recap	p. 269
Exercises	p. 269
Modular Arithmetic	p. 271
A New Context for Basic Operations	p. 271
Modular Addition and Multiplication	p. 272
Modular Subtraction	p. 274
Modular Division	p. 275
A Note on Notation	p. 280
Recap	p. 280
Exercises	p. 281
The Chinese Remainder Theorem	p. 283
Solving One Equation	p. 283
Solving Two Equations	p. 285
Recap	p. 287
Exercises	p. 287
Factoring	p. 288
Infinitely Many Primes	p. 290
A Formula for Greatest Common Divisor	p. 291
Irrationality of [square root]2	p. 292
Recap	p. 294
Exercises	p. 294
Algebra	p. 299
Groups	p. 299
Operations	p. 299
Properties of Operations	p. 300
Groups	p. 302
Examples	p. 304
Recap	p. 308
Exercises	p. 308
Group Isomorphism	p. 310
The Same?	p. 310
Cyclic Groups	p. 312
Recap	p. 315
Exercises	p. 315
Subgroups	p. 316
LaGrange's Theorem	p. 319
Recap	p. 323
Exercises	p. 323
Fermat's Little Theorem	p. 325
First Proof	p. 326
Second Proof	p. 327
Third Proof	p. 330
Euler's Theorem	p. 331
Primality Testing	p. 332
Recap	p. 333
Exercises	p. 333
Public-Key Cryptography I: Introduction	p. 334
The Problem: Private Communication in Public	p. 334
Factoring	p. 334
Words to Numbers	p. 335
Cryptography and the Law	p. 337
Recap	p. 337
Exercises	p. 337
Public-Key Cryptography II: Rabin's Method	p. 337
Square Roots Modulo n	p. 338
The Encryption and Decryption Procedures	p. 343
Recap	p. 343
Exercises	p. 343
Public-Key Cryptography III: RSA	p. 345
The RSA Encryption and Decryption Functions	p. 345
Security	p. 347
Recap	p. 349
Exercises	p. 349
Graphs	p. 351
Graph Theory Fundamentals	p. 351
Map Coloring	p. 351
Three Utilities	p. 353
Seven Bridges	p. 353
What Is a Graph?	p. 354
Adjacency	p. 355
A Matter of Degree	p. 357
Further Notation and Vocabulary	p. 359
Recap	p. 359
Exercises	p. 360
Subgraphs	p. 362
Induced and Spanning Subgraphs	p. 362
Cliques and Independent Sets	p. 365
Complements	p. 366
Recap	p. 367
Exercises	p. 368
Connection	p. 369
Walks	p. 369
Paths	p. 370
Disconnection	p. 374
Recap	p. 375
Exercises	p. 375
Trees	p. 377
Cycles	p. 377
Forests and Trees	p. 377
Properties of Trees	p. 378
Leaves	p. 380
Spanning Trees	p. 382
Recap	p. 383
Exercises	p. 383
Eulerian Graphs	p. 385
Necessary Conditions	p. 386
Main Theorems	p. 387
Unfinished Business	p. 390
Recap	p. 390
Exercises	p. 390
Coloring	p. 391
Core Concepts	p. 392
Bipartite Graphs	p. 394
The Ease of Two-Coloring and the Difficulty of Three-Coloring	p. 398
Recap	p. 399
Exercises	p. 399
Planar Graphs	p. 400
Dangerous Curves	p. 400
Embedding	p. 401
Euler's Formula	p. 402
Nonplanar Graphs	p. 405
Coloring Planar Graphs	p. 406
Recap	p. 409
Exercises	p. 409
Partially Ordered Sets	p. 411
Partially Ordered Sets Fundamentals	p. 411
What Is a Poset?	p. 411
Notation and Language	p. 414
Recap	p. 416
Exercises	p. 416
Max and Min	p. 417
Recap	p. 419
Exercises	p. 419
Linear Orders	p. 420
Recap	p. 423
Exercises	p. 423
Linear Extensions	p. 423
Sorting	p. 427
Linear Extensions of Infinite Posets	p. 429
Recap	p. 430
Exercises	p. 430
Dimension	p. 431
Realizers	p. 431
Dimension	p. 434
Embedding	p. 436
Recap	p. 438
Exercises	p. 439
Lattices	p. 439
Meet and Join	p. 439
Lattices	p. 442
Recap	p. 445
Exercises	p. 445
Appendices	p. 447
Lots of Hints and Comments; Some Answers	p. 447
Glossary	p. 469
Fundamentals	p. 476
Numbers	p. 476
Operations	p. 476
Ordering	p. 476
Substitution	p. 477
Index	p. 479
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