x

Our Privacy Policy has changed. By using this site, you agree to the Privacy Policy.

Mathematics A Discrete Introduction

ISBN-10: 0534356389
ISBN-13: 9780534356385
Edition: 2000
List price: $160.95
30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Learn more about our returns policy

Description: 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  More...

what's this?
Rush Rewards U
Members Receive:
coins
coins
You have reached 400 XP and carrot coins. That is the daily max!
You could win $10,000

Get an entry for every item you buy, rent, or sell.

Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Add to cart
Study Briefs
Calculus 1 Online content $4.95 $1.99
Add to cart
Study Briefs
Algebra Online content $4.95 $1.99
Add to cart
Study Briefs
Introduction to Logic Online content $4.95 $1.99
Add to cart
Study Briefs
Business Math Formulas Online content $4.95 $1.99

Customers also bought

Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading

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

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.

Fundamentalsp. 1
Definitionp. 1
Recapp. 4
Exercisesp. 4
Theoremp. 7
The Nature of Truthp. 7
If-Thenp. 9
If and Only Ifp. 11
And, Or, and Notp. 12
What Theorems Are Calledp. 13
Vacuous Truthp. 13
Recapp. 14
Exercisesp. 14
Proofp. 15
Proving If-and-Only-If Theoremsp. 19
Recapp. 22
Exercisesp. 22
Counterexamplep. 22
Recapp. 24
Exercisesp. 24
Boolean Algebrap. 25
More Operationsp. 28
Recapp. 29
Exercisesp. 29
Collectionsp. 33
Listsp. 33
Counting Two-Element Listsp. 34
Longer Listsp. 36
Recapp. 40
Exercisesp. 40
Factorialp. 41
Much Ado about 0!p. 42
Product Notationp. 43
Recapp. 44
Exercisesp. 44
Sets I: Introduction, Subsetsp. 46
Relationships Between Setsp. 47
Counting Subsetsp. 49
Power Setp. 50
Recapp. 51
Exercisesp. 51
Quantifiersp. 52
There Isp. 52
For Allp. 53
Negating Quantified Statementsp. 54
Combining Quantifiersp. 55
Recapp. 56
Exercisesp. 56
Sets II: Operationsp. 58
Union and Intersectionp. 58
The Size of a Unionp. 60
Difference and Symmetric Differencep. 63
Cartesian Productp. 67
Recapp. 68
Exercisesp. 68
Counting and Relationsp. 72
Relationsp. 72
Properties of Relationsp. 75
Recapp. 76
Exercisesp. 76
Equivalence Relationsp. 78
Equivalence Classesp. 82
Recapp. 85
Exercisesp. 85
Partitionsp. 87
Counting Classes/Partsp. 90
Recapp. 93
Exercisesp. 93
Binomial Coefficientsp. 94
Calculating (n k)p. 98
Pascal's Trianglep. 100
A Formula for (n k)p. 102
Recapp. 104
Exercisesp. 104
Counting Multisetsp. 108
Multisetsp. 109
Formulas for ((n k))p. 110
Recapp. 114
Exercisesp. 114
Inclusion-Exclusionp. 116
How to Use Inclusion-Exclusionp. 119
Derangementsp. 121
A Ghastly Formulap. 124
Recapp. 124
Exercisesp. 124
More Proofp. 126
Contradictionp. 126
Proof by Contrapositivep. 126
Reductio ad Absurdump. 128
A Matter of Stylep. 132
Recapp. 132
Exercisesp. 132
Smallest Counterexamplep. 133
Well-Orderingp. 139
Recapp. 145
Exercisesp. 145
And Finallyp. 146
Inductionp. 146
Strong Inductionp. 149
A More Complicated Examplep. 151
Recapp. 154
Exercisesp. 154
A Matter of Stylep. 157
Functionsp. 158
Functionsp. 158
Domain and Imagep. 160
Pictures of Functionsp. 161
Counting Functionsp. 162
Inverse Functionsp. 163
Counting Functions, Againp. 167
Recapp. 169
Exercisesp. 169
The Pigeonhole Principlep. 171
Cantor's Theoremp. 174
Recapp. 176
Exercisesp. 176
Compositionp. 177
Identity Functionp. 180
Recapp. 181
Exercisesp. 181
Permutationsp. 183
Cycle Notationp. 184
Calculations with Permutationsp. 187
Transpositionsp. 188
Recapp. 193
Exercisesp. 194
Symmetryp. 196
Symmetries of a Squarep. 196
Symmetries as Permutationsp. 198
Combining Symmetriesp. 198
Formal Definition of Symmetryp. 200
Recapp. 201
Exercisesp. 201
Assorted Notationp. 202
Big Ohp. 202
[Omega] and [Theta]p. 205
Little Ohp. 206
Floor and Ceilingp. 207
Recapp. 208
Exercisesp. 208
Probabilityp. 209
Sample Spacep. 209
Recapp. 212
Exercisesp. 212
Eventsp. 213
Combining Eventsp. 216
The Birthday Problemp. 218
Recapp. 219
Exercisesp. 219
Conditional Probability and Independencep. 221
Independencep. 223
Independent Repeated Trialsp. 226
The Monty Hall Problemp. 227
Recapp. 228
Exercisesp. 228
Random Variablesp. 231
Random Variables as Eventsp. 232
Independent Random Variablesp. 234
Recapp. 235
Exercisesp. 235
Expectationp. 236
Linearity of Expectationp. 241
Product of Random Variablesp. 245
Expected Value as a Measure of Centralityp. 248
Variancep. 249
Recapp. 252
Exercisesp. 253
Number Theoryp. 255
Dividingp. 255
Div and Modp. 258
Recapp. 259
Exercisesp. 259
Greatest Common Divisorp. 260
Calculating the gcdp. 261
Correctnessp. 263
How Fast?p. 264
An Important Theoremp. 266
Recapp. 269
Exercisesp. 269
Modular Arithmeticp. 271
A New Context for Basic Operationsp. 271
Modular Addition and Multiplicationp. 272
Modular Subtractionp. 274
Modular Divisionp. 275
A Note on Notationp. 280
Recapp. 280
Exercisesp. 281
The Chinese Remainder Theoremp. 283
Solving One Equationp. 283
Solving Two Equationsp. 285
Recapp. 287
Exercisesp. 287
Factoringp. 288
Infinitely Many Primesp. 290
A Formula for Greatest Common Divisorp. 291
Irrationality of [square root]2p. 292
Recapp. 294
Exercisesp. 294
Algebrap. 299
Groupsp. 299
Operationsp. 299
Properties of Operationsp. 300
Groupsp. 302
Examplesp. 304
Recapp. 308
Exercisesp. 308
Group Isomorphismp. 310
The Same?p. 310
Cyclic Groupsp. 312
Recapp. 315
Exercisesp. 315
Subgroupsp. 316
LaGrange's Theoremp. 319
Recapp. 323
Exercisesp. 323
Fermat's Little Theoremp. 325
First Proofp. 326
Second Proofp. 327
Third Proofp. 330
Euler's Theoremp. 331
Primality Testingp. 332
Recapp. 333
Exercisesp. 333
Public-Key Cryptography I: Introductionp. 334
The Problem: Private Communication in Publicp. 334
Factoringp. 334
Words to Numbersp. 335
Cryptography and the Lawp. 337
Recapp. 337
Exercisesp. 337
Public-Key Cryptography II: Rabin's Methodp. 337
Square Roots Modulo np. 338
The Encryption and Decryption Proceduresp. 343
Recapp. 343
Exercisesp. 343
Public-Key Cryptography III: RSAp. 345
The RSA Encryption and Decryption Functionsp. 345
Securityp. 347
Recapp. 349
Exercisesp. 349
Graphsp. 351
Graph Theory Fundamentalsp. 351
Map Coloringp. 351
Three Utilitiesp. 353
Seven Bridgesp. 353
What Is a Graph?p. 354
Adjacencyp. 355
A Matter of Degreep. 357
Further Notation and Vocabularyp. 359
Recapp. 359
Exercisesp. 360
Subgraphsp. 362
Induced and Spanning Subgraphsp. 362
Cliques and Independent Setsp. 365
Complementsp. 366
Recapp. 367
Exercisesp. 368
Connectionp. 369
Walksp. 369
Pathsp. 370
Disconnectionp. 374
Recapp. 375
Exercisesp. 375
Treesp. 377
Cyclesp. 377
Forests and Treesp. 377
Properties of Treesp. 378
Leavesp. 380
Spanning Treesp. 382
Recapp. 383
Exercisesp. 383
Eulerian Graphsp. 385
Necessary Conditionsp. 386
Main Theoremsp. 387
Unfinished Businessp. 390
Recapp. 390
Exercisesp. 390
Coloringp. 391
Core Conceptsp. 392
Bipartite Graphsp. 394
The Ease of Two-Coloring and the Difficulty of Three-Coloringp. 398
Recapp. 399
Exercisesp. 399
Planar Graphsp. 400
Dangerous Curvesp. 400
Embeddingp. 401
Euler's Formulap. 402
Nonplanar Graphsp. 405
Coloring Planar Graphsp. 406
Recapp. 409
Exercisesp. 409
Partially Ordered Setsp. 411
Partially Ordered Sets Fundamentalsp. 411
What Is a Poset?p. 411
Notation and Languagep. 414
Recapp. 416
Exercisesp. 416
Max and Minp. 417
Recapp. 419
Exercisesp. 419
Linear Ordersp. 420
Recapp. 423
Exercisesp. 423
Linear Extensionsp. 423
Sortingp. 427
Linear Extensions of Infinite Posetsp. 429
Recapp. 430
Exercisesp. 430
Dimensionp. 431
Realizersp. 431
Dimensionp. 434
Embeddingp. 436
Recapp. 438
Exercisesp. 439
Latticesp. 439
Meet and Joinp. 439
Latticesp. 442
Recapp. 445
Exercisesp. 445
Appendicesp. 447
Lots of Hints and Comments; Some Answersp. 447
Glossaryp. 469
Fundamentalsp. 476
Numbersp. 476
Operationsp. 476
Orderingp. 476
Substitutionp. 477
Indexp. 479
Table of Contents provided by Syndetics. All Rights Reserved.

×
Free shipping on orders over $35*

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

Learn more about the TextbookRush Marketplace.

×