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Discrete Algorithmic Mathematics : Ak Peters Ser. - Stephen B. Maurer

Discrete Algorithmic Mathematics

Ak Peters Ser.


Published: 1st August 2004
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Thoroughly revised for a one-semester course, this well-known and highly regarded book is an outstanding text for undergraduate discrete mathematics. It has been updated with new or extended discussions of order notation, generating functions, chaos, aspects of statistics, and computational biology. Written in a lively, clear style that talks to the reader, the book is unique for its emphasis on algorithmics and the inductive and recursive paradigms as central mathematical themes. It includes a broad variety of applications, not just to mathematics and computer science, but to natural and social science as well. A manual of selected solutions is available for sale to students; see sidebar. A complete solution manual is available free to instructors who have adopted the book as a required text. To request a copy of the complete solutions contact Susannah Sieper at 303-817-1996 or email marketing@akpeters.com. The authors have created an Errata sheet, which they update periodically. Selected excerpts are available for evaluation: - Contents - Instructor's Preface - Chapter Summaries - Recursive Algorithms - Induction and Recursive Algorithms - Shortest Paths - Combinatorial Identities and Combinatorial Arguments

The exposition is self-contained, complemented by diverse exercises and also accompanied by an introduction to mathematical reasoning ! this book is an excellent textbook for a one-semester undergraduate course and it includes a lot of additional material to choose from. --EMS, March 2006 In a textbook, it is necessary to select carefully the statements and difficulty of the problems ! in this textbook, this is fully achieved ! This review considers this book an excellent one. --The Mathematical Gazette, March 2006

List of Algorithms
Instructor's Prefacep. ix
Student's Prefacep. xiv
Chapter Summariesp. xvii
Pathways Through the Bookp. xx
Problem Difficulty Ratingp. xxii
Symbols, Notation, Abbreviations and Conventionsp. xxiii
Prologue: What Is Discrete Algorithmic Mathematics?p. 1
Mathematical Preliminariesp. 9
Sets, Relations, and Functionsp. 9
Some Important Functionsp. 20
Growth Rates and Order Notationp. 30
Summation and Product Notationp. 40
Matrix Algebrap. 50
The Language and Methods of Reasoningp. 56
Supplementary Problemsp. 69
Algorithmsp. 73
Some Examples of Algorithmsp. 73
Aspects of ALp. 88
Recursive Algorithmsp. 94
Algorithmic Language: Procedures and Functionsp. 105
The Analysis of Algorithmsp. 117
Supplementary Problemsp. 131
Mathematical Inductionp. 135
Introductionp. 135
First Examplesp. 137
Strong Induction and Other Variantsp. 151
Induction and Recursive Algorithmsp. 158
Induction and Iterative Algorithmsp. 168
How to Conjecture What to Provep. 180
Inductive Definitionsp. 194
Faulty Inductionsp. 201
Supplementary Problemsp. 210
Graphs and Treesp. 217
Examples and Terminologyp. 217
Paths, Cycles and the Adjacency Matrixp. 236
Eulerian and Hamiltonian Paths and Cyclesp. 250
Shortest Pathsp. 266
Breadth First Search and Depth First Searchp. 278
Coloring Problemsp. 285
Treesp. 296
Supplementary Problemsp. 311
Fundamental Counting Methodsp. 321
Introductionp. 321
First Examples: The Sum and Product Rulesp. 322
Subtler Examples and Further Rulesp. 329
Permutations and Combinationsp. 341
Combinatorial Identities and Combinatorial Argumentsp. 348
The Binomial Theoremp. 355
Four Common Problems with Balls and Urnsp. 365
Generating Functionsp. 375
Combinatorial Algorithmsp. 385
Algorithmic Pigeonholesp. 399
Supplementary Problemsp. 406
Difference Equationsp. 411
Introductionp. 411
Modeling with Difference Equationsp. 413
Getting Information from Difference Equationsp. 426
Terminology and a Fundamental Theoremp. 433
Constant Coefficient Homogeneous Linear Difference Equationsp. 439
Qualitative Analysisp. 451
Nonhomogeneous Difference Equationsp. 457
Applications to Algorithmsp. 462
Variable Coefficients, Sums, and Recent Advances in Computer Algebrap. 479
Nonlinear Difference Equationsp. 484
Finite Differencesp. 495
Supplementary Problemsp. 508
Probabilityp. 513
Introductionp. 513
Probability Spacep. 517
Conditional Probability, Independence, and Bayes' Theoremp. 527
Random Variables and Distributionsp. 539
Expected Valuep. 557
Variancep. 569
Statistical Estimationp. 577
Applications to Algorithms: Proofs of Prior Claimsp. 586
Recursive Methods in Probabilityp. 595
Supplementary Problemsp. 606
An Introduction to Mathematical Logicp. 611
Introduction and Terminologyp. 611
The Propositional Calculusp. 616
Validity and Tautologyp. 630
Algorithm Verificationp. 637
Boolean Algebrap. 643
The Predicate Calculusp. 663
Algorithm Verification Using the Predicate Calculusp. 676
Theorems and Proofsp. 682
Supplementary Problemsp. 689
Epilogue: Coming Full Circle with Biology and Minimax Theoremsp. 691
DNA Matchingp. 691
Algorithmic Mathematics and Minimax Theoremsp. 707
Final Problemsp. 717
Referencesp. 723
Limitsp. 729
Hints and Answersp. 733
Indexp. 761
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781568811666
ISBN-10: 1568811667
Series: Ak Peters Ser.
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 803
Published: 1st August 2004
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 24.77 x 19.68  x 5.08
Weight (kg): 1.68
Edition Number: 3
Edition Type: New edition