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06764cam a2200481 i 4500 |
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20250820112757.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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250820t20242024njum ob u001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781394235940 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
139423595X |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1394235968 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
1394235976 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781394235957 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781394235964 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781394235971 |
| Qualifying information |
electronic book |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Cancelled/invalid ISBN |
9781394235940 |
| Qualifying information |
hardcover |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)1429725364 |
| 041 ## - LANGUAGE CODE |
|---|
| Language code of text/sound track or separate title |
eng |
| 042 ## - AUTHENTICATION CODE |
|---|
| Authentication code |
pcc |
| 050 04 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA164 |
| Item number |
.A4693 2024 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
511/.6 |
| Edition number |
23/eng/20240412 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Preferred name for the person |
Alzalg, Baha, |
| Authority record control number |
https://id.loc.gov/authorities/names/n2024013890 |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Combinatorial and algorithmic mathematics : |
| Remainder of title |
from foundation to optimization / |
| Statement of responsibility, etc |
Baha Alzalg, the University of Jordan, Amman, Jordan. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc |
Hoboken, NJ : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
2024. |
| 264 #4 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Date of publication, distribution, etc |
©2024. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 online resource (xxi, 506 pages) : |
| Other physical details |
illustrations (chiefly color) |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent. |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia. |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier. |
| 340 ## - PHYSICAL MEDIUM |
|---|
| Source |
rdacc |
| Authority record control number or standard number |
http://rdaregistry.info/termList/RDAColourContent/1003. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - CONTENTS |
|---|
| Formatted contents note |
Table of Contents<br/>About the Author xiii<br/><br/>Preface xv<br/><br/>Acknowledgments xvii<br/><br/>About the Companion Website xxi<br/><br/>Part I Foundations 1<br/><br/>1 Mathematical Logic 3<br/><br/>1.1 Propositions 3<br/><br/>1.2 Logical Operators 6<br/><br/>1.3 Propositional Formulas 15<br/><br/>1.4 Logical Normal Forms 24<br/><br/>1.5 The Boolean Satisfiability Problem 29<br/><br/>1.6 Predicates and Quantifiers 30<br/><br/>1.7 Symbolizing Statements of the Form "All P Are Q" 37<br/><br/>2 Set-Theoretic Structures 51<br/><br/>2.1 Induction 51<br/><br/>2.2 Sets 54<br/><br/>2.3 Relations 59<br/><br/>2.4 Partitions 64<br/><br/>2.5 Functions 65<br/><br/>3 Analytic and Algebraic Structures 77<br/><br/>3.1 Sequences 77<br/><br/>3.2 Summations and Series 81<br/><br/>3.3 Matrices, Subspaces, and Bases 87<br/><br/>3.4 Convexity, Polyhedra, and Cones 91<br/><br/>3.5 Farkas' Lemma and Its Variants 95<br/><br/>Part II Combinatorics 103<br/><br/>4 Graphs105<br/><br/>4.1 Basic Graph Definitions 106<br/><br/>4.2 Isomorphism and Properties of Graphs 113<br/><br/>4.3 Eulerian and Hamiltonian Graphs 118<br/><br/>4.4 Graph Coloring 122<br/><br/>4.5 Directed Graphs 125<br/><br/>5 Recurrences 133<br/><br/>5.1 Guess-and-Confirm 133<br/><br/>5.2 Recursion-Iteration 136<br/><br/>5.3 Generating Functions 138<br/><br/>5.4 Recursion-Tree 140<br/><br/>6 Counting149<br/><br/>6.1 Binomial Coefficients and Identities 149<br/><br/>6.2 Fundamental Principles of Counting 154<br/><br/>6.3 The Pigeonhole Principle 161<br/><br/>6.4 Permutations 163<br/><br/>6.5 Combinations 166<br/><br/>Part III Algorithms 179<br/><br/>7 Analysis of Algorithms 181<br/><br/>7.1 Constructing and Comparing Algorithms 182<br/><br/>7.2 Running Time of Algorithms 189<br/><br/>7.3 Asymptotic Notation 199<br/><br/>7.4 Analyzing Decision-Making Statements 211<br/><br/>7.5 Analyzing ProgramsWithout Function Calls 213<br/><br/>7.6 Analyzing Programs with Function Calls 219<br/><br/>7.7 The Complexity Class NP-Complete 224<br/><br/>8 Array and Numeric Algorithms 241<br/><br/>8.1 Array Multiplication Algorithms 241<br/><br/>8.2 Array Searching Algorithms 244<br/><br/>8.3 Array Sorting Algorithms 248<br/><br/>8.4 Euclid's Algorithm 253<br/><br/>8.5 Newton's Method Algorithm 255<br/><br/>9 Elementary Combinatorial Algorithms 267<br/><br/>9.1 Graph Representations 267<br/><br/>9.2 Breadth-First Search Algorithm 270<br/><br/>9.3 Applications of Breadth-First Search 273<br/><br/>9.4 Depth-First Search Algorithm 277<br/><br/>9.5 Applications of Depth-First Search 279<br/><br/>9.6 Topological Sort 283<br/><br/>Part IV Optimization 293<br/><br/>10 Linear Programming 295<br/><br/>10.1 Linear Programming Formulation and Examples 296<br/><br/>10.2 The Graphical Method 302<br/><br/>10.3 Standard Form Linear Programs 309<br/><br/>10.4 Geometry of Linear Programming 311<br/><br/>10.5 The Simplex Method 320<br/><br/>10.6 Duality in Linear Programming 339<br/><br/>10.7 A Homogeneous Interior-Point Method 347<br/><br/>11 Second-Order Cone Programming 363<br/><br/>11.1 The Second-Order Cone and Its Algebraic Structure 363<br/><br/>11.2 Second-Order Cone Programming Formulation 368<br/><br/>11.3 Applications in Engineering and Finance 370<br/><br/>11.4 Duality in Second-Order Cone Programming 375<br/><br/>11.5 A Primal-Dual Path-Following Algorithm 379<br/><br/>11.6 A Homogeneous Self-Dual Algorithm 386<br/><br/>12 Semidefinite Programming and Combinatorial Optimization 395<br/><br/>12.1 The Cone of Positive Semidefinite Matrices 395<br/><br/>12.2 Semidefinite Programming Formulation 399<br/><br/>12.3 Applications in Combinatorial Optimization 401<br/><br/>12.4 Duality in Semidefinite Programming 405<br/><br/>12.5 A Primal–Dual Path-Following Algorithm 408<br/><br/>Exercises 417<br/><br/>Notes and Sources 418<br/><br/>References 418<br/><br/>Appendix A Solutions to Chapter Exercises 421<br/><br/>References 487<br/><br/>Bibliography 489<br/><br/>Index 501 |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
"Throughout operations research, computer science and pure and applied mathematics, combinatorics problems arise frequently, where the solution is to find the "optimal" object from a finite set of mathematical objects. Typically, it is impractical to search exhaustively for all possible solutions. The development of efficient algorithms for exploring the solution space is known as combinatorial optimisation. Many problems, such as network optimisation, supply chain management, data compression, resource allocation and game theory - indeed most of machine learning, AI, and current high profile computer science topics rely on optimisation. Together, combinatorial and algorithmic mathematics provide powerful tools for solving these real-world problems, and for in-demand subjects such as data science, machine learning, and artificial intelligence, a unified knowledge of discrete structures, algorithms and combinatorial optimization is considered essential"-- |
| Assigning source |
Provided by publisher. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
|---|
| Biographical or historical note |
About the Author<br/>Baha Alzalg is a Professor in the Department of Mathematics at the University of Jordan in Amman, Jordan. He has also held the post of visiting associate professor in the Department of Computer Science and Engineering at the Ohio State University in Columbus, Ohio. His research interests include topics in optimization theory, applications, and algorithms, with an emphasis on interior-point methods for cone programming. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Algorithms. |
| Authority record control number |
https://id.loc.gov/authorities/subjects/sh85003487. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Combinatorial analysis. |
| Authority record control number |
https://id.loc.gov/authorities/subjects/sh85028802. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Combinatorial optimization. |
| Authority record control number |
https://id.loc.gov/authorities/subjects/sh85028809. |
| 655 #4 - INDEX TERM--GENRE/FORM |
|---|
| Genre/form data or focus term |
Electronic books. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
https://onlinelibrary.wiley.com/doi/book/10.1002/9781394235971 |
| Link text |
Full text is available at Wiley Online Library Click here to view |
| 942 ## - ADDED ENTRY ELEMENTS |
|---|
| Source of classification or shelving scheme |
|
| Item type |
EBOOK |