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The Mathematics of Networks

Edited by: Stefan A. Burr
Available Formats:
Softcover ISBN: 978-0-8218-0031-7
Product Code: PSAPM/26
142 pp
List Price: $33.00 MAA Member Price:$29.70
AMS Member Price: $26.40 Electronic ISBN: 978-0-8218-9241-1 Product Code: PSAPM/26.E 142 pp List Price:$31.00
MAA Member Price: $27.90 AMS Member Price:$24.80
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $49.50 MAA Member Price:$44.55
AMS Member Price: $39.60 Click above image for expanded view The Mathematics of Networks Edited by: Stefan A. Burr Available Formats:  Softcover ISBN: 978-0-8218-0031-7 Product Code: PSAPM/26 142 pp  List Price:$33.00 MAA Member Price: $29.70 AMS Member Price:$26.40
 Electronic ISBN: 978-0-8218-9241-1 Product Code: PSAPM/26.E 142 pp
 List Price: $31.00 MAA Member Price:$27.90 AMS Member Price: $24.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$49.50
MAA Member Price: $44.55 AMS Member Price:$39.60
• Book Details

Proceedings of Symposia in Applied Mathematics
Volume: 261982
MSC: Primary 90;

The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably. A number of more specialized topics are introduced, including areas of active research and a wide variety of applications.

Frank Boesch gives the basic definitions in the mathematics of networks and in the closely-related topic of graph theory. He discusses two of the most fundamental network problems — the shortest path problem and the minimum spanning tree problem as well as some of their variants. Boesch also gives an interesting presentation in the area of network reliability. Frances Yao considers maximum flows in networks, the problem most often thought of in connection with the mathematics of networks. Richard Karp gives an account of the computational complexity of network problems. Using the case study method, Shen Lin demonstrates the effective use of heuristic algorithms in network design. Four applications of the mathematics of networks are presented by Daniel Kleitman. These include: the design of irrigation systems, the theory of electrical networks, the scheduling of delivery trucks, and the physics of ice. Finally, Nicholas Pippenger presents a chapter on telephone switching networks, an area of network theory that leads to difficult mathematics drawn from such apparently unrelated fields as harmonic analysis.

• Articles
• Frank Boesch - Introduction to basic network problems
• Frances Yao - Maximum flows in networks
• R. M. Karp - The computational complexity of network problems
• Shen Lin - Effective use of heuristic algorithms in network design
• Daniel J. Kleitman - Some practical network problems
• Nicholas Pippenger - Telephone switching networks
• Stefan A. Burr - Concluding remarks
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Volume: 261982
MSC: Primary 90;

The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably. A number of more specialized topics are introduced, including areas of active research and a wide variety of applications.

Frank Boesch gives the basic definitions in the mathematics of networks and in the closely-related topic of graph theory. He discusses two of the most fundamental network problems — the shortest path problem and the minimum spanning tree problem as well as some of their variants. Boesch also gives an interesting presentation in the area of network reliability. Frances Yao considers maximum flows in networks, the problem most often thought of in connection with the mathematics of networks. Richard Karp gives an account of the computational complexity of network problems. Using the case study method, Shen Lin demonstrates the effective use of heuristic algorithms in network design. Four applications of the mathematics of networks are presented by Daniel Kleitman. These include: the design of irrigation systems, the theory of electrical networks, the scheduling of delivery trucks, and the physics of ice. Finally, Nicholas Pippenger presents a chapter on telephone switching networks, an area of network theory that leads to difficult mathematics drawn from such apparently unrelated fields as harmonic analysis.