Matroids: A Geometric Introduction

Matroids: A Geometric Introduction
Author :
Publisher : Cambridge University Press
Total Pages : 411
Release :
ISBN-10 : 9780521145688
ISBN-13 : 0521145686
Rating : 4/5 (88 Downloads)

Synopsis Matroids: A Geometric Introduction by : Gary Gordon

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Matroid Theory

Matroid Theory
Author :
Publisher : OUP Oxford
Total Pages : 0
Release :
ISBN-10 : 0199603391
ISBN-13 : 9780199603398
Rating : 4/5 (91 Downloads)

Synopsis Matroid Theory by : James Oxley

This major revision of James Oxley's classic Matroid Theory provides a comprehensive introduction to the subject, covering the basics to more advanced topics. With over 700 exercises and proofs of all relevant major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science.

Matroid Theory

Matroid Theory
Author :
Publisher : Courier Corporation
Total Pages : 450
Release :
ISBN-10 : 9780486474397
ISBN-13 : 0486474399
Rating : 4/5 (97 Downloads)

Synopsis Matroid Theory by : D. J. A. Welsh

The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.

Theory of Matroids

Theory of Matroids
Author :
Publisher : Cambridge University Press
Total Pages : 341
Release :
ISBN-10 : 9780521309370
ISBN-13 : 0521309379
Rating : 4/5 (70 Downloads)

Synopsis Theory of Matroids by : Neil White

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

Matroid Theory and its Applications in Electric Network Theory and in Statics

Matroid Theory and its Applications in Electric Network Theory and in Statics
Author :
Publisher : Springer Science & Business Media
Total Pages : 542
Release :
ISBN-10 : 9783662221433
ISBN-13 : 3662221438
Rating : 4/5 (33 Downloads)

Synopsis Matroid Theory and its Applications in Electric Network Theory and in Statics by : Andras Recski

I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen eral tools that can be learned and then applied, to various problems. Matroid theory is one of these tools. (2) Within combinatorics, the relative importance of algorithms has in creased with the spread of computers. Classical analysis did not even consider problems where "only" a finite number of cases were to be studied. Now such problems are not only considered, but their complexity is often analyzed in con siderable detail. Some questions of this type (for example, the determination of when the so called "greedy" algorithm is optimal) cannot even be answered without matroidal tools.

Matrices and Matroids for Systems Analysis

Matrices and Matroids for Systems Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 500
Release :
ISBN-10 : 3540660240
ISBN-13 : 9783540660248
Rating : 4/5 (40 Downloads)

Synopsis Matrices and Matroids for Systems Analysis by : Kazuo Murota

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

A Source Book in Matroid Theory

A Source Book in Matroid Theory
Author :
Publisher :
Total Pages : 424
Release :
ISBN-10 : UCSD:31822002756054
ISBN-13 :
Rating : 4/5 (54 Downloads)

Synopsis A Source Book in Matroid Theory by : Joseph P. S. Kung

Topics in Matroid Theory

Topics in Matroid Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 138
Release :
ISBN-10 : 9781461489573
ISBN-13 : 1461489571
Rating : 4/5 (73 Downloads)

Synopsis Topics in Matroid Theory by : Leonidas S. Pitsoulis

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

Combinatorial Optimization

Combinatorial Optimization
Author :
Publisher : Courier Corporation
Total Pages : 404
Release :
ISBN-10 : 9780486143668
ISBN-13 : 048614366X
Rating : 4/5 (68 Downloads)

Synopsis Combinatorial Optimization by : Eugene Lawler

Perceptive text examines shortest paths, network flows, bipartite and nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. Suitable for courses in combinatorial computing and concrete computational complexity.

A Lost Mathematician, Takeo Nakasawa

A Lost Mathematician, Takeo Nakasawa
Author :
Publisher : Springer Science & Business Media
Total Pages : 238
Release :
ISBN-10 : 9783764385736
ISBN-13 : 3764385731
Rating : 4/5 (36 Downloads)

Synopsis A Lost Mathematician, Takeo Nakasawa by : Hirokazu Nishimura

Matroid theory was invented in the middle of the 1930s by two mathematicians independently, namely, Hassler Whitney in the USA and Takeo Nakasawa in Japan. Whitney became famous, but Nakasawa remained anonymous until two decades ago. He left only four papers to the mathematical community, all of them written in the middle of the 1930s. It was a bad time to have lived in a country that had become as eccentric as possible. Just as Nazism became more and more flamboyant in Europe in the 1930s, Japan became more and more esoteric and fanatical in the same time period. This book explains the little that is known about Nakasawa’s personal life in a Japan that had, among other failures, lost control over its military. This book contains his four papers in German and their English translations as well as some extended commentary on the history of Japan during those years. The book also contains 14 photos of him or his family. Although the veil of mystery surrounding Nakasawa’s life has only been partially lifted, the work presented in this book speaks eloquently of a tragic loss to the mathematical community.