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Graph Theory in Memory of G.A. Dirac
This volume is a tribute to the life and mathematical work of G.A. Dirac (1925-1984). One of the leading graph theorists, he developed methods of great originality and made many fundamental discoveries.The forty-two papers are all concerned with (or related to) Dirac's main lines of research. A number of mathematicians pay tribute to his memory by presenting new results in different areas of graph theory. Among the topics included are paths and cycles, hamiltonian graphs, vertex colouring and critical graphs, graphs and surfaces, edge-colouring, and infinite graphs.Some of the papers were originally presented at a meeting held in Denmark in 1985. Attendance being by invitation only, some 55 mathematicians from 14 countries participated in various lectures and discussions on graph theory related to the work of Dirac. This volume contains contributions from others as well, so should not be regarded only as the proceedings of that meeting. A problems section is included, as well as a listing of Dirac's own publications.
Combinatorial Optimization
This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented.
Mastering the History of Pure and Applied Mathematics
The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.
Optical Illusions in Rome: A Mathematical Travel Guide
Optical Illusions in Rome is a beautifully written and richly illustrated guide that takes the reader on a tour through ingenious uses of geometry to create illusory impressions of space and grandeur in Italian Renaissance art and architecture in the Eternal City. The book takes us to some of the most striking and historically important uses of optical illusion and includes works of Peruzzi, Borromini, and Pozzo. The artworks are analyzed geometrically and placed in their historical context. The notes on visiting the art described make the volume the perfect companion for a study trip to Rome. A chapter on the principles of perspective geometry and a collection of exercises make the book a w...
Nexus Network Journal 14,1
The Winter 2012 (vol. 14 no. 1) issue of the Nexus Network Journal is dedicated to the theme “Architecture, Systems Research and Computational Sciences”. This is an outgrowth of the session by the same name which took place during the eighth international, interdisciplinary conference “Nexus 2010: Relationships between Architecture and Mathematics, held in Porto, Portugal, in June 2010. Today computer science is an integral part of even strictly historical investigations, such as those concerning the construction of vaults, where the computer is used to survey the existing building, analyse the data and draw the ideal solution. What the papers in this issue make especially evident is that information technology has had an impact at a much deeper level as well: architecture itself can now be considered as a manifestation of information and as a complex system. The issue is completed with other research papers, conference reports and book reviews.
Nexus Network Journal 14,2
This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.
Digital Wood Design
This book explores various digital representation strategies that could change the future of wooden architectures by blending tradition and innovation. Composed of 61 chapters, written by 153 authors hailing from 5 continents, 24 countries and 69 research centers, it addresses advanced digital modeling, with a particular focus on solutions involving generative models and dynamic value, inherent to the relation between knowing how to draw and how to build. Thanks to the potential of computing, areas like parametric design and digital manufacturing are opening exciting new avenues for the future of construction. The book’s chapters are divided into five sections that connect digital wood design to integrated approaches and generative design; to model synthesis and morphological comprehension; to lessons learned from nature and material explorations; to constructive wisdom and implementation-related challenges; and to parametric transfigurations and morphological optimizations.
Nexus Network Journal 14,3
The Winter 2012 (vol. 14 no. 3) issue of the Nexus Network Journal features seven original papers dedicated to the theme “Digital Fabrication”. Digital fabrication is changing architecture in fundamental ways in every phase, from concept to artifact. Projects growing out of research in digital fabrication are dependent on software that is entirely surface-oriented in its underlying mathematics. Decisions made during design, prototyping, fabrication and assembly rely on codes, scripts, parameters, operating systems and software, creating the need for teams with multidisciplinary expertise and different skills, from IT to architecture, design, material engineering, and mathematics, among others The papers grew out of a Lisbon symposium hosted by the ISCTE-Instituto Universitario de Lisboa entitled “Digital Fabrication – A State of the Art”. The issue is completed with four other research papers which address different mathematical instruments applied to architecture, including geometric tracing systems, proportional systems, descriptive geometry and correspondence analysis. The issue concludes with a book review.
Brooks' Theorem
Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory -- it is mentioned/treated in all general monographs on graph theory. It has sparked research in several directions. This book presents a comprehensive overview of this development and see it in context. It describes results, both early and recent, and explains relations: the various proofs, the many extensions and similar results for other graph parameters. It serves as a valuable reference to a wealth of information, now scattered in journals, proceedings and dissertations. The reader gets easy access to this wealth of information in comprehensive form, including best known proofs of the results described. Each chapter ends in a note section with historical remarks, comments and further results. The book is also suitable for graduate courses in graph theory and includes exercises. The book is intended for readers wanting to dig deeper into graph coloring theory than what is possible in the existing book literature. There is a comprehensive list of references to original sources.
