Groups, Combinatorics and Geometry (London Mathematical Society Lecture Note)
Since the classification of finite simple groups was announced in 1980 the subject has continued to expand opening many new areas of research. This volume contains a collection of papers, both survey and research, arising from the 1990 Durham conference in which the excellent progress of the decade was surveyed and new goals considered. The material is divided into eight sections: sporadic groups; moonshine; local and geometric methods in group theory; geometries and related groups; finite and a...
A Survey of Binary Systems (Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge, NF 20)
by Richard Hubert Bruck
Invariant Methods in Discrete and Computational Geometry
Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience:...
Sequences, Groups, and Number Theory (Trends in Mathematics)
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by i...
Relationen und Graphen (Mathematik fur Informatiker)
by Gunther Schmidt and Thomas Strohlein
Dieses Buch gibt eine neuartige systematische Darstellung der Diskreten Mathematik; sie orientiert sich an Methoden der Relationenalgebra. Ahnlich wie man es sonst nur fur die weit entwickelte Analysis im kontinuierlichen Fall und die Matrizenrechnung gewohnt ist, stellt dieses Buch auch fur die Behandlung diskreter Probleme geeignete Techniken und Hilfsmittel sowie eine einheitliche Theorie bereit. Die einzelnen Kapitel beginnen jeweils mit anschaulichen und motivierenden Beispielen und behande...
A Lifetime of Excursions Through Random Walks and Lévy Processes (Progress in Probability, #78)
This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area fo...
Mathematical Foundations of Computer Science 1999 (Lecture Notes in Computer Science, #1672)
This volume contains papers selected for presentation during the 24th Interna tional Symposium on Mathematical Foundations of Computer Science held on September 6-10, 1999 in Szklarska Por^ba, Poland. The symposium, organized alternately in the Czech Republic, Slovakia, and Poland, focuses on theoretical aspects and mathematical foundations of computer science. The scientific program of the symposium consists of five invited talks given by Martin Dyer, Dexter Kozen, Giovanni Manzini, Sergio Raj...
Computer Science Logic (Lecture Notes in Computer Science, #832)
by E Borger, Yuri Gurevich, and K Meinke
Knowledge Spaces
The book describes up-to-date applications and relevant theoretical results. These applications come from various places, but the most important one, numerically speaking, is the internet based educational system ALEKS. The ALEKS system is bilingual English-Spanish and covers all of mathematics, from third grade to the end of high school, and chemistry. It is also widely used in higher education because US students are often poorly prepared when they reach the university level. The chapter by Ta...
Walks on Ordinals and Their Characteristics (Progress in Mathematics, #263)
by Stevo Todorcevic
The walks on ordinals and analysis of their characteristics is a subject matter started by the author some twenty years ago in order to disprove a particular extension of the Ramsey theorem. A further analysis has shown however that the resulting method is quite useful in detecting critical mathematical objects in contexts where only rough classifications are possible. The book gives a careful and comprehensive account of the method and gathers many of these applications in a unified and compreh...
Automatic Sequences (De Gruyter Expositions in Mathematics, #36)
by Friedrich von Haeseler
Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and forma...
"Graph Factors and Matching Extensions" deals with two important branches of graph theory - factor theory and extendable graphs. Due to the mature techniques and wide ranges of applications, factors and matchings become useful tools in investigation of many theoretical problems and practical issues. This book includes basic techniques, theoretical foundations, as well as recent advances in the field. It also discusses open problems and conjectures to inspire the readers. This book is primarily a...
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The book’s 20 chapters are grouped into six main areas: algebra...
In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structur...
Les Systemes Dynamiques Discrets (Mathematiques Et Applications, #19)
by Francois Robert
Un systeme dynamique discret est un ensemble fini d'elements, prenant chacun un nombre fini d'etats, et evoluant, dans un temps discret, par interactions mutuelles. Ce livre est consacre a l'analyse de la dynamique temporelle de tels systemes. Grace a des outils de metrique discrete, on etablit des resultats de convergence globale (contraction booleenne) convergence locale vers un point fixe ou vers un cycle, et ceci pour differents modes operatoires.
The Mathematics of Paul Erdos (Algorithms and Combinatorics, #14)
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdos, one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdos' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 900 pages, arranged into two volumes. These volumes contain both high level research articles as well as "key" articles which survey some of the cornersto...
This is a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupli...
Algorithms in Bioinformatics (Lecture Notes in Computer Science, #2149)
We are very pleased to present the proceedings of the First Workshop on Bio- formatics (WABI 2001), which took place in Aarhus on August 28{31, 2001, under the auspices of the European Association for Theoretical Computer S- ence (EATCS) and the Danish Center for Basic Research in Computer Science (BRICS). TheWorkshop onAlgorithmsinBioinformatics coversresearch onallaspects of algorithmic work in bioinformatics. The emphasis is on discrete algorithms that address important problems in molecular...
Il volume fornisce una presentazione della modellistica matematica discreta ed una introduzione all'analisi dei sistemi dinamici discreti. Sono illustrate alcune tecniche per le equazioni alle differenze lineari, si studiano le proprietA qualitative delle soluzioni e la loro struttura nel caso di modelli non lineari, con particolare riferimento alle proprietA di stabilitA . La materia A] presentata in modo unitario, sviluppando dapprima esempi e motivazioni, per poi affrontarne la modellazione,...
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as...
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatmen...
Kombinatorik, Wahrscheinlichkeitsrechnung, Kettenbr che Und Diophantische Gleichungen (Sammlung Schubert)
by Hermann Schubert