Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999

Mathematics. --- Mathematics, general. --- Number Theory. --- Geometry. --- Combinatorics. --- Analysis. --- Computer Science, general. --- Mathematics. --- Computer science. --- Global analysis (Mathematics). --- Combinatorics. --- Geometry. --- Number theory. --- Mathématiques --- Informatique --- Analyse globale (Mathématiques) --- Géométrie --- Théorie des nombres

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time. The book is aimed at graduate students and researchers who want to learn about this topic without reading all the original articles. The primary proof techniques used involve linear algebraic arguments, finite field arithmetic, some elementary number theory, and combinatorial enumeration. Some computer results not previously found in the literature also are mentioned in the text. The authors have included a comprehensive bibliography which will become an invaluable resource. Gary Ebert is Professor of Mathematics at the University of Delaware, USA. Susan Barwick is a Senior Lecturer of Mathematics at the University of Adelaide, Australia. .

Mathematics. --- Group Theory and Generalizations. --- Algebra. --- Combinatorics. --- Geometry. --- Group theory. --- Mathématiques --- Algèbre --- Groupes, Théorie des --- Géométrie --- Projective planes. --- Manifolds (Mathematics). --- Nets (Mathematics). --- Surfaces, Algebraic. --- Projective planes --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Théorie des groupes --- Geometry, Projective. --- Projective geometry --- Planes, Projective --- Combinatorics --- Algebra --- Mathematical analysis --- Euclid's Elements --- Groups, Theory of --- Substitutions (Mathematics) --- Math --- Science --- Geometry, Modern --- Geometry, Projective

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications. Key features: * Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees * Subsequent chapters examine specialized topics and applications * Numerous examples and illustrations * Comprehensive index and bibliography, with suggested literature for more advanced material New to the second edition: * New chapters on labeling and on communications networks and small-worlds * Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems * Many additional changes, improvements, and corrections throughout resulting from classroom use and feedback Striking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites. ----- From a review of the first edition: "Altogether the book gives a comprehensive introduction to graphs, their theory and their application…The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well… It is very useful that the solutions of these exercises are collected in an appendix." —Simulation News Europe.

Graph theory --- Combinatorial analysis --- Théorie des graphes --- Analyse combinatoire --- Algorithms. --- Electronic books. -- local. --- Graph theory. --- Mathematics --- Algebra --- Physical Sciences & Mathematics --- 519.1 --- Graphs, Theory of --- Theory of graphs --- Topology --- Combinatorics. Graph theory --- Extremal problems --- 519.1 Combinatorics. Graph theory --- Graphes, Théorie des --- Théorie des graphes --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Algorism --- Mathematics. --- Algebra. --- Matrix theory. --- Applied mathematics. --- Engineering mathematics. --- Mathematical logic. --- Discrete mathematics. --- Combinatorics. --- Discrete Mathematics. --- Applications of Mathematics. --- Mathematical Logic and Foundations. --- Linear and Multilinear Algebras, Matrix Theory. --- Arithmetic --- Foundations --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Math --- Science --- Combinatorics --- Mathematical analysis --- Graphes, Théorie des. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Engineering --- Engineering analysis --- Théorie des graphes.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Near polygons were introduced about 25 years ago and studied intensively in the 1980s. In recent years the subject has regained interest. This monograph gives an extensive overview of the basic theory of general near polygons. The first part of the book includes a discussion of the classes of dense near polygons, regular near polygons, and glued near polygons. Also valuations, one of the most important tools for classifying dense near polygons, are treated in detail. The second part of the book discusses the classification of dense near polygons with three points per line. The book is self-contained and almost all theorems are accompanied with proofs. Several new results are presented. Many known results occur in a more general form and the proofs are often more streamlined than their original versions. The volume is aimed at advanced graduate students and researchers in the fields of combinatorics and finite geometry.

Mathematics. --- Order, Lattices, Ordered Algebraic Structures. --- Combinatorics. --- Algebra. --- Mathématiques --- Algèbre --- Finite geometries. --- Graph theory. --- Steiner systems. --- Steiner systems --- Finite geometries --- Graph theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Graphs, Theory of --- Theory of graphs --- Geometries, Finite --- Networks, Steiner --- Steiner networks --- Steiner triple systems --- Systems, Steiner --- Triple systems, Steiner --- Extremal problems --- Ordered algebraic structures. --- Combinatorial analysis --- Topology --- Combinatorial geometry --- Block designs --- Combinatorics --- Mathematical analysis --- Algebraic structures, Ordered --- Structures, Ordered algebraic

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The advanced course on The geometry of the word problem for ?nitely presented groups was held July 5-15, 2005, at the Centre de Recerca Matematica ` in B- laterra (Barcelona). It was aimed at young researchersand recent graduates int- ested in geometricapproachesto grouptheory,in particular,to the wordproblem. Three eight-hour lecture series were delivered and are the origin of these notes. There were also problem sessions and eight contributed talks. The course was the closing activity of a research program on The geometry of the word problem, held during the academic year 2004-05 and coordinated by Jos´ eBurilloandEnricVenturafromtheUniversitatPolit` ecnicadeCatalunya,and Noel Brady,fromOklahoma University. Thirty-?vescientists participated in these events, in visits to the CRM of between one week and the whole year. Two weekly seminars and countless informal meetings contributed to a dynamic atmosphere of research. The authors of these notes would like to express their gratitude to the m- velous sta? at the CRM, director Manuel Castellet and all the secretaries, for providing great facilities and a very pleasant working environment. Also, the - thors thank Jos´ e Burillo and Enric Ventura for organising the research year, for ensuring its smooth running, and for the invitations to give lecture series. - nally, thanks are due to all those who attended the courses for their interest, their questions, and their enthusiasm.

Geometric group theory. --- Finite groups. --- Word problems (Mathematics) --- Problems, Word (Mathematics) --- Story problems (Mathematics) --- Mathematics --- Groups, Finite --- Group theory --- Modules (Algebra) --- Word problems (Mathematics). --- Group theory. --- Discrete groups. --- Combinatorics. --- Algebra. --- Group Theory and Generalizations. --- Convex and Discrete Geometry. --- Order, Lattices, Ordered Algebraic Structures. --- Mathematical analysis --- Combinatorics --- Algebra --- Groups, Discrete --- Infinite groups --- Groups, Theory of --- Substitutions (Mathematics) --- Discrete mathematics --- Finite groups --- Geometric group theory --- 512.54 --- 514.7 --- 512.54 Groups. Group theory --- Groups. Group theory --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Differential geometry. Algebraic and analytic methods in geometry --- Convex geometry . --- Discrete geometry. --- Ordered algebraic structures. --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Geometry --- Combinatorial geometry