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Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad. Research Problems in Discrete Geometry is the result of a 25-year-old project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. Important features include: * More than 500 open problems, some old, others new and never before published; * Each chapter divided into self-contained sections, each section ending with an extensive bibliography; * A great selection of research problems for graduate students looking for a dissertation topic; * A comprehensive survey of discrete geometry, highlighting the frontiers and future of research; * More than 120 figures; * A preface to an earlier version written by the late Paul Erdos. Peter Brass is Associate Professor of Computer Science at the City College of New York. William O. J. Moser is Professor Emeritus at McGill University. Janos Pach is Distinguished Professor at The City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the Rényi Institute, Budapest.
Discrete geometry. --- Géométrie discrète --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Géométrie discrète --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Mathematics. --- Convex geometry. --- Convex and Discrete Geometry. --- Combinatorial geometry --- Math --- Science --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .
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Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. It is a wonderful source of ideas for students. The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A.Shor and Yu.A.Volkov have been added as supplements to this book.
Polyhedra --- Convex surfaces --- Polyèdres --- Surfaces convexes --- Polyhedra. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Convex surfaces. --- Polyèdres --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Convex areas --- Polyhedral figures --- Polyhedrons --- Mathematics. --- Visualization. --- Convex geometry. --- Discrete geometry. --- Convex and Discrete Geometry. --- Combinatorial geometry --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Math --- Science --- Convex domains --- Surfaces --- Geometry, Solid --- Shapes --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .
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This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov.
Infinite groups. --- Ergodic theory. --- Selfadjoint operators. --- Differential topology. --- Geometry, Differential --- Topology --- Operators, Selfadjoint --- Self-adjoint operators --- Linear operators --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Groups, Infinite --- Group theory --- Group theory. --- Topological Groups. --- Combinatorics. --- Operator theory. --- Global differential geometry. --- Algebraic topology. --- Group Theory and Generalizations. --- Topological Groups, Lie Groups. --- Operator Theory. --- Differential Geometry. --- Algebraic Topology. --- Functional analysis --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Topological --- Groups, Theory of --- Substitutions (Mathematics) --- Topological groups. --- Lie groups. --- Differential geometry. --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups
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Combinatorial geometry --- Geometry --- Géométrie combinatoire --- Géométrie --- Congresses. --- Data processing --- Congrès --- Informatique --- Algebra --- Technology - General --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Geometric combinatorics --- Geometrical combinatorics --- Computer science. --- Data structures (Computer science). --- Algorithms. --- Computer science --- Computer graphics. --- Convex geometry. --- Discrete geometry. --- Computer Science. --- Computer Graphics. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Data Structures. --- Convex and Discrete Geometry. --- Mathematics. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer mathematics --- Discrete mathematics --- Algorism --- Arithmetic --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Informatics --- Science --- Digital techniques --- Foundations --- Combinatorial analysis --- Discrete geometry --- Computational complexity. --- Computer software. --- Data structures (Computer scienc. --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Software, Computer --- Computer systems --- Complexity, Computational --- Machine theory --- Computer science—Mathematics. --- Convex geometry . --- Discrete mathematics. --- Artificial intelligence—Data processing. --- Data Science. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis
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