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Mathematical Foundations of Computer Science 2007 ; 32nd International Symposium, MFCS 2007 Ceský Krumlov, Czech Republic, August 26-31, 2007, Proceedings
This book constitutes the refereed proceedings of the 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007, held in Cesk?? Krumlov, Czech Republic, August 26-31, 2007. All current aspects in theoretical computer science and its mathematical foundations are addressed.
Mathematical foundations of computer science 2006 ; 31st International Symposium, MFCS 2006, Stará Lesná, Slovakia, August 28-September 1, 2006, Proceedings
This book constitutes the refereed proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006, held in Stará Lesná, Slovakia in August/September 2006. The 62 revised full papers presented together with the full papers or abstracts of 7 invited talks were carefully reviewed and selected from 174 submissions. All current aspects in theoretical computer science and its mathematical foundations are addressed, ranging from algorithms and data structures, to complexity, automata, semantics, logic, formal specifications, models of computation, concurrency theory, computational geometry, parallel and distributed computing, networks, bioinformatics, quantum computing, cryptography, knowledge-based systems, and artificial intelligence.
Mathematical Foundations of Computer Science 2005 ; 30th International Symposium, MFCS 2005, Gdansk, Poland, August29-September 2. 2005, Proceedings
Constitutes the proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science, MFCS 2005, held in Gdansk, Poland in August/September 2005. The 62 papers address various aspects in theoretical computer science, ranging from quantum computing, approximation, automata, circuits, scheduling, games, and more.
Mathematical Events of the Twentieth Century
Russian mathematics (later Soviet mathematics, and Russian mathematics once again) occupies a special place in twentieth-century mathematics. In addition to its well-known achievements, Russian mathematics established a unique style of research based on the existence of prominent mathematical schools. These schools were headed by recognized leaders, who became famous due to their talents and outstanding contributions to science. The present collection is intended primarily to gather in one book the t- timonies of the participants in the development of mathematics over the past century. In their articles the authors have expressed their own points of view on the events that took place. The editors have not felt that they had a right to make any changes, other than stylistic ones, or to add any of their own commentary to the text. Naturally, the points of view of the authors should not be construed as those of the editors. The list of mathematicians invited to participate in the present edition was quite long.
Material Inhomogeneities and their Evolution : A Geometric Approach
The first part of the book deals with the geometrical description of uniform bodies and their homogeneity (i.e., integrability) conditions. In the second part, a theory of material evolution is developed and its relevance in various applied contexts discussed. The necessary geometrical notions are introduced as needed in the first two parts but often without due attention to an uncompromising mathematical rigour. This task is left for the third part of the book, which is a highly technical compendium of those concepts of modern differential geometry that are invoked in the first two parts (differentiable manifolds, Lie groups, jets, principal fibre bundles, G-structures, connections, frame bundles, integrable prolongations, groupoids, etc.).
Matematica e cultura 2008 = mathematics and culture 2008
In this new book, the tenth of the series that began in Venice with the meetings "Mathematics and culture" that many have tried to imitate, we talk about all this and among others Simon Singh (author of the best seller "The last theorem di Fermat "), in her third presence in Venice, and Siobhan Roberts (author of" The king of infinite space. History of the man who saved geometry "). Venice bridge between mathematics and culture.
Matematica e cultura 2007 = Mathematics and culture 2007
We talk about theater even if the page cannot tell about Bustric's unforgettable show. And about art, and applied arts, such as geometric structure and spiritual meaning of the Zen garden of Ryoanji in Kyoto, and of soap bubbles, which are almost never lacking in Venetian encounters, Four-dimensional bubbles and gigantic bubbles that serve as a model for the Olympic swimming pool in Bejing
MacLaurins Physical Dissertations
The Scottish mathematician Colin MacLaurin (1698-1746) is best known for developing and extending Newton’s work in calculus, geometry and gravitation; his 2-volume work "Treatise of Fluxions" (1742) was the first systematic exposition of Newton’s methods. It is well known that MacLaurin was awarded prizes by the Royal Academy of Sciences, Paris, for his earlier work on the collision of bodies (1724) and the tides (1740); however, the contents of these essays are less familiar – although some of the material is discussed in the Treatise of Fluxions - and the essays themselves often hard to obtain.
Machine Learning Refined : Foundations, Algorithms, and Applications
Provides students with the fundamental knowledge and practical tools needed to conduct research and build data-driven products. The authors prioritize geometric intuition and algorithmic thinking, and include detail on all the essential mathematical prerequisites, to offer a fresh and accessible way to learn. Practical applications are emphasized, with examples from disciplines including computer vision, natural language processing, economics, neuroscience, recommender systems, physics, and biology.
Machine learning refined : Foundations, algorithms, and applications
Providing a unique approach to machine learning, this text contains fresh and intuitive, yet rigorous, descriptions of all fundamental concepts necessary to conduct research, build products, tinker, and play. By prioritizing geometric intuition, algorithmic thinking, and practical real world applications in disciplines including computer vision, natural language processing, economics, neuroscience, recommender systems, physics, and biology, this text provides readers with both a lucid understanding of foundational material as well as the practical tools needed to solve real-world problems. With in-depth Python and MATLAB/OCTAVE-based computational exercises and a complete treatment of cutting edge numerical optimization techniques, this is an essential resource for students and an ideal reference for researchers and practitioners working in machine learning, computer science, electrical engineering, signal processing, and numerical optimization
Machine learning methods for reverse engineering of defective structured surfaces
Pascal Laube presents machine learning approaches for three key problems of reverse engineering of defective structured surfaces: parametrization of curves and surfaces, geometric primitive classification and inpainting of high-resolution textures. The proposed methods aim to improve the reconstruction quality while further automating the process. The contributions demonstrate that machine learning can be a viable part of the CAD reverse engineering pipeline.
Macchine matematiche : Dalla storia alla scuola = Mathematical Machines: From History to School
Presents the main mathematical machines for drawing curves, for applying geometrical transformations or for making classical perspectives.The publication constitutes an example of how history of mathematics may be useful for teaching today’s mathematics.
Loop Spaces, Characteristic Classes and Geometric Quantization
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Logical approaches to computational barriers ; 2nd Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006, Proceedings
The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, and computational learning. Applications are everywhere, especially, in algebra, analysis and geometry, or data types and programming. This volume, Logical Approaches to Computational Barriers, is the proce- ings of the second in a series of conferences of CiE that was held at the Depa- ment of Computer Science, Swansea University, 30 June - 5 July, 2006.
Location Theory : A Unified Approach
Although modern location theory is now more than 90 years old, the focus of researchers in this area has been mainly problem oriented. However, a common theory, which keeps the essential characteristics of classical location models, is still missing. This monograph addresses this issue. A flexible location problem called the Ordered Median Problem (OMP) is introduced. For all three main subareas of location theory (continuous, network and discrete location) structural properties of the OMP are presented and solution approaches provided. Numerous illustrations and examples help the reader to become familiar with this new location model.
Linear Differential Equations and Group Theory from Riemann to Poincaré
A study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Linear Algebraic Monoids
The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.
Lie Theory Vol.229 : Unitary Representations and Compactifications of Symmetric Spaces
It focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.
Lie Sphere Geometry : With Applications to Submanifolds
Provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
