Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
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Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Achim Menges
Publisher: John Wiley & Sons
ISBN: 047066570X
Category : Architecture
Languages : en
Pages : 230
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Book Description
The current transition from Computer Aided Design (CAD) to Computational Design in architecture represents a profound shift in design thinking and methods. Representation is being replaced by simulation, and the crafting of objects is moving towards the generation of integrated systems through designer-authored computational processes. While there is a particular history of such an approach in architecture, its relative newness requires the continued progression of novel modes of design thinking for the architect of the 21st century. This AD Reader establishes a foundation for such thinking. It includes multifaceted reflections and speculations on the profound influence of computational paradigms on architecture. It presents relevant principles from the domains of mathematics and computer science, developmental and evolutionary biology, system science and philosophy, establishing a discourse for computational design thinking in architecture. Rather than a merely technical approach, the book will discuss essential intellectual concepts that are fundamental not only for a discourse on computational design but also for its practice. This anthology provides a unique collection of seminal texts by authors, who have either provided a significant starting point through which a computational approach to design has been pursued or have played a considerable role in shaping the field. An important aspect of this book is the manner in which adjacent fields and historical texts are connected. Both the source of original inspiration and scientific thought are presented alongside contemporary writings on the continually evolving computational design discourse. Emerging from the field of science, principally the subjects of morphogenesis, evolution and mathematics, selected texts provide a historical basis for a reconfigured mindset of processes that generate, arrange and describe form. Juxtaposed against more contemporary statements regarding the influence of computation on design thinking, the book offers advancements of fundamental texts to the particular purpose of establishing novel thought processes for architecture, theoretically and practically. The first reader to provide an effective framework for computational thinking in design. Includes classic texts by Johan W. von Goethe, D’Arcy Thompson, Ernst Mayr, Ludwig von Bertalanffy, Gordan Pask, Christopher Alexander, John H. Holland, Nicholas Negroponte, William Mitchell, Peter J. Bentley & David W. Corne, Sanford Kwinter, John Frazer, Kostis Terzidis, Michael Weinstock and Achim Menges Features new writing by: Mark Burry, Jane Burry, Manuel DeLanda and Peter Trummer.
Author: James M. Van Verth
Publisher: CRC Press
ISBN: 0123742978
Category : Art
Languages : en
Pages : 706
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Book Description
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.
Author: Xin-she Yang
Publisher: World Scientific Publishing Company
ISBN: 9814635804
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.
Author: Brendan Harmon
Publisher: Taylor & Francis
ISBN: 1040014380
Category : Architecture
Languages : en
Pages : 232
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Book Description
This book is a guide to computational design for landscape architects replete with extensive tutorials. It introduces algorithmic approaches for modeling and designing landscapes. The aim of this book is to use algorithms to understand and design landscape as a generative system, i.e. to harness the processes that shape landscape to generate new forms. An algorithmic approach to design is gently introduced through visual programming with Grasshopper, before more advanced methods are taught in Python, a high-level programming language. Topics covered include parametric design, randomness and noise, waves and attractors, lidar, drone photogrammetry, point cloud modeling, terrain modeling, earthworks, digital fabrication, and more. The chapters include sections on theory, methods, and either visual programming or scripting. Online resources for the book include code and datasets so that readers can easily follow along and try out the methods presented. This book is a much-needed guide, both theoretical and practical, on computational design for students, educators, and practitioners of landscape architecture.
Author: Terri Peters
Publisher: John Wiley & Sons
ISBN: 1118786661
Category : Architecture
Languages : en
Pages : 585
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Book Description
Smartgeometry (SG) is a key influence on the architectural community who explore creative computational methods for the design of buildings. An informal international network of practitioners and researchers, the group meets annually to experiment with new technologies and collaborate to develop digital design techniques. When SG was founded in 2001 by London-based architects and friends Hugh Whitehead (Foster + Partners), J Parrish (AECOM) and Lars Hesselgren (PLP), there was little in the way of parametric tools for architecture. SG was founded to encourage the development, discussion and experimentation of digital design techniques driven by design intent rather than on construction specifications. SG calls for a re-consideration of the design process, where the creation of computational mechanisms become an integral part of designing – not a task done prior to or separate from the process. In the early years of the workshops this need for new ways of design thinking led to the development of Bentley ́s GenerativeComponents software. In recent years, the ecology of these design environments has diversified to include multiple software platforms, as well as innovative fabrication techniques and interactive environments. SG has grown accordingly from a handful of experts to an international network of designers who are defining the future of design. Founded by digital pioneers, it creates the algorithmic designers of the future. Inside Smartgeometry can be seen as a retroactive manifesto for SG, examining and contextualising the work of the SG community: the digital spaces, prototypes and buildings designed using bespoke tools created in response to architectural ideas. From interactive crowd-sourcing tools to responsive agent-based systems to complex digitally fabricated structures, it explores more than a decade of advances that have been influential for architecture. Through 23 original texts including reflections by the founders, and key contributors such as Robert Aish, Martin Bechthold, Mark Burry, Chris Williams and Robert Woodbury, the book offers a critical state of the art of computational design for architecture. Many international design and engineering firms have participated in SG and the book includes chapters by practitioners from offices such as CASE, Design2Production, Foster + Partners, Grimshaw, Populous and SOM.
Author: Franco P. Preparata
Publisher: Springer Science & Business Media
ISBN: 1461210984
Category : Mathematics
Languages : en
Pages : 413
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Book Description
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392
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Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Author: Marco Benini
Publisher: World Scientific
ISBN: 9811245231
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Author: Michael Riggin
Publisher: Lulu.com
ISBN: 1329968484
Category : Art
Languages : en
Pages : 138
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Book Description
Conference Proceedings of the 2015 PRACTICE Symposium of Computational Processes in Architecture and Design, chaired by Rajaa Issa and Michael Riggin. Includes papers presented at the conference and a poster session of work. Papers included: 'Essential Education for Computational Design in Architecture' by Rajaa Issa, 'FPD: First Person Designer' by Ben Regnier, 'Dynamic Acoustics: From Parametric Design to Digital Fabrication' by Erik Luhtala, 'Immersive Environments and Gestural Modeling' by P. Casey Mahon, 'Dynamic Architectural Systems' by Anthony Mull, 'Urban Acupuncture Through Algorithmic Zoning' by Ryan Stangl, 'Computational Architecture: Quantifying the Qualitative' by Hannah Hobbs, and 'Practical Deformation: A Study of Wood Bending Techniques Through Computational Logic' by Jose Villamizar. Poster session includes work by Andrew Reeder, Erik Luhtala, Anthony Mull, Roger Flores, and student work from courses taught by Rajaa Issa and Michael Riggin.
