| computational geometry online course: Computational Geometry Mark de Berg, Marc van Krefeld, Mark Overmars, Otfried Cheong, 2013-04-17 Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains-computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms playafundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study. |
| computational geometry online course: Discrete and Computational Geometry, 2nd Edition Satyan L. Devadoss, Joseph O'Rourke, 2025-07-08 The essential introduction to discrete and computational geometry—now fully updated and expanded Discrete and Computational Geometry bridges the theoretical world of discrete geometry with the applications-driven realm of computational geometry, offering a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. Beginning with polygons and ending with polyhedra, it explains how to capture the shape of data given by a set of points, from convex hulls and triangulations to Voronoi diagrams, geometric duality, chains, linkages, and alpha complexes. Connections to real-world applications are made throughout, and algorithms are presented independent of any programming language. Now fully updated and expanded, this richly illustrated textbook is an invaluable learning tool for students in mathematics, computer science, engineering, and physics. Now with new sections on duality and on computational topology Project suggestions at the end of every chapter Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and fully updated unsolved problems Uniquely designed for a one-semester class Accessible to college sophomores with minimal background Also suitable for more advanced students Online solutions manual (available to instructors) |
| computational geometry online course: Computational Geometry Franco P. Preparata, Michael I. Shamos, 2012-12-06 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 |
| computational geometry online course: A First Course in Computational Algebraic Geometry Wolfram Decker, Gerhard Pfister, 2013-02-07 A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular. |
| computational geometry online course: Computational Geometry in C Joseph O'Rourke, 1998-10-13 This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp. |
| computational geometry online course: Computational Geometry for Ships H. Nowacki, M.I.G. Bloor, B. Oleksiewicz, 1995-03 This book offers an advanced course on ?Computational Geometry for Ships?. It takes into account the recent rapid progress in this field by adapting modern computational methodology to ship geometric applications. Preliminary curve and surface techniques are included to educate engineers in the use of mathematical methods to assist in CAD and other design areas. In addition, there is a comprehensive study of interpolation and approximation techniques, which is reinforced by direct application to ship curve design, ship curve fairing techniques and other related disciplines. The design, evaluation and production of ship surface geometries are further demonstrated by including current and evolving CAD modelling systems. |
| computational geometry online course: Forbidden Configurations in Discrete Geometry David Eppstein, 2018-05-17 Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems. |
| computational geometry online course: Multiple View Geometry in Computer Vision Richard Hartley, Andrew Zisserman, 2004-03-25 A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book. |
| computational geometry online course: Computational Algebra: Course And Exercises With Solutions Ihsen Yengui, 2021-05-17 This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course. |
| computational geometry online course: Geometric Approximation Algorithms Sariel Har-Peled, 2011 Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas. |
| computational geometry online course: Shape Interrogation for Computer Aided Design and Manufacturing Nicholas M. Patrikalakis, Takashi Maekawa, 2002-02-14 Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between the areas geometric modeling and solid modeling. Apart from the differential geometry topics covered, the entire book is based on the unifying concept of recasting all shape interrogation problems to the solution of a nonlinear system. It provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, and geodesics. |
| computational geometry online course: Essential Mathematics for Games and Interactive Applications James M. Van Verth, Lars M. Bishop, 2008-05-19 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. |
| computational geometry online course: Handbook of Research on Integrating Computer Science and Computational Thinking in K-12 Education Keengwe, Jared, Wachira, Patrick, 2019-12-13 As technology continues to develop and prove its importance in modern society, certain professions are acclimating. Aspects such as computer science and computational thinking are becoming essential areas of study. Implementing these subject areas into teaching practices is necessary for younger generations to adapt to the developing world. There is a critical need to examine the pedagogical implications of these technological skills and implement them into the global curriculum. The Handbook of Research on Integrating Computer Science and Computational Thinking in K-12 Education is a collection of innovative research on the methods and applications of computer science curriculum development within primary and secondary education. While highlighting topics including pedagogical implications, comprehensive techniques, and teacher preparation models, this book is ideally designed for teachers, IT consultants, curriculum developers, instructional designers, educational software developers, higher education faculty, administrators, policymakers, researchers, and graduate students. |
| computational geometry online course: Geometric Algebra for Computer Science Leo Dorst, Daniel Fontijne, Stephen Mann, 2010-07-26 Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing* Written by leaders in the field providing essential information on this new technique for 3D graphics* This full colour book includes a website with GAViewer, a program to experiment with GA |
| computational geometry online course: Delaunay Mesh Generation Siu-Wing Cheng, Tamal K. Dey, Jonathan Shewchuk, 2012-12-04 Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software. |
| computational geometry online course: Lectures on Discrete Geometry Jiri Matousek, 2013-12-01 Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Computer Science at Charles University in Prague. His research has contributed to several of the considered areas and to their algorithmic applications. This is his third book. |
| computational geometry online course: Polyhedral Computation , 2009 Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general-purpose algorithms. They are, however, highly structured, and attention has turned to exploiting this structure, particularly symmetry. Initial applications of this approach have permitted computations previously far out of reach, but much remains to be understood and validated experimentally. The papers in this volume give a good snapshot of the ideas discussed at a Workshop on Polyhedral Computation held at the CRM in Montréal in October 2006 and, |
| computational geometry online course: Computer Aided Geometric Design Robert E. Barnhill, Richard F. Riesenfeld, 2014-05-10 Computer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers. |
| computational geometry online course: Supercomputing Vladimir Voevodin, Sergey Sobolev, 2017-03-09 This book constitutes the refereed proceedings of the Second Russian Supercomputing Days, RuSCDays 2016, held in Moscow, Russia, in September 2016. The 28 revised full papers presented were carefully reviewed and selected from 94 submissions. The papers are organized in topical sections on the present of supercomputing: large tasks solving experience; the future of supercomputing: new technologies. |
| computational geometry online course: 3D Math Primer for Graphics and Game Development Fletcher Dunn, 2011-11-02 This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for |
| computational geometry online course: Mathematics and Computation Avi Wigderson, 2019-10-29 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 |
| computational geometry online course: Computational Complexity Sanjeev Arora, Boaz Barak, 2009-04-20 New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students. |
| computational geometry online course: Ideals, Varieties, and Algorithms David Cox, John Little, DONAL OSHEA, 2013-04-17 We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra. |
| computational geometry online course: Computational Topology for Data Analysis Tamal Krishna Dey, Yusu Wang, 2022-03-10 This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises. |
| computational geometry online course: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-06-05 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. The color images and text in this book have been converted to grayscale. |
| computational geometry online course: Directory of Distance Learning Opportunities Modoc Press, Inc., 2003-02-28 This book provides an overview of current K-12 courses and programs offered in the United States as correspondence study, or via such electronic delivery systems as satellite, cable, or the Internet. The Directory includes over 6,000 courses offered by 154 institutions or distance learning consortium members. Following an introduction that describes existing practices and delivery methods, the Directory offers three indexes: • Subject Index of Courses Offered, by Level • Course Level Index • Geographic Index All information was supplied by the institutions. Entries include current contact information, a description of the institution and the courses offered, grade level and admission information, tuition and fee information, enrollment periods, delivery information, equipment requirements, credit and grading information, library services, and accreditation. |
| computational geometry online course: Efficient Approximation and Online Algorithms Evripidis Bampis, 2006-02-06 This book provides a good opportunity for computer science practitioners and researchers to get in sync with current state-of-the-art and future trends in the field of combinatorial optimization and online algorithms. Recent advances in this area are presented focusing on the design of efficient approximation and on-line algorithms. One central idea in the book is to use a linear program relaxation of the problem, randomization and rounding techniques. |
| computational geometry online course: Simulation, Modeling, and Programming for Autonomous Robots Noriako Ando, Stephen Balakirsky, Thomas Hemker, Monica Reggiani, Oskar von Stryk, 2010-11-05 Why are the many highly capable autonomous robots that have been promised for novel applications driven by society, industry, and research not available - day despite the tremendous progress in robotics science and systems achieved during the last decades? Unfortunately, steady improvements in speci?c robot abilities and robot hardware have not been matched by corresponding robot performance in real world environments. This is mainly due to the lack of - vancements in robot software that master the development of robotic systems of ever increasing complexity. In addition, fundamental open problems are still awaiting sound answers while the development of new robotics applications s- fersfromthelackofwidelyusedtools,libraries,andalgorithmsthataredesigned in a modular and performant manner with standardized interfaces. Simulation environments are playing a major role not only in reducing development time and cost, e. g. , by systematic software- or hardware-in-the-loop testing of robot performance, but also in exploring new types of robots and applications. H- ever,their use may still be regardedwith skepticism. Seamless migrationof code using robot simulators to real-world systems is still a rare circumstance, due to the complexity of robot, world, sensor, and actuator modeling. These challenges drive the quest for the next generation of methodologies and tools for robot development. The objective of the International Conference on Simulation, Modeling, and ProgrammingforAutonomous Robots (SIMPAR) is to o?er a unique forum for these topics and to bring together researchersfrom academia and industry to identify and solve the key issues necessary to ease the development of increasingly complex robot software. |
| computational geometry online course: Probability and Computing Michael Mitzenmacher, Eli Upfal, 2005-01-31 Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool. |
| computational geometry online course: Foundations of Algorithms Richard Neapolitan, Kumarss Naimipour, 2009-12-28 Foundations of Algorithms, Fourth Edition offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity. The volume is accessible to mainstream computer science students who have a background in college algebra and discrete structures. To support their approach, the authors present mathematical concepts using standard English and a simpler notation than is found in most texts. A review of essential mathematical concepts is presented in three appendices. The authors also reinforce the explanations with numerous concrete examples to help students grasp theoretical concepts. |
| computational geometry online course: Tractability Lucas Bordeaux, Youssef Hamadi, Pushmeet Kohli, 2014-02-06 An overview of the techniques developed to circumvent computational intractability, a key challenge in many areas of computer science. |
| computational geometry online course: Application of Big Data, Blockchain, and Internet of Things for Education Informatization Yinjun Zhang, Nazir Shah, 2024-06-30 The five-volume set LNICST 580-584 constitutes the proceedings of the Third EAI International Conference on Application of Big Data, Blockchain, and Internet of Things for Education Informatization, BigIoT-EDU 2023, held in Liuzhou, China, during August 29–31, 2023. The 272 full papers presented in these proceedings were carefully reviewed and selected from 718 submissions. With a primary focus on research fields such as Digitization of education, Smart classrooms and Massive Online Open Courses (MOOCs), these papers are organized in the following topical sections across the five volumes: Part I: Application of data mining in smart education; Application of intelligent algorithms in English teaching. Part II: Application of decision tree algorithm in intelligent management system of universities; Research on the application of Big data in smart teaching. Part III: Exploration of the application of computer-aided technology in intelligent translation; Application of neural network algorithms in intelligent teaching; Application of artificial intelligence algorithms in the field of smart education. Part IV: Research on smart teaching in deep learning; Research and application of recommendation algorithms in personalized intelligent education; Application of cloud computing in intelligent teaching resource library; Application research of computer-aided online intelligent teaching. Part V: Application and practice of new media in smart teaching; Application of clustering algorithm in intelligent education resource library; Application of association rule algorithm in intelligent education system. |
| computational geometry online course: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| computational geometry online course: Rippling: Meta-Level Guidance for Mathematical Reasoning Alan Bundy, 2005-06-30 Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike. |
| computational geometry online course: Algorithms in Combinatorial Geometry Herbert Edelsbrunner, 2012-12-06 Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field. |
| computational geometry online course: Art Gallery Theorems and Algorithms Joseph O'Rourke, 1987 Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry. |
| computational geometry online course: Approximation and Online Algorithms Klaus Jansen, Roberto Solis-Oba, 2004-02-03 The Workshop on Approximation and Online Algorithms (WAOA 2003) focused on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications ar- ing from a variety of ?elds. The workshop also covered experimental research on approximation and online algorithms. WAOA 2003 took place in Budapest, Hungary, from September 16 to September 18. The workshop was part of the ALGO 2003 event, which also hosted ESA 2003, WABI 2003, and ATMOS 2003. TopicsofinterestforWAOA2003were:competitiveanalysis,inapproximab- ityresults,randomizationtechniques,approximationclasses,scheduling,coloring and partitioning, cuts and connectivity, packing and covering, geometric pr- lems, network design, and applications to game theory and ?nancial problems. In response to our call for papers we received 41 submissions. Each submission was reviewed by at least 3 referees, who judged the papers on originality, quality, and consistency with the topics of the conference. Based on these reviews the program committee selected 19 papers for presentation at the workshop and for publication in this proceedings. This volume contains the 19 selected papers and 5 invited abstracts from an ARACNE minisymposium which took place as part of WAOA. |
| computational geometry online course: Computational Conformal Geometry Xianfeng David Gu, Shing-Tung Yau, 2008 Computational conformal geometry is an emerging inter-disciplinary field, which applies algebraic topology, differential geometry and Riemann surface theories in geometric modelling, computer graphics, computer vision, medical imaging, visualization, scientifice computations and many other engineering fields.--Back cover. |
| computational geometry online course: Understanding Machine Learning Shai Shalev-Shwartz, Shai Ben-David, 2014-05-19 Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage. |
| computational geometry online course: A Short Course in Computational Geometry and Topology Herbert Edelsbrunner, 2014-04-28 This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields. |
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COMPUTATIONAL | English meaning - Cambridge Dictionary
COMPUTATIONAL definition: 1. involving the calculation of answers, amounts, results, etc.: 2. using computers to study…. Learn more.
Computational science - Wikipedia
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, …
COMPUTATIONAL Definition & Meaning - Merriam-Webster
The meaning of COMPUTATION is the act or action of computing : calculation. How to use computation in a sentence.
Computational - Definition, Meaning & Synonyms
Computational is an adjective referring to a system of calculating or "computing," or, more commonly today, work involving computers. Tasks with a lot of computational steps are best …
What does computational mean? - Definitions.net
Computational refers to anything related to computers, computing (the use or operation of computers), computer science, or the processes involved in manipulating and processing data …
Computational - definition of computational by ... - The Free …
Define computational. computational synonyms, computational pronunciation, computational translation, English dictionary definition of computational. n. 1. a. The act or process of …
computational adjective - Definition, pictures, pronunciation and …
Definition of computational adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
COMPUTATIONAL - Definition & Translations | Collins English …
Discover everything about the word "COMPUTATIONAL" in English: meanings, translations, synonyms, pronunciations, examples, and grammar insights - all in one comprehensive guide.
Computational Definition & Meaning - YourDictionary
Computational definition: Of or relating to
computation.
COMPUTATIONAL - Definition & Meaning - Reverso English …
Computational definition: related to the process of calculating or using computers. Check meanings, examples, usage tips, pronunciation, domains, and related words. Discover …
