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Books > Computing & IT > Applications of computing > Computer modelling & simulation

Guide to Industrial Analytics - Solving Data Science Problems for Manufacturing and the Internet of Things (Hardcover, 1st ed.... Guide to Industrial Analytics - Solving Data Science Problems for Manufacturing and the Internet of Things (Hardcover, 1st ed. 2021)
Richard Hill, Stuart Berry
R2,116 Discovery Miles 21 160 Ships in 18 - 22 working days

This textbook describes the hands-on application of data science techniques to solve problems in manufacturing and the Industrial Internet of Things (IIoT). Monitoring and managing operational performance is a crucial activity for industrial and business organisations. The emergence of low-cost, accessible computing and storage, through Industrial Digital Technologies (IDT) and Industry 4.0, has generated considerable interest in innovative approaches to doing more with data. Data science, predictive analytics, machine learning, artificial intelligence and general approaches to modelling, simulating and visualising industrial systems have often been considered topics only for research labs and academic departments. This textbook debunks the mystique around applied data science and shows readers, using tutorial-style explanations and real-life case studies, how practitioners can develop their own understanding of performance to achieve tangible business improvements. All exercises can be completed with commonly available tools, many of which are free to install and use. Readers will learn how to use tools to investigate, diagnose, propose and implement analytics solutions that will provide explainable results to deliver digital transformation.

Modeling, Simulation, And Control Of Flexible Manufacturing Systems: A Petri Net Approach (Hardcover): Kurapati Venkatesh,... Modeling, Simulation, And Control Of Flexible Manufacturing Systems: A Petri Net Approach (Hardcover)
Kurapati Venkatesh, MengChu Zhou
R2,904 Discovery Miles 29 040 Ships in 18 - 22 working days

One critical barrier leading to successful implementation of flexible manufacturing and related automated systems is the ever-increasing complexity of their modeling, analysis, simulation, and control. Research and development over the last three decades has provided new theory and graphical tools based on Petri nets and related concepts for the design of such systems. The purpose of this book is to introduce a set of Petri-net-based tools and methods to address a variety of problems associated with the design and implementation of flexible manufacturing systems (FMSs), with several implementation examples.There are three ways this book will directly benefit readers. First, the book will allow engineers and managers who are responsible for the design and implementation of modern manufacturing systems to evaluate Petri nets for applications in their work. Second, it will provide sufficient breadth and depth to allow development of Petri-net-based industrial applications. Third, it will allow the basic Petri net material to be taught to industrial practitioners, students, and academic researchers much more efficiently. This will foster further research and applications of Petri nets in aiding the successful implementation of advanced manufacturing systems.

Advanced Computer Performance Modeling and Simulation (Hardcover): Kallol Bagchi, Jean Walrand, George Zobrist Advanced Computer Performance Modeling and Simulation (Hardcover)
Kallol Bagchi, Jean Walrand, George Zobrist
R3,512 Discovery Miles 35 120 Ships in 10 - 15 working days

Addresses the major issues involved in computer design and architectures. Dealing primarily with theory, tools, and techniques as related to advanced computer systems, it provides tutorials and surveys and relates new important research results. Each chapter provides background information, describes and analyzes important work done in the field, and provides important direction to the reader on future work and further readings. The topics covered include hierarchical design schemes, parallel and distributed modeling and simulation, parallel simulation tools and techniques, theoretical models for formal and performance modeling, and performance evaluation techniques.

Agricultural Systems Modeling and Simulation (Hardcover, illustrated edition): Robert M. Peart, W. David Shoup Agricultural Systems Modeling and Simulation (Hardcover, illustrated edition)
Robert M. Peart, W. David Shoup
R12,042 Discovery Miles 120 420 Ships in 10 - 15 working days

Offers a treatment of modern applications of modelling and simulation in crop, livestock, forage/livestock systems, and field operations. The book discusses methodologies from linear programming and neutral networks, to expert or decision support systems, as well as featuring models, such as SOYGRO, CROPGRO and GOSSYM/COMAX. It includes coverage on evaporation and evapotranspiration, the theory of simulation based on biological processes, and deficit irrigation scheduling.

Building Energy Modeling with OpenStudio - A Practical Guide for Students and Professionals (Hardcover, 1st ed. 2018): Larry... Building Energy Modeling with OpenStudio - A Practical Guide for Students and Professionals (Hardcover, 1st ed. 2018)
Larry Brackney, Andrew Parker, Daniel Macumber, Kyle Benne
R2,229 Discovery Miles 22 290 Ships in 10 - 15 working days

This textbook teaches the fundamentals of building energy modeling and analysis using open source example applications built with the US DOE's OpenStudio modeling platform and EnergyPlus simulation engine. Designed by researchers at US National Laboratories to support a new generation of high performance buildings, EnergyPlus and OpenStudio are revolutionizing how building energy modeling is taught in universities and applied by professional architects and engineers around the world. The authors, all researchers at National Renewable Energy Laboratory and members of the OpenStudio software development team, present modeling concepts using open source software that may be generally applied using a variety of software tools commonly used by design professionals. The book also discusses modeling process automation in the context of OpenStudio Measures-small self-contained scripts that can transform energy models and their data-to save time and effort. They illustrate key concepts through a sophisticated example problem that evolves in complexity throughout the book. The text also examines advanced topics including daylighting, parametric analysis, uncertainty analysis, design optimization, and model calibration. Building Energy Modeling with OpenStudio teaches students to become sophisticated modelers rather than simply proficient software users. It supports undergraduate and graduate building energy courses in Architecture, and in Mechanical, Civil, Architectural, and Sustainability Engineering.

Multiple Model Approaches To Nonlinear Modelling And Control (Hardcover): R. Murray-Smith, T. Johansen Multiple Model Approaches To Nonlinear Modelling And Control (Hardcover)
R. Murray-Smith, T. Johansen
R4,784 R1,998 Discovery Miles 19 980 Save R2,786 (58%) Ships in 10 - 15 working days


Contents:
1. Basic Principles: The Operating Regime Approach 2. Modelling: Fuzzy Set Methods for Local Modelling Identification 3. Modelling of Electrically Stimulated Muscle 4. Process Modelling Using a Functional State Approach 5. Markov Mixtures of Experts 6. Active Learning With Mixture Models 7. Local Learning in Local Model Networks 8. Side Effects of Normalising Basic Functions 9. Control: Heterogeneous Control Laws 10. Local Laguerre Models 11. Multiple Model Adaptive Control 12. H Control Using Multiple Linear Models 13. Synthesis of Fuzzy Control Systems Based on Linear Takagi-Sugeno Fuzzy Models

GPU PRO 360 Guide to GPGPU - Guide to GPGPU (Hardcover): Wolfgang Engel GPU PRO 360 Guide to GPGPU - Guide to GPGPU (Hardcover)
Wolfgang Engel
R4,235 Discovery Miles 42 350 Ships in 10 - 15 working days

Wolfgang Engel's GPU Pro 360 Guide to GPGPU gathers all the cutting-edge information from his previous seven GPU Pro volumes into a convenient single source anthology that covers general purpose GPU. This volume is complete with 19 articles by leading programmers that focus on the techniques that go beyond the normal pixel and triangle scope of GPUs and take advantage of the parallelism of modern graphics processors to accomplish such tasks. GPU Pro 360 Guide to GPGPU is comprised of ready-to-use ideas and efficient procedures that can help solve many computer graphics programming challenges that may arise. Key Features: Presents tips & tricks on real-time rendering of special effects and visualization data on common consumer software platforms such as PCs, video consoles, mobile devices Covers specific challenges involved in creating games on various platforms Explores the latest developments in rapidly evolving field of real-time rendering Takes practical approach that helps graphics programmers solve their daily challenges

Distributed Simulation (Hardcover): John A. Hamilton, David A. Nash, Udo W. Pooch Distributed Simulation (Hardcover)
John A. Hamilton, David A. Nash, Udo W. Pooch
R3,838 R3,380 Discovery Miles 33 800 Save R458 (12%) Ships in 10 - 15 working days

Simulation is a multi-disciplinary field, and significant simulation research is dispersed across multiple fields of study. Distributed computer systems, software design methods, and new simulation techniques offer synergistic multipliers when joined together in a distributed simulation. Systems of most interest to the simulation practitioner are often the most difficult to model and implement.
Distributed Simulation brings together the many complex technologies for distributed simulation. There is strong emphasis on emerging simulation methodologies, including object-oriented, multilevel, and multi-resolution simulation. Finally, one concise text provides a strong foundation for the development of high fidelity simulations in heterogeneous distributed computing environments!

Spatial Analytical (Paperback): Manfred M. Fischer Spatial Analytical (Paperback)
Manfred M. Fischer
R1,980 Discovery Miles 19 800 Ships in 10 - 15 working days

The ability to manipulate spatial data in different forms and to extract additional meaning from them is at the heart of GIS, yet genuine spatial analysis tools are rarely incorporated into commercial software, thus seriously limiting their usefulness. The future of GIS technology wil depend largely on the incorporation of more powerful analytical and modelling functions - and there is agreement within the GIS community of the urgent need to address these issues. This text attempts this task. It presents the latest information on incorporating spatial analysis tools into GIS, and includes concepts and applications from both the environmental and socio-econimc sciences.

Numerical Solutions for Partial Differential Equations - Problem Solving Using Mathematica (Hardcover, New): Victor... Numerical Solutions for Partial Differential Equations - Problem Solving Using Mathematica (Hardcover, New)
Victor Grigor'e Ganzha, Evgenii Vasilev Vorozhtsov
R5,517 Discovery Miles 55 170 Ships in 10 - 15 working days

Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra MathematicaA(R) can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.

Digital Mayhem 3D Machine Techniques - Where Inspiration, Techniques and Digital Art meet (Hardcover): Duncan Evans Digital Mayhem 3D Machine Techniques - Where Inspiration, Techniques and Digital Art meet (Hardcover)
Duncan Evans
R3,945 Discovery Miles 39 450 Ships in 10 - 15 working days

Inspire your own creativity with Digital Mayhem 3D Machine Techniques. Compiled by Duncan Evans, founder of 3D Artist Magazine, this book is the next installment of the Digital Mayhem series. Explore, page after page, spectacular machine images created by the industry's top talent. With over 500 stunning images, Digital Mayhem 3D Machine Techniques is not your basic software manual. It is where technique and inspiration meet - a detailed and innovative guide to great machine images. Each chapter contains vibrant images and an explanation of the artist's workflow, including a step-by-step tutorial to help you achieve similar results. From pre-viz to post production, this book takes you through the whole process of creating your very own machine masterpiece! Get inside the minds of the artists with breakdown overviews and supporting imagery to explain what went into their piece. Expand your digital canvas to include a variety of software techniques, tools and workflows. Visit the companion website for additional resources to help you develop your machine technique skills. Key Features Tutorials and images are provided by artists who are from all regions of the world Every image is coupled with a description of the artists' techniques and their problem solving solutions. Helps anyone develop time saving workflow tricks, apply software shortcuts, and keep abreast of industry trends Each artist highlights a specific creative technique or design element, offering cutting-edge insight and technical know-how of digital masters

Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere (Hardcover, 1st ed. 2020): Xueshang Feng Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere (Hardcover, 1st ed. 2020)
Xueshang Feng
R3,946 Discovery Miles 39 460 Ships in 18 - 22 working days

The book covers intimately all the topics necessary for the development of a robust magnetohydrodynamic (MHD) code within the framework of the cell-centered finite volume method (FVM) and its applications in space weather study. First, it presents a brief review of existing MHD models in studying solar corona and the heliosphere. Then it introduces the cell-centered FVM in three-dimensional computational domain. Finally, the book presents some applications of FVM to the MHD codes on spherical coordinates in various research fields of space weather, focusing on the development of the 3D Solar-InterPlanetary space-time Conservation Element and Solution Element (SIP-CESE) MHD model and its applications to space weather studies in various aspects. The book is written for senior undergraduates, graduate students, lecturers, engineers and researchers in solar-terrestrial physics, space weather theory, modeling, and prediction, computational fluid dynamics, and MHD simulations. It helps readers to fully understand and implement a robust and versatile MHD code based on the cell-centered FVM.

Advanced Structural Equation Modeling - Issues and Techniques (Hardcover): George A Marcoulides, Randall E. Schumacker Advanced Structural Equation Modeling - Issues and Techniques (Hardcover)
George A Marcoulides, Randall E. Schumacker
R4,517 Discovery Miles 45 170 Ships in 10 - 15 working days

By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.

Handbook of Environmental and Ecological Modeling (Hardcover): Sven E. Jorgensen Handbook of Environmental and Ecological Modeling (Hardcover)
Sven E. Jorgensen
R7,948 Discovery Miles 79 480 Ships in 10 - 15 working days

With descriptions of hundreds of the most important environmental and ecological models, this handbook is a unique and practical reference source. The Handbook of Environmental and Ecological Modeling is ideal for those working in environmental modeling, including regulators and managers who wish to understand the models used to make assessments. Overviews of more than 360 models are easily accessed in this handbook, allowing readers to quickly locate information they need about models available in a given ecosystem.
The material in the Handbook of Environmental and Ecological Modeling is logically arranged according to ecosystem. Each of the sixteen chapters of the handbook covers a particular ecosystem, and includes not only the descriptions of the models, but also an overview of the state-of-the-art in modeling for that particular ecosystem. A summary of the spectrum of available models is also provided in each chapter. The extensive table of contents and the easy-to-use index put materials immediately at your fingertips.

Experimental and Numerical Study of Glass Facade Breakage Behavior under Fire Conditions - Fire Safety Engineering (Hardcover,... Experimental and Numerical Study of Glass Facade Breakage Behavior under Fire Conditions - Fire Safety Engineering (Hardcover, 1st ed. 2019)
Yu Wang
R4,011 Discovery Miles 40 110 Ships in 18 - 22 working days

This book presents the comprehensive results of experimental and numerical investigations of glass facade breakage behavior under fire conditions. First of all, full-scale frame and point-supported glass facades, incorporating single, double and coated glazing, were tested under pool fire conductions. The results determined the effects of different glass frames, types of glass, and thermal shocks on breakage behavior. Small-scale tests, using the Material Testing System (MTS) 810, Netzsch Dilatometer and FE-SEM, were also performed at different temperatures to determine the basic mechanical properties of glazing. In addition, a three-dimensional dynamic model was developed to predict stress distribution, crack initiation and propagation, and has since been employed to identify the breakage mechanisms of different types of glass facade. The numerical results showed very good agreement with the experimental results and verified the model's ability to accurately predict breakage. Lastly, a theoretical model based on incident heat flux was developed to predict the breakage time and heat transfer in glazing, which served to reveal the nature of interactions between fire and glass.

Intellectual Property Rights and Emerging Technology - 3D Printing in China (Hardcover): Hing Kai Chan, Hui Leng Choo, Onyeka... Intellectual Property Rights and Emerging Technology - 3D Printing in China (Hardcover)
Hing Kai Chan, Hui Leng Choo, Onyeka Osuji, James Griffin
R4,488 Discovery Miles 44 880 Ships in 10 - 15 working days

3D printing poses many challenges to the traditional law of intellectual property (IP). This book develops a technical method to help overcome some of these legal challenges and difficulties. This is a collection of materials from empirical interviews, workshops and publications that have been carried out in one of the world's leading research projects into the legal impact of 3D printing. The project was designed to establish what legal challenges 3D printing companies thought they faced, and having done that, to establish a technical framework for a solution.

Circuit Simulation Methods and Algorithms (Hardcover, First): Jan Ogrodzki Circuit Simulation Methods and Algorithms (Hardcover, First)
Jan Ogrodzki; Series edited by J.K. Fidler
R5,619 R4,957 Discovery Miles 49 570 Save R662 (12%) Ships in 10 - 15 working days

Circuit Simulation Methods and Algorithms provides a step-by-step theoretical consideration of methods, techniques, and algorithms in an easy-to-understand format. Many illustrations explain more difficult problems and present instructive circuits.
The book works on three levels:
o The simulator-user level for practitioners and students who want to better understand circuit simulators.
o The basic theoretical level, with examples, dedicated to students and beginning researchers.
o The thorough level for deep insight into circuit simulation based on computer experiments using PSPICE and OPTIMA.
Only basic mathematical knowledge, such as matrix algebra, derivatives, and integrals, is presumed.

Practical Guide to Digital Manufacturing - First-Time-Right for Design of Products, Machines, Processes and System Integration... Practical Guide to Digital Manufacturing - First-Time-Right for Design of Products, Machines, Processes and System Integration (Hardcover, 1st ed. 2021)
Zhuming Bi; Contributions by Wen-Jun Chris Zhang
R2,945 Discovery Miles 29 450 Ships in 18 - 22 working days

This book covers the subject of digital manufacturing. It provides a practical guide for readers on using computer aided design (CAD), computer aided engineering (CAE) and computer aided manufacturing (CAM) and other computer assistive tools for the design of products, machines, processes and system integrations through the case studies of engineering projects. The book introduces a thorough theoretical foundation and discussion of the historical development, and enabling technologies of digital manufacturing. It also covers a broad range of computer aided tools for a variety of applications including: geometric modelling; assembly modelling; motion simulation; finite element analysis; manufacturing process simulation; machining programming; product data management; and, product lifecycle management. Practical Guide to Digital Manufacturing uses many real-world case studies to illustrate the discussed applications, making it easily readable for undergraduate and graduate students, as well as engineers with the needs of computer-aided design and manufacturing knowledge and skills.

Practice of Bayesian Probability Theory in Geotechnical Engineering (Hardcover, 1st ed. 2021): Wanhuan Zhou, Zhenyu Yin,... Practice of Bayesian Probability Theory in Geotechnical Engineering (Hardcover, 1st ed. 2021)
Wanhuan Zhou, Zhenyu Yin, Ka-Veng Yuen
R4,001 Discovery Miles 40 010 Ships in 10 - 15 working days

This book introduces systematically the application of Bayesian probabilistic approach in soil mechanics and geotechnical engineering. Four typical problems are analyzed by using Bayesian probabilistic approach, i.e., to model the effect of initial void ratio on the soil-water characteristic curve (SWCC) of unsaturated soil, to select the optimal model for the prediction of the creep behavior of soft soil under one-dimensional straining, to identify model parameters of soils and to select constitutive model of soils considering critical state concept. This book selects the simple and easy-to-understand Bayesian probabilistic algorithm, so that readers can master the Bayesian method to analyze and solve the problem in a short time. In addition, this book provides MATLAB codes for various algorithms and source codes for constitutive models so that readers can directly analyze and practice. This book is useful as a postgraduate textbook for civil engineering, hydraulic engineering, transportation, railway, engineering geology and other majors in colleges and universities, and as an elective course for senior undergraduates. It is also useful as a reference for relevant professional scientific researchers and engineers.

Modeling, Identification and Simulation of Dynamical Systems (Hardcover): P.P.J.Van Den Bosch, A.C.Van Der Klauw Modeling, Identification and Simulation of Dynamical Systems (Hardcover)
P.P.J.Van Den Bosch, A.C.Van Der Klauw
R6,752 Discovery Miles 67 520 Ships in 10 - 15 working days

This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics.
Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems.

Workbook of Atmospheric Dispersion Estimates - An Introduction to Dispersion Modeling, Second Edition (Hardcover, 2nd edition):... Workbook of Atmospheric Dispersion Estimates - An Introduction to Dispersion Modeling, Second Edition (Hardcover, 2nd edition)
D. Bruce Turner
R7,879 Discovery Miles 78 790 Ships in 10 - 15 working days

This completely updated and revised Second Edition of the popular Workbook of Atmospheric Dispersion Estimates provides an important foundation for understanding dispersion modeling as it is being practiced today. The book and accompanying diskette will help you determine the impacts of various sources of air pollution, including the effects of wind and turbulence, plume rise, and Gaussian dispersion and its limitations. Information is shown in summary graphs as well as in equations. The programs included on the diskette allow you to "get the feel" for the results you'll obtain through the input of various combinations of parameter values. The sensitivity of data to various parameters can be easily explored by changing one value and seeing the effect on the results. The book presents 37 example problems with solutions to show the estimation of atmospheric pollutant concentrations for many situations.

Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes (Hardcover): A. Weron, Aleksand Janicki Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes (Hardcover)
A. Weron, Aleksand Janicki
R7,622 Discovery Miles 76 220 Ships in 10 - 15 working days

Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.

Integrating Research on the Graphical Representation of Functions (Hardcover): Thomas A. Romberg, Elizabeth Fennema, Thomas P... Integrating Research on the Graphical Representation of Functions (Hardcover)
Thomas A. Romberg, Elizabeth Fennema, Thomas P Carpenter
R4,501 Discovery Miles 45 010 Ships in 10 - 15 working days

This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes.
The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.

Rules of the Mind (Hardcover): John R. Anderson Rules of the Mind (Hardcover)
John R. Anderson
R4,512 Discovery Miles 45 120 Ships in 10 - 15 working days

Related to the earlier well-known ACT production system theory, this book's basic goal is to present evidence for the psychological reality of a production system model of mind. Distinguished from the original theory in three ways, this volume uses the rational analyses of Anderson (1990) to improve upon that theory and extend its scope. It also relates the theory to a great deal of new data on the performance and acquisition of cognitive skills.
The new theory -- ACT-R -- involves a neurally plausible implementation of a production system architecture. Rational analysis is used to structure and parameterize the system to yield optimal information processing. The theory is applicable to a wide variety of research disciplines, including memory, problem solving, and skill acquisition. Using intelligent tutors, much of the data is concerned with the acquisition of cognitive skills. The book provides analyses of data sets describing the extended course of the acquisition of mathematical and computer programming skills.

Rules of the Mind (Paperback): John R. Anderson Rules of the Mind (Paperback)
John R. Anderson
R2,022 Discovery Miles 20 220 Ships in 10 - 15 working days

Related to the earlier well-known ACT production system theory, this book's basic goal is to present evidence for the psychological reality of a production system model of mind. Distinguished from the original theory in three ways, this volume uses the rational analyses of Anderson (1990) to improve upon that theory and extend its scope. It also relates the theory to a great deal of new data on the performance and acquisition of cognitive skills.
The new theory -- ACT-R -- involves a neurally plausible implementation of a production system architecture. Rational analysis is used to structure and parameterize the system to yield optimal information processing. The theory is applicable to a wide variety of research disciplines, including memory, problem solving, and skill acquisition. Using intelligent tutors, much of the data is concerned with the acquisition of cognitive skills. The book provides analyses of data sets describing the extended course of the acquisition of mathematical and computer programming skills.

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