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Games are a natural activity—we all know how to play. Perhaps this is the key feature that explains the increase in the use of game-based learning (GBL) strategies: Applying games to education converts education into a universal activity. Over the last ten years, the way in which education and training is delivered has considerably changed, not only due to a new technologic environment—plenty of social networks, MOOCs, etc.—but also because of the appearance of new methodologies. Such new methodologies are shifting the center of gravity: from the teacher to the student, with the aim of awakening relational aspects, as well as promoting imagination and divergent thinking. One new approach that holds considerable promise for helping to engage learners is, indeed, game-based learning (GBL). However, while a growing number of institutions are beginning to see the validity of GBL, there are still many challenges to overcome before this type of learning can become widespread.In this Special Issue, we want to gather several studies and experiences in GBL to be shared with other teachers and researchers.

Humanities --- Education --- gamification --- education --- literature survey --- publication analysis --- teacher instruction --- motivation --- curricular integration --- mathematics instruction --- escape room --- review --- assessment --- computational thinking --- functions --- future teachers --- Scratch --- serious games --- game-based learning --- higher education --- teacher predispositions --- gamification in education --- gamifying learning --- STEAM education --- mathematics --- Brazil --- Spain --- traditional games --- ethnomathematics --- steam --- intercultural education --- primary education --- board games --- global change --- environmental engagement --- teacher training --- Education for sustainability --- role-playing games --- second language instruction --- educational game --- board game --- learning tool --- teaching-learning process --- interdisciplinary learning --- science learning --- marine environment --- environmental awareness --- skills development --- mathematical problem-solving --- video games --- emotions --- Portal 2 --- n/a

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Games are a natural activity—we all know how to play. Perhaps this is the key feature that explains the increase in the use of game-based learning (GBL) strategies: Applying games to education converts education into a universal activity. Over the last ten years, the way in which education and training is delivered has considerably changed, not only due to a new technologic environment—plenty of social networks, MOOCs, etc.—but also because of the appearance of new methodologies. Such new methodologies are shifting the center of gravity: from the teacher to the student, with the aim of awakening relational aspects, as well as promoting imagination and divergent thinking. One new approach that holds considerable promise for helping to engage learners is, indeed, game-based learning (GBL). However, while a growing number of institutions are beginning to see the validity of GBL, there are still many challenges to overcome before this type of learning can become widespread.In this Special Issue, we want to gather several studies and experiences in GBL to be shared with other teachers and researchers.

Humanities --- Education --- gamification --- education --- literature survey --- publication analysis --- teacher instruction --- motivation --- curricular integration --- mathematics instruction --- escape room --- review --- assessment --- computational thinking --- functions --- future teachers --- Scratch --- serious games --- game-based learning --- higher education --- teacher predispositions --- gamification in education --- gamifying learning --- STEAM education --- mathematics --- Brazil --- Spain --- traditional games --- ethnomathematics --- steam --- intercultural education --- primary education --- board games --- global change --- environmental engagement --- teacher training --- Education for sustainability --- role-playing games --- second language instruction --- educational game --- board game --- learning tool --- teaching-learning process --- interdisciplinary learning --- science learning --- marine environment --- environmental awareness --- skills development --- mathematical problem-solving --- video games --- emotions --- Portal 2

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Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.

Algebraic spaces. --- Ramsey theory. --- Ramsey theory --- Algebraic spaces --- Mathematics --- Algebra --- Physical Sciences & Mathematics --- Spaces, Algebraic --- Geometry, Algebraic --- Combinatorial analysis --- Graph theory --- Analytic set. --- Axiom of choice. --- Baire category theorem. --- Baire space. --- Banach space. --- Bijection. --- Binary relation. --- Boolean prime ideal theorem. --- Borel equivalence relation. --- Borel measure. --- Borel set. --- C0. --- Cantor cube. --- Cantor set. --- Cantor space. --- Cardinality. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Combinatorics. --- Compact space. --- Compactification (mathematics). --- Complete metric space. --- Completely metrizable space. --- Constructible universe. --- Continuous function (set theory). --- Continuous function. --- Corollary. --- Countable set. --- Counterexample. --- Decision problem. --- Dense set. --- Diagonalization. --- Dimension (vector space). --- Dimension. --- Discrete space. --- Disjoint sets. --- Dual space. --- Embedding. --- Equation. --- Equivalence relation. --- Existential quantification. --- Family of sets. --- Forcing (mathematics). --- Forcing (recursion theory). --- Gap theorem. --- Geometry. --- Ideal (ring theory). --- Infinite product. --- Lebesgue measure. --- Limit point. --- Lipschitz continuity. --- Mathematical induction. --- Mathematical problem. --- Mathematics. --- Metric space. --- Metrization theorem. --- Monotonic function. --- Natural number. --- Natural topology. --- Neighbourhood (mathematics). --- Null set. --- Open set. --- Order type. --- Partial function. --- Partially ordered set. --- Peano axioms. --- Point at infinity. --- Pointwise. --- Polish space. --- Probability measure. --- Product measure. --- Product topology. --- Property of Baire. --- Ramsey's theorem. --- Right inverse. --- Scalar multiplication. --- Schauder basis. --- Semigroup. --- Sequence. --- Sequential space. --- Set (mathematics). --- Set theory. --- Sperner family. --- Subsequence. --- Subset. --- Subspace topology. --- Support function. --- Symmetric difference. --- Theorem. --- Topological dynamics. --- Topological group. --- Topological space. --- Topology. --- Tree (data structure). --- Unit interval. --- Unit sphere. --- Variable (mathematics). --- Well-order. --- Zorn's lemma.

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Many industries, such as transportation and manufacturing, use control systems to insure that parameters such as temperature or altitude behave in a desirable way over time. For example, pilots need assurance that the plane they are flying will maintain a particular heading. An integral part of control systems is a mechanism for failure detection to insure safety and reliability. This book offers an alternative failure detection approach that addresses two of the fundamental problems in the safe and efficient operation of modern control systems: failure detection--deciding when a failure has occurred--and model identification--deciding which kind of failure has occurred. Much of the work in both categories has been based on statistical methods and under the assumption that a given system was monitored passively. Campbell and Nikoukhah's book proposes an "active" multimodel approach. It calls for applying an auxiliary signal that will affect the output so that it can be used to easily determine if there has been a failure and what type of failure it is. This auxiliary signal must be kept small, and often brief in duration, in order not to interfere with system performance and to ensure timely detection of the failure. The approach is robust and uses tools from robust control theory. Unlike some approaches, it is applicable to complex systems. The authors present the theory in a rigorous and intuitive manner and provide practical algorithms for implementation of the procedures.

System failures (Engineering) --- Fault location (Engineering) --- Signal processing. --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Location of system faults --- System fault location (Engineering) --- Dynamic testing --- Failure of engineering systems --- Reliability (Engineering) --- Systems engineering --- A priori estimate. --- AIXI. --- Abuse of notation. --- Accuracy and precision. --- Additive white Gaussian noise. --- Algorithm. --- Approximation. --- Asymptotic analysis. --- Bisection method. --- Boundary value problem. --- Calculation. --- Catastrophic failure. --- Combination. --- Computation. --- Condition number. --- Continuous function. --- Control theory. --- Control variable. --- Decision theory. --- Derivative. --- Detection. --- Deterministic system. --- Diagram (category theory). --- Differential equation. --- Discrete time and continuous time. --- Discretization. --- Dynamic programming. --- Engineering design process. --- Engineering. --- Equation. --- Error message. --- Estimation theory. --- Estimation. --- Finite difference. --- Gain scheduling. --- Inequality (mathematics). --- Initial condition. --- Integrator. --- Invertible matrix. --- Laplace transform. --- Least squares. --- Likelihood function. --- Likelihood-ratio test. --- Limit point. --- Linear programming. --- Linearization. --- Mathematical optimization. --- Mathematical problem. --- Maxima and minima. --- Measurement. --- Method of lines. --- Monotonic function. --- Noise power. --- Nonlinear control. --- Nonlinear programming. --- Norm (mathematics). --- Numerical analysis. --- Numerical control. --- Numerical integration. --- Observational error. --- Open problem. --- Optimal control. --- Optimization problem. --- Parameter. --- Partial differential equation. --- Piecewise. --- Pointwise. --- Prediction. --- Probability. --- Random variable. --- Realizability. --- Remedial action. --- Requirement. --- Rewriting. --- Riccati equation. --- Runge–Kutta methods. --- Sampled data systems. --- Sampling (signal processing). --- Scientific notation. --- Scilab. --- Shift operator. --- Signal (electrical engineering). --- Sine wave. --- Solver. --- Special case. --- Stochastic Modeling. --- Stochastic calculus. --- Stochastic interpretation. --- Stochastic process. --- Stochastic. --- Theorem. --- Time complexity. --- Time-invariant system. --- Trade-off. --- Transfer function. --- Transient response. --- Uncertainty. --- Utilization. --- Variable (mathematics). --- Variance.

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This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws-PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs-mixed type, free boundaries, and corner singularities-that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Shock waves --- Von Neumann algebras. --- MATHEMATICS / Differential Equations / Partial. --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Shock (Mechanics) --- Waves --- Diffraction --- Diffraction. --- Mathematics. --- A priori estimate. --- Accuracy and precision. --- Algorithm. --- Andrew Majda. --- Attractor. --- Banach space. --- Bernhard Riemann. --- Big O notation. --- Boundary value problem. --- Bounded set (topological vector space). --- C0. --- Calculation. --- Cauchy problem. --- Coefficient. --- Computation. --- Computational fluid dynamics. --- Conjecture. --- Conservation law. --- Continuum mechanics. --- Convex function. --- Degeneracy (mathematics). --- Demetrios Christodoulou. --- Derivative. --- Dimension. --- Directional derivative. --- Dirichlet boundary condition. --- Dirichlet problem. --- Dissipation. --- Ellipse. --- Elliptic curve. --- Elliptic partial differential equation. --- Embedding problem. --- Equation solving. --- Equation. --- Estimation. --- Euler equations (fluid dynamics). --- Existential quantification. --- Fixed point (mathematics). --- Flow network. --- Fluid dynamics. --- Fluid mechanics. --- Free boundary problem. --- Function (mathematics). --- Function space. --- Fundamental class. --- Fundamental solution. --- Fundamental theorem. --- Hyperbolic partial differential equation. --- Initial value problem. --- Iteration. --- Laplace's equation. --- Linear equation. --- Linear programming. --- Linear space (geometry). --- Mach reflection. --- Mathematical analysis. --- Mathematical optimization. --- Mathematical physics. --- Mathematical problem. --- Mathematical proof. --- Mathematical theory. --- Mathematician. --- Melting. --- Monotonic function. --- Neumann boundary condition. --- Nonlinear system. --- Numerical analysis. --- Parameter space. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Phase boundary. --- Phase transition. --- Potential flow. --- Pressure gradient. --- Quadratic function. --- Regularity theorem. --- Riemann problem. --- Scientific notation. --- Self-similarity. --- Special case. --- Specular reflection. --- Stefan problem. --- Structural stability. --- Subspace topology. --- Symmetrization. --- Theorem. --- Theory. --- Truncation error (numerical integration). --- Two-dimensional space. --- Unification (computer science). --- Variable (mathematics). --- Velocity potential. --- Vortex sheet. --- Vorticity. --- Wave equation. --- Weak convergence (Hilbert space). --- Weak solution.