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This is the first of two volumes of a stateoftheart survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and nonNoetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: nonnoetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics.
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This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert's 16th problem. This book is intended for graduate students, postdoctors and researchers in the area of theories and applications of dynamical systems. For all engineers who are interested the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of an oneyear course on nonlinear differential equations.
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This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interest to researchers in the field of applied mathematics, geophysics and mathematical biology.
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This book explains how mathematical tools can be used to solve problems in signal processing. Assuming an advanced undergraduate or graduatelevel understanding of mathematics, this second edition contains new chapters on convolution and the vector DFT, planewave propagation, and the BLUE and Kalman filters. It expands the material on Fourier analysis to three new chapters to provide additional background information, presents realworld examples of applications that demonstrate how mathematics is used in remote sensing, and includes robust appendices and problems for classroom use.
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This is the second of two volumes of a stateoftheart survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and nonNoetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: nonnoetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and more.
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The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME13). ICME13 took place from 24th 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik  GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current stateoftheart of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teachingandlearning processes.The book introduces the major activities of ICME13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings.
teaching mathematics  learning mathematics  mathematics education
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The proceedings of the international conference “SMSEC2014”, a joint conference of the first “Social Modeling and Simulations” and the 10th “Econophysics Colloquium”, held in Kobe in November 2014 with 174 participants, are gathered herein. Cutting edge scientific researches on various social phenomena are reviewed. New methods for analysis of big data such as financial markets, automobile traffics, epidemic spreading, worldtrades and social media communications are provided to clarify complex interaction and distributions underlying in these social phenomena. Robustness and fragility of social systems are discussed based on agent models and complex network models. Techniques about high performance computers are introduced for simulation of complicated social phenomena. Readers will feel the researchers minds that deep and quantitative understanding will make it possible to realize comprehensive simulations of our whole society in the near future, which will contribute to wide fields of industry also to scientific policy decision.
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This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.
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This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 37, 2011. This volume addresses the common ground in the mathematical and computational procedures required for largescale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences.
Mathematics  Mathematics  Geography  Earth Science
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This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a selfcontained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a singlesemester course; only a basic knowledge of graduate level probability theory is assumed.
Mathematics  Probabilities  Discrete mathematics  Geometry  Mathematical physics
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