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| cluster meaning in math: Mathematical Classification and Clustering Boris Mirkin, 2013-12-01 I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in this book is quite interesting and stimulating in paradigms, clustering and optimization. On the other hand, it has a substantial application appeal. The book will be useful both to specialists and students in the fields of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. Panos Pardalos, Series Editor. |
| cluster meaning in math: Effective Math Instruction Jared Dupree, 2016-02-01 This easy-to-use classroom resource provides a series of lessons, templates, and exemplars for practical classroom application, and will help teachers understand the content standards and the mathematical practice standards in order to develop meaningful mathematics lessons. This book primarily focuses on teachers' procedural knowledge of standards implementation as they apply the information and resources presented in this book. Mathematical rigor in the classroom for students includes lessons that target conceptual knowledge, procedural knowledge, factual knowledge, meta-cognitive knowledge, and the application of this knowledge in context. It also includes opportunities for teachers to develop all three dimensions of rigor as it applies to the Common Core. |
| cluster meaning in math: Statistical Learning with Math and Python Joe Suzuki, 2021-08-03 The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building Python programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning. Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning. |
| cluster meaning in math: Fundamentals of Mathematics Denny Burzynski, Wade Ellis, 2008 Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject. |
| cluster meaning in math: Algebraic Geometry and Number Theory victor ginzburg, 2007-12-31 This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld. Original research articles reflect the range of Drinfeld's work, and his profound contributions to the Langlands program, quantum groups, and mathematical physics are paid particular attention. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory. |
| cluster meaning in math: Lecture Notes on Cluster Algebras Robert J. Marsh, 2013 Cluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field while giving a taste of the wide connections between cluster algebras and other areas of mathematics. The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included. This book ends with a description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial geometry. |
| cluster meaning in math: Advances in K-means Clustering Junjie Wu, 2012-07-09 Nearly everyone knows K-means algorithm in the fields of data mining and business intelligence. But the ever-emerging data with extremely complicated characteristics bring new challenges to this old algorithm. This book addresses these challenges and makes novel contributions in establishing theoretical frameworks for K-means distances and K-means based consensus clustering, identifying the dangerous uniform effect and zero-value dilemma of K-means, adapting right measures for cluster validity, and integrating K-means with SVMs for rare class analysis. This book not only enriches the clustering and optimization theories, but also provides good guidance for the practical use of K-means, especially for important tasks such as network intrusion detection and credit fraud prediction. The thesis on which this book is based has won the 2010 National Excellent Doctoral Dissertation Award, the highest honor for not more than 100 PhD theses per year in China. |
| cluster meaning in math: Mathematical Analysis S. C. Malik, Savita Arora, 1992 The Book Is Intended To Serve As A Text In Analysis By The Honours And Post-Graduate Students Of The Various Universities. Professional Or Those Preparing For Competitive Examinations Will Also Find This Book Useful.The Book Discusses The Theory From Its Very Beginning. The Foundations Have Been Laid Very Carefully And The Treatment Is Rigorous And On Modem Lines. It Opens With A Brief Outline Of The Essential Properties Of Rational Numbers And Using Dedekinds Cut, The Properties Of Real Numbers Are Established. This Foundation Supports The Subsequent Chapters: Topological Frame Work Real Sequences And Series, Continuity Differentiation, Functions Of Several Variables, Elementary And Implicit Functions, Riemann And Riemann-Stieltjes Integrals, Lebesgue Integrals, Surface, Double And Triple Integrals Are Discussed In Detail. Uniform Convergence, Power Series, Fourier Series, Improper Integrals Have Been Presented In As Simple And Lucid Manner As Possible And Fairly Large Number Solved Examples To Illustrate Various Types Have Been Introduced.As Per Need, In The Present Set Up, A Chapter On Metric Spaces Discussing Completeness, Compactness And Connectedness Of The Spaces Has Been Added. Finally Two Appendices Discussing Beta-Gamma Functions, And Cantors Theory Of Real Numbers Add Glory To The Contents Of The Book. |
| cluster meaning in math: Illustrated Dictionary of Mathematics Yule Bricks, 2004-02 Lotus Press |
| cluster meaning in math: Cluster Algebras and Poisson Geometry Michael Gekhtman, Michael Shapiro, Alek Vainshtein, 2010 The first book devoted to cluster algebras, this work contains chapters on Poisson geometry and Schubert varieties; an introduction to cluster algebras and their main properties; and geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems. |
| cluster meaning in math: Registration and Recognition in Images and Videos Roberto Cipolla, Sebastiano Battiato, Giovanni Maria Farinella, 2013-11-19 Computer vision is the science and technology of making machines that see. It is concerned with the theory, design and implementation of algorithms that can automatically process visual data to recognize objects, track and recover their shape and spatial layout. The International Computer Vision Summer School - ICVSS was established in 2007 to provide both an objective and clear overview and an in-depth analysis of the state-of-the-art research in Computer Vision. The courses are delivered by world renowned experts in the field, from both academia and industry and cover both theoretical and practical aspects of real Computer Vision problems. The school is organized every year by University of Cambridge (Computer Vision and Robotics Group) and University of Catania (Image Processing Lab). Different topics are covered each year. This edited volume contains a selection of articles covering some of the talks and tutorials held during the last editions of the school. The chapters provide an in-depth overview of challenging areas with key references to the existing literature. |
| cluster meaning in math: Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof Kristen N. Bieda, AnnaMarie Conner, Karl W. Kosko, Megan Staples, 2022-03-03 This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets. |
| cluster meaning in math: Windows on Mathematical Meanings Richard Noss, Celia Hoyles, 2012-12-06 This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces. |
| cluster meaning in math: Teaching and Learning Secondary School Mathematics Ann Kajander, Jennifer Holm, Egan J Chernoff, 2018-10-24 This volume brings together recent research and commentary in secondary school mathematics from a breadth of contemporary Canadian and International researchers and educators. It is both representative of mathematics education generally, as well as unique to the particular geography and culture of Canada. The chapters address topics of broad applicability such as technology in learning mathematics, recent interest in social justice contexts in the learning of mathematics, as well as Indigenous education. The voices of classroom practitioners, the group ultimately responsible for implementing this new vision of mathematics teaching and learning, are not forgotten. Each section includes a chapter written by a classroom teacher, making this volume unique in its approach. We have much to learn from one another, and this volume takes the stance that the development of a united vision, supported by both research and professional dialog, provides the first step. |
| cluster meaning in math: The Math Teachers Know Brent Davis, Moshe Renert, 2013-07-18 What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms. |
| cluster meaning in math: Common Core Standards for Elementary Grades 3-5 Math & English Language Arts Amber Evenson, Monette McIver, Susan Ryan, Amitra Schwols, 2013-03-12 Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This Quick-Start Guide provides a succinct, all-in-one look at * The content, structure, terminology, and emphases of the Common Core standards for mathematics and English language arts in the upper elementary grades. * The meaning of the individual standards within each of the four ELA-literacy strands and five math domains, with an emphasis on areas that represent the most significant changes to business as usual. * How the standards connect across and within strands, domains, and grade levels to develop foundational language arts, literacy, and mathematics learning--and prepare students for success in the critical middle school years. Here, teachers of grades 3-5 and elementary school leaders will find information they need to begin adapting their practices to help all students master the new and challenging material contained in the standards. A practical lesson planning process to use with the Common Core, based on Classroom Instruction That Works, 2nd Ed., is included, along with six sample lessons. LEARN THE ESSENTIALS OF THE COMMON CORE The grade-level and subject-specific Quick-Start Guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons. |
| cluster meaning in math: Intelligent Information and Database Systems Ngoc-Thanh Nguyen, Boonwat Attachoo, Bogdan Trawinski, Kulwadee Somboonviwat, 2014-02-28 The two-volume set LNAI 8397 and LNAI 8398 constitutes the refereed proceedings of the 6th Asian Conference on Intelligent Information and Database Systems, ACIIDS 2014, held in Bangkok, Thailand in April 2014. The 125 revised papers presented were carefully reviewed and selected from 300 submissions. Suggestion: The aim of the conference is to provide an internationally respected forum for scientific research in the technologies and applications of intelligent information and database systems. The papers are organized in topical sections on Natural Language and Text Processing, Intelligent Information Retrieval, Semantic Web, Social Networks and Recommendation Systems, Intelligent Database Systems, Decision Support Systems, Computer Vision Techniques, Machine Learning and Data Mining, Multiple Model Approach to Machine Learning, MMAML 2014, Computational Intelligence, CI 2014, Engineering Knowledge and Semantic Systems , IWEKSS 2014, Innovations in Intelligent Computation and Applications, IICA 2014, Modelling and Optimization Techniques in Information Systems, Database Systems and Industrial Systems, MOT 2014, Innovation via Collective Intelligences and Globalization in Business Management, ICIGBM 2014, Intelligent Supply Chains, ISC 2014, and Human Motion: Acquisition, Processing, Analysis, Synthesis and Visualization for Massive Datasets, HMMD 2014. |
| cluster meaning in math: Common Core Standards for Elementary Grades K–2 Math & English Language Arts Amber Evenson, Monette McIver, Susan Ryan, Amitra Schwols, 2013-05-20 Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This Quick-Start Guide provides a succinct, all-in-one look at * The content, structure, terminology, and emphases of the Common Core standards for mathematics and English language arts and literacy in the lower elementary grades. * The meaning of the individual standards within each of the four ELA/literacy strands and five math domains, with an emphasis on areas that represent the most significant changes to business as usual. * How the standards connect across and within strands, domains, and grade levels to develop the foundational language arts, literacy, and mathematics understanding that will support a lifetime of successful learning. Here, teachers of grades K–2 and elementary school leaders will find information they need to begin adapting their practices to help all students master the new and challenging material contained in the standards. A practical lesson planning process to use with the Common Core, based on Classroom Instruction That Works, 2nd Ed., is included, along with six sample lessons. LEARN THE ESSENTIALS OF THE COMMON CORE The grade-level and subject-specific Quick-Start Guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons. |
| cluster meaning in math: Linguistic Influences on Mathematical Cognition Ann Dowker, Hans-Christoph Nuerk, 2017-06-16 For many years, an abstract, amodal semantic magnitude representation, largely independent of verbal linguistic representations, has been viewed as the core numerical or mathematical representation This assumption has been substantially challenged in recent years. Linguistic properties affect not only verbal representations of numbers,but also numerical magnitude representation, spatial magnitude representations, calculation, parity representation, place-value representation and even early number acquisition. Thus, we postulate that numerical and arithmetic processing are not fully independent of linguistic processing. This is not to say, that in patients, magnitude processing cannot function independently of linguistic processing we just suppose, these functions are connected in the functioning brain. So far, much research about linguistic influences on numerical cognition has simply demonstrated that language influences number without investigating the level at which a particular language influence operates. After an overview, we present new findings on language influences on seven language levels: - Conceptual: Conceptual properties of language - Syntactic: The grammatical structure of languages beyond the word level influences - Semantic: The semantic meaning or existence of words - Lexical: The lexical composition of words, in particular number words - Visuo-spatial-orthographic: Orthographic properties, such as the writing/reading direction of a language. - Phonological: Phonological/phonetic properties of languages - Other language-related skills: Verbal working memory and other cognitive skills related to language representations We hope that this book provides a new and structured overview on the exciting influences of linguistic processing on numerical cognition at almost all levels of language processing. |
| cluster meaning in math: Data Analysis with Mplus Christian Geiser, 2012-12-05 A practical introduction to using Mplus for the analysis of multivariate data, this volume provides step-by-step guidance, complete with real data examples, numerous screen shots, and output excerpts. The author shows how to prepare a data set for import in Mplus using SPSS. He explains how to specify different types of models in Mplus syntax and address typical caveats--for example, assessing measurement invariance in longitudinal SEMs. Coverage includes path and factor analytic models as well as mediational, longitudinal, multilevel, and latent class models. Specific programming tips and solution strategies are presented in boxes in each chapter. The companion website (www.guilford.com/geiser-materials) features data sets, annotated syntax files, and output for all of the examples. Of special utility to instructors and students, many of the examples can be run with the free demo version of Mplus. |
| cluster meaning in math: Making Presentation Math Computable André Greiner-Petter, 2023-01-24 This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book. |
| cluster meaning in math: Academic Language in Diverse Classrooms: Mathematics, Grades 3–5 Margo Gottlieb, Gisela Ernst-Slavit, 2013-02-27 Help your students unlock important mathematical concepts! If you’ve ever watched a student struggle with learning math concepts, you know that academic English can sometimes create stumbling blocks to understanding. To grasp complicated concepts, build skills, and demonstrate achievement, students need to master academic language in math. The Common Core and ELD standards provide pathways to academic success through academic language. Using an integrated Curricular Framework, districts, schools and professional learning communities can: Design and implement thematic units for learning Draw from content and language standards to set targets for all students Examine standards-centered materials for academic language Collaborate in planning instruction and assessment within and across lessons Consider linguistic and cultural resources of the students Create differentiated content and language objectives Delve deeply into instructional strategies involving academic language Reflect on teaching and learning Each grade-specific chapter models the types of interactions and learning experiences that help students master both math content and academic language. This essential book shows you why mastery of academic language is the key to students’ academic success. With growing numbers of English Language Learners in our classrooms, teachers need to be able to help students as they learn academic vocabulary and concepts. This series offers teachers a practical support, complete with abundant rubrics and detailed plans for teaching math vocabulary! —Renee Peoples, Teacher Swain County Schools, Bryson City, NC |
| cluster meaning in math: Essential Math for AI Hala Nelson, 2023-01-04 Companies are scrambling to integrate AI into their systems and operations. But to build truly successful solutions, you need a firm grasp of the underlying mathematics. This accessible guide walks you through the math necessary to thrive in the AI field such as focusing on real-world applications rather than dense academic theory. Engineers, data scientists, and students alike will examine mathematical topics critical for AI--including regression, neural networks, optimization, backpropagation, convolution, Markov chains, and more--through popular applications such as computer vision, natural language processing, and automated systems. And supplementary Jupyter notebooks shed light on examples with Python code and visualizations. Whether you're just beginning your career or have years of experience, this book gives you the foundation necessary to dive deeper in the field. Understand the underlying mathematics powering AI systems, including generative adversarial networks, random graphs, large random matrices, mathematical logic, optimal control, and more Learn how to adapt mathematical methods to different applications from completely different fields Gain the mathematical fluency to interpret and explain how AI systems arrive at their decisions |
| cluster meaning in math: Elementary Cluster Analysis James C. Bezdek, 2022-10-17 The availability of packaged clustering programs means that anyone with data can easily do cluster analysis on it. But many users of this technology don't fully appreciate its many hidden dangers. In today's world of grab and go algorithms, part of my motivation for writing this book is to provide users with a set of cautionary tales about cluster analysis, for it is very much an art as well as a science, and it is easy to stumble if you don't understand its pitfalls. Indeed, it is easy to trip over them even if you do! The parenthetical word usually in the title is very important, because all clustering algorithms can and do fail from time to time. Modern cluster analysis has become so technically intricate that it is often hard for the beginner or the non-specialist to appreciate and understand its many hidden dangers. Here's how Yogi Berra put it, and he was right: In theory there's no difference between theory and practice. In practice, there is ~Yogi Berra This book is a step backwards, to four classical methods for clustering in small, static data sets that have all withstood the tests of time. The youngest of the four methods is now almost 50 years old: Gaussian Mixture Decomposition (GMD, 1898) SAHN Clustering (principally single linkage (SL, 1909)) Hard c-means (HCM, 1956, also widely known as (aka) k-means) Fuzzy c-means (FCM, 1973, reduces to HCM in a certain limit) The dates are the first known writing (to me, anyway) about these four models. I am (with apologies to Marvel Comics) very comfortable in calling HCM, FCM, GMD and SL the Fantastic Four. Cluster analysis is a vast topic. The overall picture in clustering is quite overwhelming, so any attempt to swim at the deep end of the pool in even a very specialized subfield requires a lot of training. But we all start out at the shallow end (or at least that's where we should start!), and this book is aimed squarely at teaching toddlers not to be afraid of the water. There is no section of this book that, if explored in real depth, cannot be expanded into its own volume. So, if your needs are for an in-depth treatment of all the latest developments in any topic in this volume, the best I can do - what I will try to do anyway - is lead you to the pool, and show you where to jump in. |
| cluster meaning in math: Math and Art Sasho Kalajdzievski, 2011-04-28 Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With downloadable resources and a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire art. Basic Math Topics and Their Visual Aspects Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions. Comprehensive Material for a Math in Art Course Providing all of the material for a complete one-semester course on mathematics in art, this self-contained text shows how artistic practice with mathematics and a comprehension of mathematical concepts are needed to logically and creatively appreciate the field of mathematics. |
| cluster meaning in math: Fuzzy Logic with Engineering Applications Timothy J. Ross, 2005-04-08 Fuzzy logic refers to a large subject dealing with a set of methods to characterize and quantify uncertainty in engineering systems that arise from ambiguity, imprecision, fuzziness, and lack of knowledge. Fuzzy logic is a reasoning system based on a foundation of fuzzy set theory, itself an extension of classical set theory, where set membership can be partial as opposed to all or none, as in the binary features of classical logic. Fuzzy logic is a relatively new discipline in which major advances have been made over the last decade or so with regard to theory and applications. Following on from the successful first edition, this fully updated new edition is therefore very timely and much anticipated. Concentration on the topics of fuzzy logic combined with an abundance of worked examples, chapter problems and commercial case studies is designed to help motivate a mainstream engineering audience, and the book is further strengthened by the inclusion of an online solutions manual as well as dedicated software codes. Senior undergraduate and postgraduate students in most engineering disciplines, academics and practicing engineers, plus some working in economics, control theory, operational research etc, will all find this a valuable addition to their bookshelves. |
| cluster meaning in math: Common Core Standards for Middle School Mathematics Amitra Schwols, Kathleen Dempsey, 2013 Smart implementation of the Common Core State Standards requires both an overall understanding of the standards and a grasp of their implications for planning, teaching, and learning. This Quick-Start Guide provides a succinct, all-in-one look at * The structure, terminology, and emphases of the Common Core mathematics standards for middle school. * The meaning of the individual content standards within all six domains--Ratios and Proportional Relationships, the Number System, Expressions and Equations, Functions, Geometry, and Statistics and Probability--with an emphasis on areas that represent the most significant changes to business as usual. * How the content standards and practice standards connect across grade levels to build on prior learning, deepen conceptual understanding, promote real-world application, and prepare students for high school level mathematics. Here, middle school mathematics teachers and teacher leaders will find information they need to begin adapting their practices to ensure that all students master the challenging material present in the standards. A practical lesson planning process to use with the Common Core, based on Classroom Instruction That Works, 2nd Ed., is included, along with three sample lessons. LEARN THE ESSENTIALS OF THE COMMON CORE The grade-level and subject-specific Quick-Start Guides in the Understanding the Common Core Standards series, edited by John Kendall, are designed to help school leaders and school staffs turn Common Core standards into coherent, content-rich curriculum and effective, classroom-level lessons. |
| cluster meaning in math: For the Learning of Mathematics , 2008 |
| cluster meaning in math: Intelligent Computer Mathematics Stephen M. Watt, Alan Sexton, James H. Davenport, Petr Sojka, Josef Urban, 2014-06-30 This book constitutes the joint refereed proceedings of Calculemus 2014, Digital Mathematics Libraries, DML 2014, Mathematical Knowledge Management, MKM 2014 and Systems and Projects, S&P 2014, held in Coimbra, Portugal, during July 7-11, 2014 as four tracks of CICM 2014, the Conferences on Intelligent Computer Mathematics. The 26 full papers and 9 Systems and Projects descriptions presented together with 5 invited talks were carefully reviewed and selected from a total of 55 submissions. The Calculemus track of CICM examines the integration of symbolic computation and mechanized reasoning. The Digital Mathematics Libraries track - evolved from the DML workshop series - features math-aware technologies, standards, algorithms and processes towards the fulfillment of the dream of a global DML. The Mathematical Knowledge Management track of CICM is concerned with all aspects of managing mathematical knowledge in the informal, semi-formal and formal settings. The Systems and Projects track presents short descriptions of existing systems or on-going projects in the areas of all the other tracks of the conference. |
| cluster meaning in math: R: Unleash Machine Learning Techniques Raghav Bali, Dipanjan Sarkar, Brett Lantz, Cory Lesmeister, 2016-10-24 Find out how to build smarter machine learning systems with R. Follow this three module course to become a more fluent machine learning practitioner. About This Book Build your confidence with R and find out how to solve a huge range of data-related problems Get to grips with some of the most important machine learning techniques being used by data scientists and analysts across industries today Don't just learn – apply your knowledge by following featured practical projects covering everything from financial modeling to social media analysis Who This Book Is For Aimed for intermediate-to-advanced people (especially data scientist) who are already into the field of data science What You Will Learn Get to grips with R techniques to clean and prepare your data for analysis, and visualize your results Implement R machine learning algorithms from scratch and be amazed to see the algorithms in action Solve interesting real-world problems using machine learning and R as the journey unfolds Write reusable code and build complete machine learning systems from the ground up Learn specialized machine learning techniques for text mining, social network data, big data, and more Discover the different types of machine learning models and learn which is best to meet your data needs and solve your analysis problems Evaluate and improve the performance of machine learning models Learn specialized machine learning techniques for text mining, social network data, big data, and more In Detail R is the established language of data analysts and statisticians around the world. And you shouldn't be afraid to use it... This Learning Path will take you through the fundamentals of R and demonstrate how to use the language to solve a diverse range of challenges through machine learning. Accessible yet comprehensive, it provides you with everything you need to become more a more fluent data professional, and more confident with R. In the first module you'll get to grips with the fundamentals of R. This means you'll be taking a look at some of the details of how the language works, before seeing how to put your knowledge into practice to build some simple machine learning projects that could prove useful for a range of real world problems. For the following two modules we'll begin to investigate machine learning algorithms in more detail. To build upon the basics, you'll get to work on three different projects that will test your skills. Covering some of the most important algorithms and featuring some of the most popular R packages, they're all focused on solving real problems in different areas, ranging from finance to social media. This Learning Path has been curated from three Packt products: R Machine Learning By Example By Raghav Bali, Dipanjan Sarkar Machine Learning with R Learning - Second Edition By Brett Lantz Mastering Machine Learning with R By Cory Lesmeister Style and approach This is an enticing learning path that starts from the very basics to gradually pick up pace as the story unfolds. Each concept is first defined in the larger context of things succinctly, followed by a detailed explanation of their application. Each topic is explained with the help of a project that solves a real-world problem involving hands-on work thus giving you a deep insight into the world of machine learning. |
| cluster meaning in math: Learning Patterns in Higher Education David Gijbels, Vincent Donche, John T. E. Richardson, Jan D. Vermunt, 2013-09-11 Learning Patterns in Higher Education brings together a cutting edge international team of contributors to critically review our current understanding of how students and adults learn, how differences and changes in the way students learn can be measured in a valid and reliable way, and how the quality of student learning may be enhanced. There is substantial evidence that students in higher education have a characteristic way of learning, sometimes called their learning orientation (Biggs 1988), learning style (Evans et al. 2010) or learning pattern (Vermunt and Vermetten 2004). However, recent research in the field of student learning has resulted in multi-faceted and sometimes contradictory results which may reflect conceptual differences and differences in measurement of student learning in each of the studies. This book deals with the need for further clarification of how students learn in higher education in the 21st century and to what extent the measurements often used in learning pattern studies are still up to date or can be advanced with present methodological and statistical insights to capture the most important differences and changes in student learning. The contributions in the book are organized in two parts: a first conceptual and psychological part in which the dimensions of student learning in the 21st century are discussed and a second empirical part in which questions related to how students’ learning can be measured and how it develops are considered. Areas covered include: Cultural influences on learning patterns Predicting learning outcomes Student centred learning environments and self-directed learning Mathematics learning This indispensable book covers multiple conceptual perspectives on how learning patterns can be described and effects and developments can be measured, and will not only be helpful for ‘learning researchers’ as such but also for educational researchers from the broad domain of educational psychology, motivation psychology and instructional sciences, who are interested in student motivation, self-regulated learning, effectiveness of innovative learning environments, as well as assessment and evaluation of student characteristics and learning process variables. |
| cluster meaning in math: Choosing a Standards-based Mathematics Curriculum Lynn T. Goldsmith, June Mark, Ilene Kantrov, 2000 Anyone responsible for the curriculum review and selection process within a district will find this book essential reading. |
| cluster meaning in math: Data Analytics Made Easy Andrea De Mauro, Francesco Marzoni, Andrew J. Walter, 2021-08-30 Learn how to gain insights from your data as well as machine learning and become a presentation pro who can create interactive dashboards Key FeaturesEnhance your presentation skills by implementing engaging data storytelling and visualization techniquesLearn the basics of machine learning and easily apply machine learning models to your dataImprove productivity by automating your data processesBook Description Data Analytics Made Easy is an accessible beginner's guide for anyone working with data. The book interweaves four key elements: Data visualizations and storytelling – Tired of people not listening to you and ignoring your results? Don't worry; chapters 7 and 8 show you how to enhance your presentations and engage with your managers and co-workers. Learn to create focused content with a well-structured story behind it to captivate your audience. Automating your data workflows – Improve your productivity by automating your data analysis. This book introduces you to the open-source platform, KNIME Analytics Platform. You'll see how to use this no-code and free-to-use software to create a KNIME workflow of your data processes just by clicking and dragging components. Machine learning – Data Analytics Made Easy describes popular machine learning approaches in a simplified and visual way before implementing these machine learning models using KNIME. You'll not only be able to understand data scientists' machine learning models; you'll be able to challenge them and build your own. Creating interactive dashboards – Follow the book's simple methodology to create professional-looking dashboards using Microsoft Power BI, giving users the capability to slice and dice data and drill down into the results. What you will learnUnderstand the potential of data and its impact on your businessImport, clean, transform, combine data feeds, and automate your processesInfluence business decisions by learning to create engaging presentationsBuild real-world models to improve profitability, create customer segmentation, automate and improve data reporting, and moreCreate professional-looking and business-centric visuals and dashboardsOpen the lid on the black box of AI and learn about and implement supervised and unsupervised machine learning modelsWho this book is for This book is for beginners who work with data and those who need to know how to interpret their business/customer data. The book also covers the high-level concepts of data workflows, machine learning, data storytelling, and visualizations, which are useful for managers. No previous math, statistics, or computer science knowledge is required. |
| cluster meaning in math: The Legacy of Felix Klein Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand, Gert Schubring, 2018-12-11 This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint. |
| cluster meaning in math: Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths Sergey Fomin, Professor Dylan Thurston, 2018-10-03 For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface. |
| cluster meaning in math: Motivational Profiles in TIMSS Mathematics Michalis P. Michaelides, Gavin T. L. Brown, Hanna Eklöf, Elena C. Papanastasiou, 2019-09-03 This open access book presents a person-centered exploration of student profiles, using variables related to motivation to do school mathematics derived from the IEA’s Trends in International Mathematics and Science Study (TIMSS) data. Statistical cluster analysis is used to identify groups of students with similar motivational profiles, across grades and over time, for multiple participating countries. While motivational variables systematically relate to school outcomes, linear relationships can obscure the diverse makeup of student subgroups, each with varying combinations of motivation, emotions, and attitudes. In this book, a person-centered analysis of distinct and meaningful motivational profiles and their differences on sociodemographic variables and mathematics performance broadens understanding about the role that motivation characteristics play in learning and achievement in mathematics. Exploiting the richness of IEA’s TIMSS data from many countries, extracted clusters reveal consistent, as well as certain nuanced patterns that are systematically linked to sociodemographic and achievement measures. Student clusters with inconsistent motivational profiles were found in all countries; mathematics self-confidence then emerged as the variable more closely associated with average achievement. The findings demonstrate that teachers, researchers, and policymakers need to take into account differential student profiles, prioritizing techniques that target skill and competence in mathematics, in educational efforts to develop student motivation. |
| cluster meaning in math: Theorizing and Measuring Affect in Mathematics Teaching and Learning Chiara Andrà, Domenico Brunetto, Francesca Martignone, 2021-01-23 This book presents a literature review of and a state-of-the-art glimpse into current research on affect-related aspects of teaching and learning in and beyond mathematics classrooms. Then, research presented at the MAVI 25 Conference, which took place in Intra (Italy) in June 2019, is grouped in thematic strands that capture cutting-edge issues related to affective components of learning and teaching mathematics. The concluding chapter summarises the main messages and sketches future directions for research on affect in mathematics education. The book is intended for researchers in mathematics education and especially graduate students and PhD candidates who are interested in emotions, attitudes, motivations, beliefs, needs and values in mathematics education. |
| cluster meaning in math: Affect and Mathematics Education Markku S. Hannula, Gilah C. Leder, Francesca Morselli, Maike Vollstedt, Qiaoping Zhang, 2019-06-03 This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education. |
| cluster meaning in math: Mathematical Reviews , 2007 |
| cluster meaning in math: Data Profiling Ziawasch Abedjan, Lukasz Golab, Felix Naumann, Thorsten Papenbrock, 2022-06-01 Data profiling refers to the activity of collecting data about data, {i.e.}, metadata. Most IT professionals and researchers who work with data have engaged in data profiling, at least informally, to understand and explore an unfamiliar dataset or to determine whether a new dataset is appropriate for a particular task at hand. Data profiling results are also important in a variety of other situations, including query optimization, data integration, and data cleaning. Simple metadata are statistics, such as the number of rows and columns, schema and datatype information, the number of distinct values, statistical value distributions, and the number of null or empty values in each column. More complex types of metadata are statements about multiple columns and their correlation, such as candidate keys, functional dependencies, and other types of dependencies. This book provides a classification of the various types of profilable metadata, discusses popular data profiling tasks, and surveys state-of-the-art profiling algorithms. While most of the book focuses on tasks and algorithms for relational data profiling, we also briefly discuss systems and techniques for profiling non-relational data such as graphs and text. We conclude with a discussion of data profiling challenges and directions for future work in this area. |
Cluster - Group sharing for friends & family. The antidote to social …
Cluster gives you a private space to share photos and memories with the people you choose, away from social media. Make your own groups and share pics, videos, comments, and chat!
CLUSTER Definition & Meaning - Merriam-Webster
The meaning of CLUSTER is a number of similar things that occur together. How to use cluster in a sentence.
CLUSTER | English meaning - Cambridge Dictionary
CLUSTER definition: 1. a group of similar things that are close together, sometimes surrounding something: 2. a group…. Learn more.
Cluster - Wikipedia
Cluster analysis, a set of techniques for grouping a set of objects based on intrinsic similarities; Cluster sampling, a sampling technique used when "natural" groupings are evident in a …
An Overview of Cluster Computing - GeeksforGeeks
An Overview of Cluster Computing - GeeksforGeeks
What is a cluster? - Princeton Research Computing
The computational systems made available by Princeton Research Computing are, for the most part, clusters. Each computer in the cluster is called a node (the term "node" comes from …
CLUSTER definition and meaning | Collins English Dictionary
A cluster of people or things is a small group of them close together. ...clusters of men in formal clothes. There's no town here, just a cluster of shops, cabins and motels at the side of the …
What does cluster mean? - Definitions.net
Definition of cluster in the Definitions.net dictionary. Meaning of cluster. What does cluster mean? Information and translations of cluster in the most comprehensive dictionary definitions …
Cluster - definition of cluster by The Free Dictionary
Define cluster. cluster synonyms, cluster pronunciation, cluster translation, English dictionary definition of cluster. n. 1. A group of the same or similar elements gathered or occurring …
Computer Clusters, Types, Uses and Applications - Baeldung
Mar 18, 2024 · In simple terms, a computer cluster is a set of computers (nodes) that work together as a single system. We can use clusters to enhance the processing power or …
Cluster - Group sharing for friends & family. The antidote to social …
Cluster gives you a private space to share photos and memories with the people you choose, away from social media. Make your own groups and share pics, videos, comments, and chat!
CLUSTER Definition & Meaning - Merriam-Webster
The meaning of CLUSTER is a number of similar things that occur together. How to use cluster in a sentence.
CLUSTER | English meaning - Cambridge Dictionary
CLUSTER definition: 1. a group of similar things that are close together, sometimes surrounding something: 2. a group…. Learn more.
Cluster - Wikipedia
Cluster analysis, a set of techniques for grouping a set of objects based on intrinsic similarities; Cluster sampling, a sampling technique used when "natural" groupings are evident in a statistical …
An Overview of Cluster Computing - GeeksforGeeks
An Overview of Cluster Computing - GeeksforGeeks
What is a cluster? - Princeton Research Computing
The computational systems made available by Princeton Research Computing are, for the most part, clusters. Each computer in the cluster is called a node (the term "node" comes from graph …
CLUSTER definition and meaning | Collins English Dictionary
A cluster of people or things is a small group of them close together. ...clusters of men in formal clothes. There's no town here, just a cluster of shops, cabins and motels at the side of the highway.
What does cluster mean? - Definitions.net
Definition of cluster in the Definitions.net dictionary. Meaning of cluster. What does cluster mean? Information and translations of cluster in the most comprehensive dictionary definitions resource …
Cluster - definition of cluster by The Free Dictionary
Define cluster. cluster synonyms, cluster pronunciation, cluster translation, English dictionary definition of cluster. n. 1. A group of the same or similar elements gathered or occurring closely …
Computer Clusters, Types, Uses and Applications - Baeldung
Mar 18, 2024 · In simple terms, a computer cluster is a set of computers (nodes) that work together as a single system. We can use clusters to enhance the processing power or increase resilience. …
