Endorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020. Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers. - Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations. - Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the Boost eBook.* *To have full access to the eBook and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/international Please note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Mechanics, including forces and equilibrium, kinematics of motion in a straight line, momentum, Newton's laws of motion, and energy, work and power.

Introduces flexible statistical models that have yet to systematically introduced in course materials. Discusses applications of the proposed modelling framework in several important statistical problems, ranging from biased sampling designs and missing data, graphical models, survival analysis, Gibbs sampler and model compatibility, and density estimations Includes real data examples to demonstrate the use of the proposed models, and estimation and inference tools.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

Learn How To Convert Web Data Into Web Knowledge

This text demonstrates how to extract knowledge by finding meaningful connections among data spread throughout the Web. Readers learn methods and algorithms from the fields of information retrieval, machine learning, and data mining which, when combined, provide a solid framework for mining the Web. The authors walk readers through the algorithms with the aid of examples and exercises.

This text is divided into three parts:

Part One, Web Structure, presents basic concepts and techniques for extracting information from the Web. Readers learn how to collect and index Web documents as well as search and rank Web pages according to their textual content and hyperlink structure.

Part Two, Web Content Management, offers two approaches, clustering and classification, for organizing Web content. For both approaches, the authors set forth specific algorithms that enable readers to convert Web data into knowledge.

Part Three, Web Usage Mining, demonstrates the application of data mining methods to uncover meaningful patterns of Internet usage.

Methods and algorithms are illustrated by simple examples. More than 100 exercises help readers assess their grasp of the material. Further, thirty-four hands-on analysis problems ask readers to use their new data mining expertise to solve real problems, working with large data sets. All the data sets needed for the examples, exercises, and analysis problems are available on the companion Web site.

The extensive use of examples, along with the opportunity to test and apply data mining skills, makes this text ideal for graduate and upper-level undergraduates in computer science andengineering. Web designers and researchers will find that this text gives them a new set of tools to further mine the Web for knowledge and move well beyond the capabilities of standard search engines.

Exam Board: SQA Level: National 5 Subject: Maths First Teaching: September 2017 First Exam: Summer 2018 Get your best grade with How to Pass National 5 Applications of Mathematics. Fully updated to account for the changes to the National 5 exam, this book contains all the advice and support you need to revise successfully. It combines an overview of the course syllabus with advice from a top expert on how to improve exam performance, so you have the best chance of success. - Refresh your knowledge with complete course notes - Prepare for the exam with top tips and hints on revision technique - Get your best grade with advice on how to gain those vital extra marks

Chemometric Techniques for Quantitative Analysis shows how to produce and use quantitative analytical calibrations in a laboratory or production environment following a variety of methods, how to estimate the time and resources needed to develop analytical calibrations, and how to employ the quantitative software provided with a wide range of instruments and commercial software packages. Among several, this bestselling volume covers basic and classical approaches, component regression; PCR in action; partial least squares; PLS in action. An extensive appendix offers a glossary, a list of errors and tests for reduced Eigenvalues.

Asia is the largest continent in the world. Five out of the top ten high performing economies in the Programme for International Student Assessment (PISA) 2018 are located in Asia. Why do Asian students perform so well in STEM-related subjects? This book answers this by examining the STEM education policies and initiatives in Asian economies, as well as the training programmes undertaken by STEM teachers in Asia. The book is broken into four sections, each accompanied by a passage of commentary that summarizes the key takeaways of the chapters. Section one focuses on STEM policy environments and how various countries have developed policies that promote STEM as an integral part of national economic development. Section two focuses on STEM teacher education in the Philippines and Thailand, while section three focuses on STEM curriculum design, context, and challenges in four Asian economies. The fourth and final section focuses on presenting snapshots of STEM education research efforts in Malaysia, South Korea, and Singapore. Written by Asian academics, this book will provide valuable insights to policy makers, educators, and researchers interested in the topic of STEM education, especially in the Asian context. Chapters 7 and 11 of this book are freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com

This book develops foundational concepts in probability and statistics with primary applications in mechanical and aerospace engineering. It develops the mindset a data analyst must have to interpret an ill-defined problem, operationalize it, collect or interpret data, and use this evidence to make decisions that can improve the quality of engineered products and systems. It was designed utilizing the latest research in statistics learning and in engagement teaching practices The author's focus is on developing students' conceptual understanding of statistical theory with the goal of effective design and conduct of experiments. Engineering statistics is primarily a form of data modeling. Emphasis is placed on modelling variation in observations, characterizing its distribution, and making inferences with regards to quality assurance and control. Fitting multivariate models, experimental design and hypothesis testing are all critical skills developed. All topics are developed utilizing real data from engineering projects, simulations, and laboratory experiences. In other words, we begin with data, we end with models. The key features are: Realistic contexts situating the learning of the statistics in actual engineering practice. A balance of rigorous mathematics, conceptual scaffolding, and real, messy data, to ensure that students learn the important concepts and can apply them in practice. The consistency of text, lecture notes, data sets, and simulations yield a coherent set of instructional resources for the instructor and a coherent set of learning experiences for the students. MatLab is used as a computational tool. Other tools are easily substituted. Table of Contents 1. Introduction 2. Dealing with Variation 3. Types of Data 4. Introduction to Probability 5. Sampling Distribution of the Mean 6. The Ten Building Blocks of Experimental Design 7. Sampling Distribution of the Proportion 8. Hypothesis Testing Using the 1-sample Statistics 9. 2-sample Statistics 10. Simple Linear Regression 11. The General Linear Model: Regression with Multiple Predictors 12. The GLM with Categorical Independent Variables: The Analysis of Variance 13. The General Linear Model: Randomized Block Factorial ANOVA 14. Factorial Analysis of Variance 15. The Bootstrap 16. Data Reduction: Principal Components Analysis Index Author Biography James A. Middleton is Professor of Mechanical and Aerospace Engineering and former Director of the Center for Research on Education in Science, Mathematics, Engineering, and Technology at Arizona State University. Previously, he held the Elmhurst Energy Chair in STEM education at the University of Birmingham in the UK. He received his Ph.D. from the University of Wisconsin-Madison. He has been Senior co-Chair of the Special Interest Group for Mathematics Education in the American Educational Research Association, and as Chair of the National Council of Teachers of Mathematics' Research Committee. He has been a consultant for the College Board, the Rand Corporation, the National Academies, the American Statistical Association, the IEEE, and numerous school systems around the United States, the UK, and Australia. He has garnered over $30 million in grants to study and improve mathematics education in urban schools.

This book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.

Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics - demonstrating our unconscious mathematical abilities.He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication.

Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. From a lifetime's thinking, he offers this extraordinary synthesis exposing the deepest connections between science, music, and mathematics, while avoiding equations and technical jargon. He begins with perception psychology and the dichotomization instinct and then takes us through biological evolution, human language, and acausality illusions all the way to the climate crisis and the weaponization of the social media, and beyond that into the deepest parts of theoretical physics - demonstrating our unconscious mathematical abilities.He also has an important message of hope for the future. Contrary to popular belief, biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is more than a simple competition between selfish genes. Rather, he suggests, in some ways it is more like turbulent fluid flow, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has worked on problems as diverse as the Sun's magnetic interior, the Antarctic ozone hole, jet streams in the atmosphere, and the psychophysics of violin sound. He has long been interested in how different branches of science can better communicate with each other and with the public, harnessing aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication.

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.

This book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.

This new edition of this standard has been extensively revised to serve the ever-increasing number of investigators who, with only a year or so of statistical training, are performing sophisticated statistical analyses on computers. It provides sound statistical methodology, practical advice on the application of this methodology, and information relating the statistics to computer manipulation and output.

Get ahead of the curve--learn about big data on the blockchain Blockchain came to prominence as the disruptive technology that made cryptocurrencies work. Now, data pros are using blockchain technology for faster real-time analysis, better data security, and more accurate predictions. Blockchain Data Analytics For Dummies is your quick-start guide to harnessing the potential of blockchain. Inside this book, technologists, executives, and data managers will find information and inspiration to adopt blockchain as a big data tool. Blockchain expert Michael G. Solomon shares his insight on what the blockchain is and how this new tech is poised to disrupt data. Set your organization on the cutting edge of analytics, before your competitors get there! Learn how blockchain technologies work and how they can integrate with big data Discover the power and potential of blockchain analytics Establish data models and quickly mine for insights and results Create data visualizations from blockchain analysis Discover how blockchains are disrupting the data world with this exciting title in the trusted For Dummies line!

GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics. Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author's previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable. Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics takes a gradual, relaxed, and discursive approach to the subject in a successful attempt to engage the reader by exploring a narrower range of themes and problems. Organized around examples with accompanying introductions and explanations, the book covers topics such as: Stochastic calculus, including discussions of random variation, integration and probability, and stochastic processes Field theory, including discussions of gauges for product spaces and quantum electrodynamics Robust and thorough appendices, examples, illustrations, and introductions for each of the concepts discussed within An introduction to basic gauge integral theory (for those unfamiliar with the author's previous book) The methods employed in this book show, for instance, that it is no longer necessary to resort to unreliable "Black Box" theory in financial calculus; that full mathematical rigor can now be combined with clarity and simplicity. Perfect for students and academics with even a passing interest in the application of the gauge integral technique pioneered by R. Henstock and J. Kurzweil, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics is an illuminating and insightful exploration of the complex mathematical topics contained within.

Master the fundamentals of SPSS with this newly updated and instructive resource The newly and thoroughly revised Second Edition of SPSS Essentials delivers a comprehensive guide for students in the social sciences who wish to learn how to use the Statistical Package for the Social Sciences (SPSS) for the effective collection, management, and analysis of data. The accomplished researchers and authors provide readers with the practical nuts and bolts of SPSS usage and data entry, with a particular emphasis on managing and manipulating data. The book offers an introduction to SPSS, how to navigate it, and a discussion of how to understand the data the reader is working with. It also covers inferential statistics, including topics like hypothesis testing, one-sample Z-testing, T-testing, ANOVAs, correlations, and regression. Five unique appendices round out the text, providing readers with discussions of dealing with real-world data, troubleshooting, advanced data manipulations, and new workbook activities. SPSS Essentials offers a wide variety of features, including: A revised chapter order, designed to match the pacing and content of typical undergraduate statistics classes An explanation of when particular inferential statistics are appropriate for use, given the nature of the data being worked with Additional material on understanding your data sample, including discussions of SPSS output and how to find the most relevant information A companion website offering additional problem sets, complete with answers Perfect for undergraduate students of the social sciences who are just getting started with SPSS, SPSS Essentials also belongs on the bookshelves of advanced placement high school students and practitioners in social science who want to brush up on the fundamentals of this powerful and flexible software package.

This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell's equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.

Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: "It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences." (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) "The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an 'appreciation of mathematics' course, among other possibilities." (G.A. Heuer, Mathematical Reviews, February, 2015) "Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers." (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)

During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23-27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee "Systems Modeling and Optimization" of the International Federation for Information Processing (IFIP TC7).

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa.

These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.

This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections.

Contributors: G. BAckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. KAhler; U. KA1/4hn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.

Provides clear guidance on leveraging computational techniques to answer social science questions In disciplines such as political science, sociology, psychology, and media studies, the use of computational analysis is rapidly increasing. Statistical modeling, machine learning, and other computational techniques are revolutionizing the way electoral results are predicted, social sentiment is measured, consumer interest is evaluated, and much more. Computational Analysis of Communication teaches social science students and practitioners how computational methods can be used in a broad range of applications, providing discipline-relevant examples, clear explanations, and practical guidance. Assuming little or no background in data science or computer linguistics, this accessible textbook teaches readers how to use state-of-the art computational methods to perform data-driven analyses of social science issues. A cross-disciplinary team of authors--with expertise in both the social sciences and computer science--explains how to gather and clean data, manage textual, audio-visual, and network data, conduct statistical and quantitative analysis, and interpret, summarize, and visualize the results. Offered in a unique hybrid format that integrates print, ebook, and open-access online viewing, this innovative resource: Covers the essential skills for social sciences courses on big data, data visualization, text analysis, predictive analytics, and others Integrates theory, methods, and tools to provide unified approach to the subject Includes sample code in Python and links to actual research questions and cases from social science and communication studies Discusses ethical and normative issues relevant to privacy, data ownership, and reproducible social science Developed in partnership with the International Communication Association and by the editors of Computational Communication Research Computational Analysis of Communication is an invaluable textbook and reference for students taking computational methods courses in social sciences, and for professional social scientists looking to incorporate computational methods into their work.

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units - ranging from grades 7 through 12 - that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!