What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know... and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.

This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.

Your logical, linear guide to the fundamentals of data science programming Data science is exploding--in a good way--with a forecast of 1.7 megabytes of new information created every second for each human being on the planet by 2020 and 11.5 million job openings by 2026. It clearly pays dividends to be in the know. This friendly guide charts a path through the fundamentals of data science and then delves into the actual work: linear regression, logical regression, machine learning, neural networks, recommender engines, and cross-validation of models. Data Science Programming All-In-One For Dummies is a compilation of the key data science, machine learning, and deep learning programming languages: Python and R. It helps you decide which programming languages are best for specific data science needs. It also gives you the guidelines to build your own projects to solve problems in real time. Get grounded: the ideal start for new data professionals What lies ahead: learn about specific areas that data is transforming Be meaningful: find out how to tell your data story See clearly: pick up the art of visualization Whether you're a beginning student or already mid-career, get your copy now and add even more meaning to your life--and everyone else's!

This revised and updated third edition offers a range of strategies, activities and ideas to bring mathematics to life in the primary classroom. Taking an innovative and playful approach to maths teaching, this book promotes creativity as a key element of practice and offers ideas to help your students develop knowledge, understanding and enjoyment of the subject. In the creative classroom, mathematics becomes a tool to build confidence, develop problem solving skills and motivate children. The fresh approaches explored in this book include a range of activities such as storytelling, music and construction, elevating maths learning beyond subject knowledge itself to enable students to see mathematics in a new way. Key chapters of this book explore: * Learning maths outdoors - make more noise, make more mess or work on a larger scale * Everyday maths - making sense of the numbers, patterns, shapes and measures children see around them * Music and maths - the role of rhythm in learning, and music and pattern in maths Stimulating, accessible and underpinned by the latest research and theory, this is essential reading for trainee and practising teachers who wish to embed creative approaches to maths teaching in their classroom.

Exam Board: Pearson Edexcel Academic Level: AS level Subject: Mathematics First teaching: September 2017 First Exams: Summer 2018 This Revision Workbook is suitable for classroom and independent study, and is the smart choice for those revising for AS level Mathematics. Organise their revision with the one topic-per-page format Speed up their revision with summary notes in short, memorable chunks Track their revision progress with at-a-glance check boxes Check their understanding with worked examples Develop their exam technique with exam-style practice questions and answers

Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities. After an introduction to the basic features of fiber-optic communications, the book outlines the nonlinear Schroedinger equation (NLSE), conserved quantities, and adiabatic dynamics of soliton parameters. It then derives the NLSE for Kerr law nonlinearity from basic principles, the inverse scattering transform, and the 1-soliton solution. The book also explains the variational principle and Lie transform. In each case of non-Kerr law solitons, the authors develop soliton dynamics, evaluated integrals of motion, and adiabatic dynamics of soliton parameters based on multiple-scale perturbation theory. The book explores intra-channel collision of optical solitons in both Hamiltonian and non-Hamiltonian type perturbations. In addition, it examines the stochastic perturbation of optical solitons, the corresponding Langevin equations, and optical couplers, followed by an introduction to optical bullets. Establishing a basis in an important yet insufficiently documented subject, Introduction to non-Kerr Law Optical Solitons will help fuel advances in optical communication systems.

The amount of data in everyday life has been exploding. This data increase has been especially significant in scientific fields, where substantial amounts of data must be captured, communicated, aggregated, stored, and analyzed. Cloud Computing with e-Science Applications explains how cloud computing can improve data management in data-heavy fields such as bioinformatics, earth science, and computer science. The book begins with an overview of cloud models supplied by the National Institute of Standards and Technology (NIST), and then: Discusses the challenges imposed by big data on scientific data infrastructures, including security and trust issues Covers vulnerabilities such as data theft or loss, privacy concerns, infected applications, threats in virtualization, and cross-virtual machine attack Describes the implementation of workflows in clouds, proposing an architecture composed of two layers-platform and application Details infrastructure-as-a-service (IaaS), platform-as-a-service (PaaS), and software-as-a-service (SaaS) solutions based on public, private, and hybrid cloud computing models Demonstrates how cloud computing aids in resource control, vertical and horizontal scalability, interoperability, and adaptive scheduling Featuring significant contributions from research centers, universities, and industries worldwide, Cloud Computing with e-Science Applications presents innovative cloud migration methodologies applicable to a variety of fields where large data sets are produced. The book provides the scientific community with an essential reference for moving applications to the cloud.

This textbook offers a systematic, self-contained account of the main contributions of modern game theory and its applications to economics. Starting with a detailed description of how to model strategic situations, the discussion proceeds by studying basic solution concepts, their main refinements, games played under incomplete information, and repeated games. For each of these theoretical developments, there is a companion set of applications that cover the most representative instances of game-theoretic analysis in economics, e.g. oligopolistic competition, public goods, coordination failures, bargaining, insurance markets, implementation theory, signaling and auctions. The theory and applications covered in the first part of the book fall under the so-called 'classical' approach to game theory, which is founded on the paradigm of players' unlimited rationality. The second part shifts towards topics that no longer abide by that paradigm. This leads to the study of topics such as the interplay between evolution and rationality.

Student Handbook for Discrete Mathematics with Ducks is a Student Reference, Review, Supplemental Learning, and Example Handbook (SRRSLEH) that mirrors the content of the author's popular textbook Discrete Mathematics with Ducks (DMwD). This handbook provides a review of key material, illustrative examples, and new problems with accompanying solutions that are helpful even for those using a traditional discrete mathematics textbook. Every chapter in SRRSLEH matches the corresponding chapter of DMwD. Chapters in SRRSLEH contain the following: A list of the notation introduced in the corresponding chapter A list of definitions that students need to know from the corresponding chapter Theorems/facts of note appearing in the corresponding chapter A list of proof techniques introduced, with templates and/or examples given for each one A selection of examples from DMwD, written out formally and briefly rather than colloquially as in DMwD A quick refresher for any discrete math student, this handbook enables students to find information easily and reminds them of the terms and results they should know during their course. Read reviews of DMwD.

Exam Board: SQA Level: Higher Subject: Maths First Teaching: 2019, First Exam: 2020 Nail your Higher Maths by working through practice questions on every topic of the curriculum, then test your understanding with mixed exam question practice. Master even the trickiest of topics by practising tons of questions Check your understanding by reviewing the example answers which contain workings-out Build your confidence with the Mixed Exam Question Practice section, to prepare for the type and level of questions you can expect in the SQA Higher Maths exam Understand how your exam will be marked with detailed answers to all of the questions Learn how to approach different types of question with hints and tips All answers can be found online at https://collins.co.uk/pages/scottish-curriculum-free-resources Can be used at school or at home – for revision, homework, independent study or exam practice. For more resources to help you do your very best, why not try Leckie’s Higher Maths Complete Revision & Practice (9780008365233).

This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook's original themes for international research in mathematics education and remains in the process a definitive resource for the field.

Education in science, technology, engineering and mathematics (STEM) is crucial for taking advantage of the prospects of new scientific discoveries initiating or promoting technological changes, and managing opportunities and risks associated with innovations. This book explores the emerging perspectives and methodologies of STEM education and its relationship to the cultural understanding of science and technology in an international context. The authors provide a unique perspective on the subject, presenting materials and experiences from non-European industrialized as well as industrializing countries, including China, Japan, South Korea, India, Egypt, Brazil and the USA. The chapters offer a wide scope of interpretations and comparative reviews of STEM education by including narrative elements about cultural developments, considering the influence of culture and social perceptions on technological and social change, and applying innovative tools of qualitative social research. The book represents a comprehensive and multidisciplinary review of the current status and future challenges facing STEM education across the world, including issues such as globalization, interdependencies of norms and values, effects on equity and social justice as well as resilience. Overall the volume provides valuable insights for a broad and comprehensive international comparison of STEM philosophies, approaches and experiences.

MACHINE LEARNING FOR BUSINESS ANALYTICS An up-to-date introduction to a market-leading platform for data analysis and machine learning Machine Learning for Business Analytics: Concepts, Techniques, and Applications with JMP Pro®, 2nd ed. offers an accessible and engaging introduction to machine learning. It provides concrete examples and case studies to educate new users and deepen existing users’ understanding of their data and their business. Fully updated to incorporate new topics and instructional material, this remains the only comprehensive introduction to this crucial set of analytical tools specifically tailored to the needs of businesses. Machine Learning for Business Analytics: Concepts, Techniques, and Applications with JMP Pro®, 2nd ed. readers will also find: Updated material which improves the book’s usefulness as a reference for professionals beyond the classroom Four new chapters, covering topics including Text Mining and Responsible Data Science An updated companion website with data sets and other instructor resources: www.jmp.com/dataminingbook A guide to JMP Pro®’s new features and enhanced functionality Machine Learning for Business Analytics: Concepts, Techniques, and Applications with JMP Pro®, 2nd ed. is ideal for students and instructors of business analytics and data mining classes, as well as data science practitioners and professionals in data-driven industries.

This book discusses recent developments in Input-Output (I/O) models for microcomputers and applications of I/O models in regional studies. It provides background information on traditional I/O models and a set of working examples of I/O applications for users.

A thorough account of the philosophy of mathematics. In a cogent account the author argues against the view that mathematics is solely logic.

This comprehensive CGP Student Book is perfect for anyone in the second year of OCR A-Level Maths - it has all the Pure Maths, Statistics and Mechanics content required for the course starting in 2017 and beyond. All the theory is clearly explained with straightforward study notes, step-by-step examples and helpful tips, plus there are plenty of essential practice questions for every topic (with fully worked answers at the back). The new problem solving and modelling requirements are covered too! To top things off, this book come with a free Online Edition (accessed using the unique code printed inside the front cover) that lets you read the entire book on a PC, Mac or tablet. For complete A-Level coverage, a Year 1 OCR Maths Student Book (9781782947226) is also available from CGP.

This book is a collection of accepted papers that were presented at the International Conference on Communication and Computing Systems (ICCCS-2016), Dronacharya College of Engineering, Gurgaon, September 9-11, 2016. The purpose of the conference was to provide a platform for interaction between scientists from industry, academia and other areas of society to discuss the current advancements in the field of communication and computing systems. The papers submitted to the proceedings were peer-reviewed by 2-3 expert referees. This volume contains 5 main subject areas: 1. Signal and Image Processing, 2. Communication & Computer Networks, 3. Soft Computing, Intelligent System, Machine Vision and Artificial Neural Network, 4. VLSI & Embedded System, 5. Software Engineering and Emerging Technologies.

Study smarter and stay on top of your discrete mathematics course with the bestselling Schaum's Outline-now with the NEW Schaum's app and website! Schaum's Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university students taking basic computer science courses. With an outline format that facilitates quick and easy review, Schaum's Outline of Discrete Mathematics, Fourth Edition helps you understand basic concepts and get the extra practice you need to excel in these courses. Coverage includes set theory; relations; functions and algorithms; logic and propositional calculus; techniques of counting; advanced counting techniques, recursion; probability; graph theory; directed graphs; binary trees; properties of the integers; languages, automata, machines; finite state machines and Turning machines; ordered sets and lattices, and Boolean algebra. Features * NEW to this edition: the new Schaum's app and website! * NEW to this edition: 20 NEW problem-solving videos online * 467 solved problems, and hundreds of additional practice problems * Outline format to provide a concise guide to the standard college course in discrete mathematics * Clear, concise explanations of discrete mathematics concepts * Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning * Increased emphasis on discrete probability and aspects of probability theory, and greater accessibility to counting techniques. * Logic chapter emphasizes the IF-THEN and IF-THEN-ELSE sequencing that occurs in computer programming * Computer arithmetic chapter covers binary and hexagon addition and multiplication * Cryptology chapter includes substitution and RSA method * Supports these major texts: Discrete Mathematics and Its Applications (Rosen), and Discrete Mathematics (Epp) * Appropriate for the following courses: Introductory Discrete Mathematics and Discrete Mathematics

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure. The unification of space and time introduced by Einstein's special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different properties The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas. Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge. Changes to the Second Edition The treatment of Minkowski space and spacetime diagrams has been expanded. Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of "area" and how it can be used to measure time and distance. Minor notational changes were made to avoid conflict with existing usage in the literature. Table of Contents Preface 1. Introduction. 2. The Physics of Special Relativity. 3. Circle Geometry. 4. Hyperbola Geometry. 5. The Geometry of Special Relativity. 6. Applications. 7. Problems III. 8. Paradoxes. 9. Relativistic Mechanics. 10. Problems II. 11. Relativistic Electromagnetism. 12. Problems III. 13. Beyond Special Relativity. 14. Three-Dimensional Spacetime Diagrams. 15. Minkowski Area via Light Boxes. 16. Hyperbolic Geometry. 17. Calculus. Bibliography. Author Biography Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.

Adaptive filters are used in many diverse applications, appearing in everything from military instruments to cellphones and home appliances. Adaptive Filtering: Fundamentals of Least Mean Squares with MATLAB (R) covers the core concepts of this important field, focusing on a vital part of the statistical signal processing area-the least mean square (LMS) adaptive filter. This largely self-contained text: Discusses random variables, stochastic processes, vectors, matrices, determinants, discrete random signals, and probability distributions Explains how to find the eigenvalues and eigenvectors of a matrix and the properties of the error surfaces Explores the Wiener filter and its practical uses, details the steepest descent method, and develops the Newton's algorithm Addresses the basics of the LMS adaptive filter algorithm, considers LMS adaptive filter variants, and provides numerous examples Delivers a concise introduction to MATLAB (R), supplying problems, computer experiments, and more than 110 functions and script files Featuring robust appendices complete with mathematical tables and formulas, Adaptive Filtering: Fundamentals of Least Mean Squares with MATLAB (R) clearly describes the key principles of adaptive filtering and effectively demonstrates how to apply them to solve real-world problems.

This handy pocket book will help veterinary nurses with all types of calculations. Numerous worked examples are included to delelop the reader's confidence in carrying out the procedures involved. Each type of calculation has its own separate section in the book and the authors have used the simplest possible method in explaining each one. The book is structured such a way that the reader can progress from a simple explanation of the arithmetic principles involved, to the application of these principles to essential veterinary calculations.

Qualified veterinary nurses and students alike will fine this book an invaluable reference source, whether performing relevant veterinary calculations or studying for professional examinations.

Key Features
Convenient size
Ideal as a self-teaching manual
Accessible and user-friendly style
Includes worked examples, self-test exercises and answers where appropriate

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.