Written by expert teachers, X-kit Achieve Study Guides are a reliable resource for learning and revising, preparing learners for tests and exams. The content is organised into units according to CAPS, and clear, step-by-step explanations help learners understand concepts. Worked examples, summary tables, highlighted keywords and definitions, and annotated diagrams enhance learners’ understanding. Learners can practice, assess and improve their skills with graded exercises and answers.

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.

Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student's experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students' backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms

ICMI (or IMUK) was founded in 1908 and initiated the establishment of national subcommissions to launch national activities in response to the IMUK agenda and to promote the reform proposals within each member country.While ICMI's activities were thoroughly studied, the activities of the national subcommissions are studied only very marginally. In the meantime, their work has been of major importance - both because of their role in exploring and documenting the development of mathematics education at the beginning of the 20th century, and because of the changes and new ideas which they brought to their countries. Importantly, even if some results of their activities were analyzed within their countries in the corresponding languages, almost nothing is known internationally. This book is planned to deepen our knowledge on at least some of the national subcommissions. The book will interest both researchers and others interested in mathematics education and its development.

Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.

This book is a series of self-contained workshops in mathematics which aim to enthuse and inspire young people, their parents and teachers. Each chapter describes how novel mathematical ideas relate to real life, and includes problem sheets, their solutions, ideas for further work, projects and field trips. The book, written in an informal style, is accessible to young people from age thirteen upwards and contains material which should stretch the brightest students.

The definitive reference book with real-world solutions you won't find anywhere else The Big Book of Dashboards presents a comprehensive reference for those tasked with building or overseeing the development of business dashboards. Comprising dozens of examples that address different industries and departments (healthcare, transportation, finance, human resources, marketing, customer service, sports, etc.) and different platforms (print, desktop, tablet, smartphone, and conference room display) The Big Book of Dashboards is the only book that matches great dashboards with real-world business scenarios. By organizing the book based on these scenarios and offering practical and effective visualization examples, The Big Book of Dashboards will be the trusted resource that you open when you need to build an effective business dashboard. In addition to the scenarios there's an entire section of the book that is devoted to addressing many practical and psychological factors you will encounter in your work. It's great to have theory and evidenced-based research at your disposal, but what will you do when somebody asks you to make your dashboard 'cooler' by adding packed bubbles and donut charts? The expert authors have a combined 30-plus years of hands-on experience helping people in hundreds of organizations build effective visualizations. They have fought many 'best practices' battles and having endured bring an uncommon empathy to help you, the reader of this book, survive and thrive in the data visualization world. A well-designed dashboard can point out risks, opportunities, and more; but common challenges and misconceptions can make your dashboard useless at best, and misleading at worst. The Big Book of Dashboards gives you the tools, guidance, and models you need to produce great dashboards that inform, enlighten, and engage.

This book covers all the content needed for AS and Year 1 of the Edexcel Statistics and Mechanics A-Level course and is fully up to date for the latest specifications. It has the clearest notes on all the theory for every topic, including annotated worked examples and explanations; hundreds of challenging questions for every chapter, including problem-solving and modelling; a realistic Practice Paper with a complete mark scheme; and a free Online Edition to read on PC, Mac or tablet (use the unique code printed inside the cover to gain full access). For full A-Level Maths coverage don't miss the Year 1 Pure Maths Student Textbook (9781789088397), and our Year 2 Student Textbooks for Pure Maths (9781789088410) and Statistics and Mechanics (9781789088427).

This open access book is the first major publication on the topic of "Interdisciplinary Mathematics Education" and arose from the work of the first International Topic Study Group of the same name at the ICME-13 conference in Hamburg in 2016. It offers extensive theoretical insights, empirical research, and practitioner accounts of interdisciplinary mathematics work in STEM and beyond (e.g. in music and the arts). Scholars and practitioners from four continents contributed to this comprehensive book, and present studies on: the conceptualizations of interdisciplinarity; implementation cases at schools and tertiary institutions; teacher education; and implications for policy and practice. Each chapter, and the book itself, closes with an assessment of the most significant aspects that those involved in policy and practice, as well as future researchers, should take into account.

This book engages with contemporary, and often polarizing, debates surrounding the risks of adolescent use of digital media and internet technologies. By drawing on multiple research studies, the text synthesizes current understandings of the impacts of social network use, online gaming, pornography, and phenomena, including cyberbullying, cyberstalking, and internet addiction, to develop recommendations for the effective identification of at-risk youth, as well as strategies for informed communication about online risks and opportunities. It shows how media discussion of risks to children and teenagers from new technology is highly emotive and often exaggerated, rooted in the “moral panic” surrounding new cultural practices that young people engage in, but which adults do not understand. Online risks are thus conceptualized as centering on three areas, specific to adolescence, which have undergone radical changes due to new internet technology. These include young people’s identity, the types of content that are accessed, and social relationships. The author shows how these matters stem from the potential of new technology to establish new interpersonal connections, emphasizing how it brings opportunities, as much as risks. As such, he provides a uniquely balanced discussion of potential dangers, while also emphasizing the opportunities for social, academic, and personal growth which new technologies afford young people. It will be indispensable for researchers and clinicians interested in assessing levels of online risk, as well as scholars and educators with interests in cyberpsychology, social psychology, cyber culture, social aspects of computing and media, and adolescent development.

The book presents the life and works of one of Germany's most famous computer scientists, Carl Adam Petri. It is written in a vivid and entertaining manner, providing an in-depth discussion of the background behind Petri's best-known contribution to computer science, the Petri net. In this way the book can be read as a first introduction to nets, but it also covers the theoretical, physical and philosophical foundations behind nets, thus facilitating a comprehensive understanding of the wider range of Petri's works. The book is intended for readers with a previous knowledge in computer science, as well as for "interested non-professionals", who want to get to know a remarkable personality of contemporary science.

The second edition of Mark Wolfmeyer's award-winning primer offers future and current math teachers an introduction to the connections that exist between mathematics and a critical orientation to education, one that accounts for race, social class, gender, sexuality, language diversity, and ability. Expanded and updated from the first edition, this book demonstrates how elements of human diversity and intersectionality have real effects in the mathematics classroom, and prepares teachers with a more critical math education that increases accessibility and equity for all students. By refocusing math learning toward the goals of democracy and social and environmental crises, the book also introduces readers to broader contemporary school policy and reform debates and struggles, especially in light of Covid-19 and the ongoing struggle for racial equity. Featuring concrete strategies and examples in both formal and informal educational settings, as well as discussion questions for teachers and students, text boxes with examples of critical education in practice, a glossary, and suggestions for further reading, Mark Wolfmeyer shows how critical mathematics education can be put into practice, relevant for undergraduate and graduate students in education, current teachers, and teacher educators.

Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity.

What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough?

Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques / International Commission for the Study and Improvement of Mathematics Education.

This volume analyzes the dominance of STEM fields in various university rankings and the reasons why many governments in the world disproportionately give value to STEM fields. Secondly, although there is general agreement that STEM fields are important, chapter authors also examine the role of interdisciplinary and multidisciplinary approaches for a revised STEM education as well as implications for the future. The book presents examples from the United States, Canada, Japan, Korea, and Taiwan.

Mathematical biology remains a fast-growing topic within applied mathematics. The Mathematical Modeling course is a common and popular course. This book aims to tailor the modeling course to life science applications. It introduces an advanced concept, Sensitivity Analysis, at an undergraduate level. The book will be attractive to any mathematician teaching biology students in a modeling or mathematical biology course.

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. The book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.

CGP have knocked it out of the park with this Exam Practice Workbook for the SQA Higher Maths course. It's loaded with realistic exam-style questions on a wide range of Higher Maths topics - perfect practice for the tough exams! For more essential revision for Higher Maths, check out our brilliant Revision Guide (ISBN: 9781782949602)

This timely resource fills a gap in existing literature on mathematical modeling by presenting both theory- and evidence-based ideas for its teaching and learning. The book outlines four key professional competencies that must be developed in order to effectively and appropriately teach mathematical modeling, and in so doing it seeks to reduce the discrepancies between educational policy and educational research versus everyday teaching practice. Among the key competencies covered are: Theoretical competency for practical work. Task competency for instructional flexibility. Instructional competency for effective and quality lessons. Diagnostic competency for assessment and grading. Learning How to Teach Mathematical Modeling in School and Teacher Education is relevant to practicing and future mathematics teachers at all levels, as well as teacher educators, mathematics education researchers, and undergraduate and graduate mathematics students interested in research based methods for teaching mathematical modeling.

What is terrorism? What can we learn and what cannot we learn from terrorism data? What are the perspectives and limitations of the analysis of terrorism data? Over the last decade, scholars have generated unprecedented insight from the statistical analysis of ever-growing databases on terrorism. Yet their findings have not reached the public. This book translates the current state of knowledge on global patterns of terrorism free of unnecessary jargon. Readers will be gradually introduced to statistical reasoning and tools applied to critically analyze terrorism data within a rigorous framework. Debunking Seven Terrorism Myths Using Statistics communicates evidence-based research work on terrorism to a general audience. It describes key statistics that provide an overview of the extent and magnitude of terrorist events perpetrated by actors independent of state governments across the world. The books brings a coherent and rigorous methodological framework to address issues stemming from the statistical analysis of terrorism data and its interpretations. Features Uses statistical reasoning to identify and address seven major misconceptions about terrorism. Discusses the implications of major issues about terrorism data on the interpretation of its statistical analysis. Gradually introduces the complexity of statistical methods to familiarize the non-statistician reader with important statistical concepts to analyze data. Use illustrated examples to help the reader develop a critical approach applied to the quantitative analysis of terrorism data. Includes chapters focusing on major aspects of terrorism: definitional issues, lethality, geography, temporal and spatial patterns, and the predictive ability of models.

Preparing for the A-Level Maths exams takes a lot of solid practice, which is precisely what you'll find in this superb Exam Practice Workbook. It covers every topic on the Edexcel Maths A-Level course so students can be sure they're prepared for the big day! Packed with exam-style questions, practice papers, useful tips, mark schemes and step-by-step solutions, this book is the perfect companion for students as they revise for their exams. We've sign-posted Problem-Solving and Modelling questions so they can be sure they're focussing their efforts on the right areas, and there's also a new section of more challenging Problem Solving questions - perfect prep for anything the exams might throw at them! Don't miss our matching A-Level Maths Edexcel Complete Revision & Practice book (9781782948087) for notes and examples on every topic.