These laminated alphabet cards reinforce both math vocabulary and language skills. Cards include several math words for each letter of the alphabet and contain a song with a math focus for each letter.

Although many books have been written about Mathematica, very few of them cover the new functionality added to the most recent versions of the program. This thoroughly revised second edition of Mathematica Beyond Mathematics: The Wolfram Language in the Real World introduces the new features using real-world examples based on the experience of the author as a consultant and Wolfram certified instructor. The examples strike a balance between relevance and difficulty in terms of Mathematica syntax, allowing readers to incrementally build up their Mathematica skills as they go through the chapters While reading this book, you will also learn more about the Wolfram Language and how to use it to solve a wide variety of problems. The author raises questions from a wide range of topics and answers them by taking full advantage of Mathematica's latest features. For example: What sources of energy does the world really use? Are our cities getting warmer? Is the novel El Quixote written in Pi? Is it possible to reliably date the Earth using radioactive isotopes? How can we find planets outside our solar system? How can we model epidemics, earthquakes and other natural phenomena? What is the best way to compare organisms genetically? This new edition introduces the new capabilities added to the latest version of Mathematica (version 13), and discusses new topics related to machine learning, big data, finance economics, and physics. New to the Second Edition Separate sections containing carefully selected additional resources that can be accessed from either Mathematica or online Online Supplementary materials including code snippets used in the book and additional examples. Updated commands to take full advantage of Mathematica 13.

Fortran remains one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities and the latest standard, Fortran 2008, includes many modern features, such as object orientation, coarrays for parallel programming, interoperability with C and various other enhancements.
Modern Fortran Explained expands on its predecessor, Fortran 95/2003 Explained. The opening chapters contain a complete description of Fortran 95, extended by Fortran 2003 allocatable array features. Coverage of the other additional features of Fortran 2003 follows, before new chapters on coarrays and the many other enhancements of Fortran 2008. The distinction between the three language levels is maintained throughout, allowing readers to understand and amend legacy code as well as the new features.
Authored by three experts in the field, two of whom have actively contributed to Fortran 2008, this is a complete and authoritative description of Fortran in its modern form. It is intended for new and existing users of the language and for all those involved in scientific and numerical computing. It is suitable as a textbook for teaching and, with its extensive Appendices and an Index, as a handy reference for practitioners.

The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view."

Learn about the most important mathematical ideas, theorems, and movements in The Maths Book.

Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Maths in this overview guide to the subject, great for novices looking to find out more and experts wishing to refresh their knowledge alike! The Maths Book brings a fresh and vibrant take on the topic through eye-catching graphics and diagrams to immerse yourself in.

This captivating book will broaden your understanding of Maths, with:

- More than 85 ideas and events key to the development of mathematics
- Packed with facts, charts, timelines and graphs to help explain core concepts
- A visual approach to big subjects with striking illustrations and graphics throughout
- Easy to follow text makes topics accessible for people at any level of understanding

The Maths Book is a captivating introduction to the world's most famous theorems, mathematicians and movements, aimed at adults with an interest in the subject and students wanting to gain more of an overview. Charting the development of maths around the world from Babylon to Bletchley Park, this book explains how maths help us understand everything from patterns in nature to artificial intelligence.

Your Maths Questions, Simply Explained

What is an imaginary number? Can two parallel lines ever meet? How can maths help us predict the future? This engaging overview explores answers to big questions like these and how they contribute to our understanding of maths. If you thought it was difficult to learn about topics like algebra and statistics, The Maths Book presents key information in an easy to follow layout. Learn about the history of maths, from ancient ideas such as magic squares and the abacus to modern cryptography, fractals, and the final proof of Fermat's Last Theorem.

The Big Ideas Series

With millions of copies sold worldwide, The Maths Book is part of the award-winning Big Ideas series from DK. The series uses striking graphics along with engaging writing, making big topics easy to understand.

The pendulum is a unique physical system which exhibits remarkably varied and complex behavior under many different conditions. It is also a system which, in its many manifestations, has left a significant imprint on human thought and culture. Using graphs, figures, and narrative to explain scientific ideas and models, Gregory Baker gives a lucid account of the physics of the pendulum, showing the reader how the context of the pendulum progresses over four centuries from that of a simple system of classical physics, to that of a chaotic system, and eventually to that of a modern quantum system. He also describes its fascinating presence in cultural history, from its role in timekeeping and measurements of the earth to its importance as a literary symbol of doom.
Seven 'tales', detailing different important facets of the pendulum, show the exciting diversity of the science of the pendulum, and its untold significance in the history of human intellectual development.

This book brings together two important trends: graph algorithms and high-performance computing. Efficient and scalable execution of graph processing applications in data or network analysis requires innovations at multiple levels: algorithms, associated data structures, their implementation and tuning to a particular hardware. Further, programming languages and the associated compilers play a crucial role when it comes to automating efficient code generation for various architectures. This book discusses the essentials of all these aspects. The book is divided into three parts: programming, languages, and their compilation. The first part examines the manual parallelization of graph algorithms, revealing various parallelization patterns encountered, especially when dealing with graphs. The second part uses these patterns to provide language constructs that allow a graph algorithm to be specified. Programmers can work with these language constructs without worrying about their implementation, which is the focus of the third part. Implementation is handled by a compiler, which can specialize code generation for a backend device. The book also includes suggestive results on different platforms, which illustrate and justify the theory and practice covered. Together, the three parts provide the essential ingredients for creating a high-performance graph application. The book ends with a section on future directions, which offers several pointers to promising topics for future research. This book is intended for new researchers as well as graduate and advanced undergraduate students. Most of the chapters can be read independently by those familiar with the basics of parallel programming and graph algorithms. However, to make the material more accessible, the book includes a brief background on elementary graph algorithms, parallel computing and GPUs. Moreover it presents a case study using Falcon, a domain-specific language for graph algorithms, to illustrate the concepts.

The Summer School has been dedicated to one of the proponents and ?rst Chairman of the Strategy Board of MACSI-net, the late Jacques Louis Lions (see the dedication by Roland Glowinski). MACSI-net is a European Network of Excellence, where both enterprises and university institutions co-operate to solve challenging problems to their mutual bene?t. In particular the network focuses on strategies to enhance interactions between industry and academia. The aim is to help industry (in particular SMEs) alert academia about industrial needs in terms of advanced mathematical and computational methods and tools. The network is mul- disciplinary oriented, combining the power of applied mathematics, scienti?c computing and engineering, for modeling and simulation. It was set up by a joint e?ort of ECCOMAS and ECMI European associations. Thisparticularevent,occurredduringMarch17-22,2003,wasajointe?ort ofthe TrainingCommittee (chairedby VC)andIndustrialRelationsComm- tee (chairedby JP)to alert both Academia and Industry about the increasing role of Multidisciplinary Methods and Tools for the design of complex pr- uctsinvariousareasofindustrialinterest.Thisincreasingcomplexityisdriven by societal constraints to be satis? ed in a simultaneous and a?ordable way. The mastering of complexity implies the sharing of di?erent tools by di?erent actors which require much higher level of communication between culturally di?erent people. The school o?ered to young researchers the opportunity to be exposed to the presentation of real industrial and societal problems and the relevant innovative methods used; the need of further contributions from mathematics to improve or provide better solutions had also been considered.

How do you predict something that has never happened before? There's a useful calculation being employed by Wall Street, Silicon Valley and maths professors all over the world, and it predicts that the human species will become extinct in 760 years. Unfortunately, there is disagreement over how to apply the formula, and some argue that we might only have twenty years left. Originally devised by British clergyman Thomas Bayes, the theorem languished in obscurity for two hundred years before being resurrected as the lynchpin of the digital economy. With brief detours into archaeology, philology, and overdue library books, William Poundstone explains how we can use it to predict pretty much anything. What is the chance that there are multiple universes? How long will Hamilton run? Will the US stock market continue to perform as well this century as it has for the last hundred years? And are we really all doomed?

Praise for the Third Edition "This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." - Electric Review Learn foundational and advanced topics in linear algebra with this concise and approachable resource A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique. The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features: A new application section on section on Google's Page Rank Algorithm. A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC). Many other illuminating applications of linear algebra with self-study questions for additional study. End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material Numerous computer exercises throughout using MATLAB(R) code Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

APPLIED MEDICAL STATISTICS An up-to-date exploration of foundational concepts in statistics and probability for medical students and researchers Medical journals and researchers are increasingly recognizing the need for improved statistical rigor in medical science. In Applied Medical Statistics, renowned statistician and researcher Dr. Jingmei Jiang delivers a clear, coherent, and accessible introduction to basic statistical concepts, ideal for medical students and medical research practitioners. The book will help readers master foundational concepts in statistical analysis and assist in the development of a critical understanding of the basic rationale of statistical analysis techniques. The distinguished author presents information without assuming the reader has a background in specialized mathematics, statistics, or probability. All of the described methods are illustrated with up-to-date examples based on real-world medical research, supplemented by exercises and case discussions to help solidify the concepts and give readers an opportunity to critically evaluate different research scenarios. Readers will also benefit from the inclusion of: A thorough introduction to basic concepts in statistics, including foundational terms and definitions, location and spread of data distributions, population parameters estimation, and statistical hypothesis tests Explorations of commonly used statistical methods, including t-tests, analysis of variance, and linear regression Discussions of advanced analysis topics, including multiple linear regression and correlation, logistic regression, and survival analysis Substantive exercises and case discussions at the end of each chapter Perfect for postgraduate medical students, clinicians, and medical and biomedical researchers, Applied Medical Statistics will also earn a place on the shelf of any researcher with an interest in biostatistics or applying statistical methods to their own field of research.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Publication of The Emperor's New Mind (OUP 1989) had caused considerable debate and Penrose's responses are included in this volume. Arising from this came the idea that large-scale quantum coherence might exist within the conscious brain, and actual conscious experience would be associated with a reduction of the quantum state. Within this collection, Penrose also proposes that a twistor might usefully be regarded as a source (or 'charge') for a massless field of spin 3/2, suggesting that the twistor space for a Ricci-flat space-time might actually be the space of such possible sources. Towards the end of the volume, Penrose begins to develop a quite different approach to incorporating full general relativity into twistor theory. This period also sees the origin of the Diosi-Penrose proposal.

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering.

This book is a study of group theoretical properties of two dis parate kinds, firstly finiteness conditions or generalizations of fini teness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S. N. Cernikov, K. A. Hirsch, A. G. Kuros, 0.]. Schmidt and H. Wie landt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A. I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967."

This book presents a collection of ethnomathematical studies of diverse mathematical practices in Afro-Brazilian, indigenous, rural and urban communities in Brazil. Ethnomathematics as a research program aims to investigate the interrelationships of local mathematical knowledge sources with broader universal forms of mathematics to understand ideas, procedures, and practices found in distinct cultural groups. Based on this approach, the studies brought together in this volume show how this research program is applied and practiced in a culturally diverse country such as Brazil, where African, indigenous and European cultures have generated different forms of mathematical practice. These studies present ethnomathematics in action, as a tool to connect the study of mathematics with the students' real life experiences, foster critical thinking and develop a mathematics curriculum which incorporates contributions from different cultural groups to enrich mathematical knowledge. By doing so, this volume shows how ethnomathematics can contribute in practice to the development of a decolonial mathematics education. Ethnomathematics in Action: Mathematical Practices in Brazilian Indigenous, Urban and Afro Communities will be of interest to educators and educational researchers looking for innovative approaches to develop a more inclusive, democratic, critical, multicultural and multiethnic mathematics education.

'Giving a talk' is one of the most important ways in which we communicate our research. The 'talk' covers everything from a ten-minute briefing on progress to a handful of colleagues, to a keynote address to a major international conference with more than a thousand delegates. Whatever the occasion, the aim is the same - to get the message across clearly and effectively. At the same time, presentational skills are becoming more important in all walks of life - and presenting science has particular issues. Our aim is to equip the reader with the basic skills needed to make a good presentation, and our approach is pragmatic, not dogmatic. We emphasise four points:
- The goal is to communicate the science to the audience.
- The speaker is responsible for everything that appears, and does not appear, on each slide.
- The structure and appearance of the presentation are part of the communication process.
- There is no standard way of doing things.
Giving a good talk on science is a skill that can be learnt like any other: in this book we take the reader through the process of presenting science to a wide variety of audiences.

Finite Mathematics and Calculus with Applications, Ninth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as "Your Turn" exercises and "Apply It" vignettes that encourage active participation. The MyMathLab(R) course for the text provides additional learning resources for students, such as video tutorials, algebra help, step-by-step examples, and graphing calculator help. The course also features many more assignable exercises than the previous edition.

For courses in Precalculus TheRule of Four: A Balanced Approach Precalculus:Graphical, Numerical, Algebraicprovides a balanced approach to problem solving and a consistent transitionfrom Precalculus to Calculus. A principal feature of this text is the balanceamong the algebraic, numerical, graphical, and verbal methods of representingproblems: the rule of 4. This approach reinforces the idea that to understand aproblem fully, students need to understand it algebraically as well asgraphically and numerically. The 10thEdition introducesgraphing technology as an essential tool for mathematical discovery andeffective problem solving. This edition also features a full chapter onStatistics to help students see that statistical analysis is an investigativeprocess.

Epitaxy is a very active area of theoretical research since several years. It is experimentally well-explored and technologically relevant for thin film growth. Recently powerful numerical techniques in combination with a deep understanding of the physical and chemical phenomena during the growth process offer the possibility to link atomistic effects at the surface to the macroscopic morphology of the film. The goal of this book is to summarize recent developments in this field, with emphasis on multiscale approaches and numerical methods. It covers atomistic, step-flow, and continuum models and provides a compact overview of these approaches. It also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.

This volume is based on lectures presented at the N.A.T.O. Advanced Studies Institute on Data Base Management Theory and Applications. The meeting took place in Estoril Portugal for a two week periQd in June 1981. The lecturers represented distinguished research centers in industry, gvvernment and academia. Lectures presented basic material in data base management, as well as sharing recent developments in the field. The participants were drawn from data processing groups in government, industry and academia, located in N.A.T.O. countries. All participants had a common goal of learning about the exciting new developments in the field of data base management with the potential for application to their fields of interest. In addition to formal lectures and the informal discussions among participants, which are characteristic of N.A.T.O. AS! gatherings, participants had the opportunity for hands-on experience in building application systems with a data base management system. Participants were organized into groups that designed and implemented application systems using data base technology on micro computers. The collection of papers is organized into four major sections. The first section deals with various aspects of data modeling from the conceptual and logical perspectives. These issues are crucial in the initial design of application systems.

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to illuminate the state of our understanding about issues related to integer addition and subtraction with a goal of highlighting how the variety of perspectives support each other or contribute to the field in unique ways. In particular, this book focuses on three main areas of integer work: students' thinking, models and metaphors, and teachers' thinking. Each chapter highlights a theoretically guided study centered on integer addition and subtraction. Internationally known scholars help connect the perspectives and offer additional insights through section commentaries. This book is an invaluable resource to those who are interested in mathematics education and numerical thinking.