'What I like best about this fascinating book is the detail. Brian Butterworth doesn't just tell us stories of animals with numerical abilities: he tells us about the underlying science. Elegantly written and a joy to read' - Professor Ian Stewart, author of What's the Use? and Taming the Infinite 'Full of thought-provoking studies and animal observations' - Booklist 'Enlightening and entertaining' - Publishers Weekly The Hidden Genius of Animals: Every pet owner thinks their own dog, cat, fish or hamster is a genius. What makes CAN FISH COUNT? so exciting is the way it unveils just how widespread intelligence is in nature. Pioneering psychologist Brian Butterworth describes the extraordinary numerical feats of all manner of species ranging from primates and mammals to birds, reptiles, fish and insects. Whether it's lions deciding to fight or flee, frogs competing for mates, bees navigating their way to food sources, fish assessing which shoal to join, or jackdaws counting friends when joining a mob - every species shares an ability to count. Homo Sapiens may think maths is our exclusive domain, but this book shows that every creature shares a deep-seated Darwinian ability to understand the intrinsic language of our universe: mathematics CAN FISH COUNT? is that special sort of science book - a global authority in his field writing an anecdotally-rich and revelatory narrative which changes the way you perceive something we take for granted.

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve as a text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation and rotation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used obtain and analyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and to study the effects of changing parameters.
The book will be useful to students and lecturers in undergraduate and graduate courses on classical mechanics, and students and lecturers in courses in computational physics.

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.

This new edition of Luke Robinson's popular textbook 'Pure Mathematics for CCEA AS Level' has been comprehensively updated to meet the requirements of the CCEA specification and fully covers unit AS1: Pure Mathematics. Following teacher feedback, it has been re-designed with a new two-colour style for ease of use. Each section of the book contains theory and examples with key words and definitions throughout. It also provides a large number of exercises, with answers included at the back of the book. Contents: Indices and Surds Quadratics Simultaneous Equations and Inequalities Algebraic Manipulation Graph Manipulation Graphs and Transformations Straight Lines Circles Binomial Expansion Trigonometry Exponentials and Logs Differentiation Integration Vectors Problem Solving

'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.

It is now possible to enter a chemistry degree course at many UK universities without any formal maths training beyond age 16. Addressing this deficiency requires students to take additional mathematics training when entering university, yet the relevance of maths to chemistry is often poorly appreciated by chemistry students. In addition, many service courses are either too abstract, or aimed at physicists and engineers, for students of chemistry, who are not inclined to study mathematical techniques "per se and "do not make the connection between the maths they are taught and the chemistry they want to study.

Based on the successful "at a Glance" approach, with integrated double page presentations explaining the mathematics required by undergraduate students of chemistry, set in context by detailed chemical examples, this book will be indispensable to all students of chemistry. By bringing the material together in this way the student is shown how to apply the maths and how it relates to familiar concepts in chemistry. By including problems (with answers) on each presentation, the student is encouraged to practice both the mathematical manipulations and the application to problems in chemistry. More detailed chemical problems at the end of each topic illustrate the range of chemistry to which the maths is relevant and help the student acquire sufficient confidence to apply it when necessary.

'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.

This volume traces back the history of interaction between the "computational" or "algorithmic" aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.

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.

This huge CGP Textbook is packed with thousands of questions for both years of A-Level Maths - it's suitable for the Edexcel, AQA, OCR and OCR MEI courses. It's perfect for helping students put their knowledge to the test and build their skills. The book also contains plenty of worked examples, practice exercises on almost every page and review questions at the end of each chapter. Better still, answers to every question are included at the back.

As data is an important asset for any organization, it is essential to apply semantic technologies in data science to fulfill the need of any organization. This volume of a two-volume handbook set provides a roadmap for new trends and future developments of data science with semantic technologies. Data Science with Semantic Technologies: New Trends and Future Developments highlights how data science enables the user to create intelligence through these technologies. In addition, this book offers the answers to various questions such as can semantic technologies be able to facilitate data science? Which type of data science problems can be tackled by semantic technologies? How can data scientists get benefited from these technologies? What is the role of semantic technologies in data science? What is the current progress and future of data science with semantic technologies? Which types of problems require the immediate attention of the researchers? What should be the vision 2030 for data science? This volume can serve as an important guide towards applications of data science with semantic technologies for the upcoming generation and thus becomes a unique resource for scholars, researchers, professionals, and practitioners in this field.

Gone are the days when data was interlinked with related data by humans and to find insights coherently, human interpretation was required. Data is no more just data. It is now considered a Thing or Entity or Concept- to bring the meaning to it, so that a machine not only understands the concept but also extrapolates the way humans do. Data Science with Semantic Technologies: Deployment and Exploration volume of a two-volume handbook set provides a roadmap for the deployment of semantic technologies in the field of data science and enables the user to create intelligence through these technologies by exploring the opportunities and eradicating the challenges in the current and future time frame. In addition, this book offers the answer to various questions like What makes a technology semantic as opposed to other approaches to data science? What is knowledge data science? How does knowledge data science relate to other fields? This book explores the optimal use of these technologies to provide the highest benefit to the user under one comprehensive source and title. As there is no dedicated book available in the market on this topic at this time, this proposed new book becomes a unique and only resource for scholars, researchers, data scientists, professionals, and practitioners. This volume can serve as an important guide towards applications of data science with semantic technologies for the upcoming generation and thus becomes a unique resource for scholars, researchers, professionals, and practitioners in this field.

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.

The book begins with a brief review of supersymmetry, and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewed leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analysing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersysmmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "amaximization". Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti- de Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Suppersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

This dictionary includes explanations of over 200 mathematical words and phrases. Other features include: multiplication tables; table of squares and cubes; frequently-used fractions, decimals and percentages; metric and imperial units; simple coordinate graphs; angle and circle rules.

In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.

Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.

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.

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.

In the new times of globalisation, international academic contacts and collaborations are ever increasing. They are taking many forms, from international conferences and publications, student and academic exchange, cross cultural research projects, curriculum development to professional development activities and affect every aspect of academic life from teaching, research to service.

This book aims to develop theoretical frameworks of the phenomena of internationalisation and globalisation. It identifies related ethical, moral, political and economic issues facing mathematics and science educators. It provides a venue for the publication of results of international comparisons on cultural differences and similarities rather than merely on achievement and outcomes. The book represents the different voices and interests from around the world rather than consensus on issues, and serves as a forum for critical discussion of the various models and forms of international projects and collaborations.

Advances in Computers, Volume 118, the latest volume in this innovative series published since 1960, presents detailed coverage of new advancements in computer hardware, software, theory, design and applications. Chapters in this updated release include Introduction to non-volatile memory technologies, The emerging phase-change memory, Phase-change memory architectures, Inter-line level schemes for handling hard errors in PCMs, Handling hard errors in PCMs by using intra-line level schemes, and Addressing issues with MLC Phase-change Memory.