The Language of Mathematics. Utilizing Math in Practice

A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics?and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.

Praise for the Second Edition «An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.» —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.

Forget the jargon. Forget the anxiety. Just remember the math. In this age of cheap calculators and powerful spreadsheets, who needs to know math? The answer is: everyone. Math is all around us. We confront it shopping in the supermarket, paying our bills, checking the sports stats, and working at our jobs. It is also one of the most fascinating-and useful-subjects. Mastering math can make a difference in your career, your studies, and your daily life. If you are among the millions of people who would love to understand math but are turned away by fear of its complexity, here is your salvation. The A to Z of Mathematics makes math simple without making it simplistic. Both easy to use and easy to read, the book covers all the topics in basic mathematics. You'll learn the definitions of such terms as «proportion»and «hexomino,» and grasp the concepts behind algebra, statistics, and other processes. The book's alphabetical arrangement helps you quickly home in on any topic, and its text is rich with stimulating examples, diagrams, and other illustrations that make the discussion crystal clear to every reader. Everyone will find something of interest in this wide-ranging guide to mathematics. The perfect antidote to math anxiety, this is an invaluable resource for parents and students, home schoolers, teachers, and anyone else who wants to improve his or her math skills and discover the amazing relevance of mathematics to the world around us.

Throughout its many editions, The Architect in Practice has remained a leading textbook used in the education of architects. While the content of the book has developed, the message and philosophy has remained constant: to provide students of architecture and young practitioners with a readable guide to the profession, outlining an architect's duties to their client and contractor, the key aspects of running a building contract, and the essentials of management, finance and drawing office procedure. The eleventh edition follows in that tradition. The text has been brought up to date to ensure it follows the new RIBA Plan of Work 2013 as the guide to the architect’s workflow. In addition, a number of changes to standard forms of contract were made with the publication of the JCT 2011 suite of contracts, and the RIBA Standard Form for the Appointment of an Architect 2010 (2012 Revision). These new forms are fully covered. In addition, the opportunity has been taken to reorganise the layout so that the content flows in a way that is more consistent with current architectural practice, and to deal with the increasing use of BIM. The eleventh edition of The Architect in Practice continues to provide the guidance and advice all students and practising architects need in the course of their studies and in their profession.

An authoritative new work exploring the themes of communication and implementation of research within developmental psychology – a scientific field with extensive real world value in addressing problems faced by individuals, families and services Brings together the insights of a stellar group of contributors with personal experience translating developmental psychology research into practice Accessibly structured into sections exploring family processes and child rearing practices; educational aspects; and clinical applications Goes beyond traditional reviews of literature in the field to report on practical implementation of research findings, including the challenges faced by authors Serves as an invaluable resource for developmental psychologists, practitioners working in the field of child development, and policymakers working on issues affecting children and families

Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested

The first comprehensive guide to research methods and technologies in psycholinguistics and the neurobiology of language Bringing together contributions from a distinguished group of researchers and practitioners, editors Annette M. B. de Groot and Peter Hagoort explore the methods and technologies used by researchers of language acquisition, language processing, and communication, including: traditional observational and behavioral methods; computational modelling; corpus linguistics; and virtual reality. The book also examines neurobiological methods, including functional and structural neuroimaging and molecular genetics. Ideal for students engaged in the field, Research Methods in Psycholinguistics and the Neurobiology of Language examines the relative strengths and weaknesses of various methods in relation to competing approaches. It describes the apparatus involved, the nature of the stimuli and data used, and the data collection and analysis techniques for each method. Featuring numerous example studies, along with many full-color illustrations, this indispensable text will help readers gain a clear picture of the practices and tools described. Brings together contributions from distinguished researchers across an array of related disciplines who explain the underlying assumptions and rationales of their research methods Describes the apparatus involved, the nature of the stimuli and data used, and the data collection and analysis techniques for each method Explores the relative strengths and weaknesses of various methods in relation to competing approaches Features numerous real-world examples, along with many full-color illustrations, to help readers gain a clear picture of the practices and tools described

This book provides a comprehensive examination of the use of MPEG-2, MPEG-4, MPEG-7, MPEG-21, and MPEG-A standards, providing a detailed reference to their application. In this book, the authors address five leading MPEG standards: MPEG-2, MPEG-4, MPEG-7, MPEG-21, and MPEG-A, focusing not only on the standards themselves, but specifically upon their application (e.g. for broadcasting media, personalised advertising and news, multimedia collaboration, digital rights management, resource adaptation, digital home systems, and so on); including MPEG cross-breed applications. In the evolving digital multimedia landscape, this book provides comprehensive coverage of the key MPEG standards used for generation and storage, distribution and dissemination, and delivery of multimedia data to various platforms within a wide variety of application domains. It considers how these MPEG standards may be used, the context of their use, and how supporting and complementary technologies and the standards interact and add value to each other. Key Features: Integrates the application of five popular MPEG standards (MPEG-2, MPEG-4, MPEG-7, MPEG-21, and MPEG-A) into one single volume, including MPEG cross-breed applications Up-to-date coverage of the field based on the latest versions of the five MPEG standards Opening chapter provides overviews of each of the five MPEG standards Contributions from leading MPEG experts worldwide Includes an accompanying website with supporting material (www.wiley.com/go/angelides_mpeg) This book provides an invaluable reference for researchers, practitioners, CTOs, design engineers, and developers. Postgraduate students taking MSc, MRes, MPhil and PhD courses in computer science and engineering, IT consultants, and system developers in the telecoms, broadcasting and publishing sectors will also find this book of interest.