This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.

As dissatisfaction with the current status of school mathematics grows worldwide, educators and professionals alike are calling for reforms and instructional changes. Yet, significant changes can only be achieved if each educator of school mathematics personally rethinks various aspects of mathematics instruction, and identifies concrete ways in which their current practice could be modified. Before such visions can be meaningfully implemented in classrooms, it is important that mathematics teachers and educators examine critically both the assumptions and implications of the vision for school mathematics that the reports propose. This book is intended to support educators in such a challenging enterprise by focusing attention on errors and their use in mathematics instruction. Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline. REVIEWS: ...Raffaella Borasi's newest book offers important contributions to the current debate on school mathematics reform. - Journal for Research in Mathematics Education There are some great bits of philosophy in this book... - Mathematics Teaching

Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too pricey? Fortunately, there's Schaum's. This all-in-one-package includes more than 650 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand. Schaum's Outline of Geometry, Sixth Edition features: * Updated content to matches the latest curriculum * Over 650 problems, solved step by step * An accessible format for quick and easy review * Clear explanations for all geometry concepts * Access to revised Schaums.com website with access to 25 problem-solving videos, and more

Rosen's Discrete Mathematics and its Applications presents a precise, relevant, comprehensive approach to mathematical concepts. This world-renowned best-selling text was written to accommodate the needs across a variety of majors and departments, including mathematics, computer science, and engineering. As the market leader, the book is highly flexible, comprehensive and a proven pedagogical teaching tool for instructors. Digital is becoming increasingly important and gaining popularity, crowning Connect as the digital leader for this discipline. McGraw-Hill Education's Connect, available as an optional add on item, is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it and how they need it - ensuring class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers and may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty.

Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This book is written by practitioners whose primary teaching subject is not math but who use math extensively in their courses in STEM disciplines, social science statistics, and their own research. Moreover, in the writing of this book, the authors have used the teaching principles of anchoring, overlearning, pruning the course to its essentials, and using simple and familiar language in word problems.

This book introduces fundamental concepts and theories in pervasive computing as well as its key technologies and applications. It explains how to design and implement pervasive middleware and real application systems, covering nearly all aspects related to pervasive computing. Key technologies in the book include pervasive computing-oriented resource management and task migration, mobile pervasive transaction, human computer interface, and context collection-oriented wireless sensor networks.

This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing * (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . * (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

In practice, actuators often undergo failures and various factors influence its effectiveness. Also due to the increasing complexity of large-scale systems, subsystems are often interconnected, whereas the interactions between any two subsystems are difficult to deal with. This book details a series of new methodologies of designing and analyzing adaptive backstepping control systems involving treatment on actuator failures, subsystem interactions and nonsmooth nonlinearities. Moreover, it discusses some interesting open issues in adaptive failure accommodation, decentralized adaptive control and distributed adaptive coordinated control.

Nature-Inspired Computing: Physics and Chemistry-Based Algorithms provides a comprehensive introduction to the methodologies and algorithms in nature-inspired computing, with an emphasis on applications to real-life engineering problems. The research interest for Nature-inspired Computing has grown considerably exploring different phenomena observed in nature and basic principles of physics, chemistry, and biology. The discipline has reached a mature stage and the field has been well-established. This endeavour is another attempt at investigation into various computational schemes inspired from nature, which are presented in this book with the development of a suitable framework and industrial applications. Designed for senior undergraduates, postgraduates, research students, and professionals, the book is written at a comprehensible level for students who have some basic knowledge of calculus and differential equations, and some exposure to optimization theory. Due to the focus on search and optimization, the book is also appropriate for electrical, control, civil, industrial and manufacturing engineering, business, and economics students, as well as those in computer and information sciences. With the mathematical and programming references and applications in each chapter, the book is self-contained, and can also serve as a reference for researchers and scientists in the fields of system science, natural computing, and optimization.

This book provides an accessible introduction to the mathematical methods of quantum optics. Starting from first principles, it reveals how a given system of atoms and a field is mathematically modelled. The method of eigenfunction expansion and the Lie algebraic method for solving equations are outlined. Analytically exactly solvable classes of equations are identified. The text also discusses consequences of Lie algebraic properties of Hamiltonians, such as the classification of their states as coherent, classical or non-classical based on the generalized uncertainty relation and the concept of quasiprobability distributions. A unified approach is developed for determining the dynamics of a two-level and a three-level atom interacting with combinations of quantized fields under certain conditions. Simple methods for solving a variety of linear and nonlinear dissipative master equations are given.

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).

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.

This new and updated second edition of Debates in Mathematics Education explores the major issues that mathematics teachers encounter in their daily lives. By engaging with established and contemporary debates, this volume promotes and supports critical reflection and aims to stimulate both novice and experienced teachers to reach informed judgements and argue their point of view with deeper theoretical knowledge and understanding. Divided into five accessible sections, this book investigates and offers fresh insight into topics of central importance in mathematics education, with this second edition including new discussions and chapters on: Classic and contemporary issues of pedagogy, politics, philosophy and sociology of mathematics education International comparisons of achievement Digital technologies for teaching Mastery in mathematics Pop culture and mathematics Whether mathematics can be harmful Designed to stimulate discussion and support you in your own research, writing and practice through suggested questions and activities throughout, Debates in Mathematics Education will be a valuable resource for any student or practising teacher, and those engaged in initial teacher education, continuing professional development or Master's level study. This book also has much to offer to those leading mathematics departments in schools and initial teacher education programmes, and to beginning doctoral students looking for a survey of the field of mathematics education research.

Practical Guidance on the Efficient Development of High-Quality Software Introduction to Software Engineering, Second Edition equips students with the fundamentals to prepare them for satisfying careers as software engineers regardless of future changes in the field, even if the changes are unpredictable or disruptive in nature. Retaining the same organization as its predecessor, this second edition adds considerable material on open source and agile development models. The text helps students understand software development techniques and processes at a reasonably sophisticated level. Students acquire practical experience through team software projects. Throughout much of the book, a relatively large project is used to teach about the requirements, design, and coding of software. In addition, a continuing case study of an agile software development project offers a complete picture of how a successful agile project can work. The book covers each major phase of the software development life cycle, from developing software requirements to software maintenance. It also discusses project management and explains how to read software engineering literature. Three appendices describe software patents, command-line arguments, and flowcharts.

The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the booklets originally produced to guide students intending to contend for placement on their country's IMO team. See also "A First Step to Mathematical Olympiad Problems" which was published in 2009. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though "A Second Step to Mathematical Olympiad Problems" is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.

Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be made, for without the existence of a coherent exposition of the total proof, there is a very real danger that it will gradually become lost to the living world of mathematics, buried within the dusty pages of forgotten journals. For it is almost impossible for the uninitiated to find the way through the tangled proof without an experienced guide; even the 500 papers themselves require careful selection from among some 2,000 articles on simple group theory, which together include often attractive byways, but which serve only to delay the journey.

Entropy is a measure of order and disorder. If left alone, aging systems go spontaneously from youthful, low entropy and order to old, high entropy and disorder. This book presents the commonality of entropy principles which govern the birth, maturation, and senescent history of aging humans, corporations, and the universe. Mainly we introduce an entropy theory of aging, based on the non-equilibrium thermodynamic ideas of Ilya Prigogine, leading to the thermodynamic concepts of Excess Entropy (EE) and Excess Entropy Production (EEP). We describe the aging process in humans in terms of the EE and EEP concepts. This book also describes the informational entropy theory and equations of Claude Shannon and the six Hershey parameters which trace and mark the lifecycle of corporations. To conclude, this volume uses classical and informational entropy concepts, equations and calculations to explain the birth, evolution, and death of our aging universe, and all of this in relation to the concept of Infinity.

This is a history of a space - a space between the Panonian plain in the East and the most northernmost bay in the Adriatic in the West, from the eastern Alps in the North and the Dinaridic mountain area in the South. It is also a history of all the different people who lived in this area. The authors show that the Slavs did not settle an empty space and simply replace the Celto-Roman inhabitants of earlier times; they are, on the contrary, presented as the result of reciprocal acculturation. The authors show that the Slovenes made more than two important appearances throughout the entire feudal era; the same holds for later periods, especially for the twentieth century. This book offers a concise and complete history of an area that finally became an integral part of Central Europe and the Balkans.

This volume shows how the history and practices of mathematics education in Korea (from Volume 7) have been influenced by Japan, America and other countries, developing into the unique Korean style of mathematics education.Research content and practices currently being conducted are also covered, as well as topics like teacher education, special mathematics education, research trends and some perspectives towards the future of mathematics education in Korea.

This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24-31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the "balancing act" between developing students' modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators

This unique proceedings volume offers one of the very first truly interdisciplinary conferences ever organized. More than 15 papers in this volume are written by some of the most acclaimed researchers in their field. Contributions range over a very wide spectrum of disciplines: biology; computer science; economics; education; health sciences; operations research; philosophy; physics; psychology; mathematics; music and sociology.