Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

In this easily readable volume, the author explains some of the reasons for our preference toward the number seven. He reviews its occurrences in our cultural, biological, chemical, physical, algebraic and geometrical world in an attempt to find the reasons behind them.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time. The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference for students at the master's or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, or professionals working in the various financial sectors. Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance

Gear up and equip your organization for an entirely new competitive landscape In The Ecosystem Economy: How to Lead in the New Age of Sectors Without Borders, two McKinsey & Company senior partners offer an incisive and eye-opening look at the emerging ecosystem economy and what it means for companies used to familiar sector siloes. In the book, you'll explore how the most successful companies in the new economy aren't the ones that have applied old-school best practices but, instead, have adopted entirely new mindsets and approaches for a fundamentally transforming market. You'll also find: Explanations of why it's so important for companies to adopt a new approach in the face of a foundationally changing economy (and what they stand to gain) How the new ecosystem economy will continue to evolve and change, dissolving the borders between the traditional sectors of the economy A comprehensive ecosystem playbook that can be applied to firms of any size and in any sector As the barriers between sectors and disciplines come down, organizations everywhere will need to reshape their thinking about value propositions, competition, partnership, organizational and operating models, and performance management. The Ecosystem Economy is your personal roadmap to navigating that new world. It's ideal for managers, executives, and other business leaders seeking fresh new strategies and practical approaches for markets that bear little resemblance to the ones that came before.

This book brings together various studies that assume phenomenology to analyze how mathematics education is affected by the experience of being in the cyberspace. The authors of the chapters included in this contributed volume work with the theoretical framework developed by authors such as Edmund Husserl, Martin Heidegger and Maurice Merleau-Ponty to investigate how mathematics is produced and comprehended in a new way of being in the world, with digital technologies. The aim of this book is not to explain the tools used and how one works with them in the cyberspace, aiming at better teaching and learning mathematics. Its purpose is to present philosophical investigations that contribute to the understanding of the complexity of the world in which we are being researchers and mathematics teachers. By doing so, Constitution and Production of Mathematics in the Cyberspace - A Phenomenological Approach will help researchers and mathematics teachers understand their role in a world in which the experience of teaching and learning mathematics is being radically changed by new technologies and new ways of being in this world.

Developed in cooperation with the International Baccalaureate (R) Enable students to construct mathematical models by exploring challenging problems and the use of technology. - Engage and excite students with examples and photos of maths in the real world, plus inquisitive starter activities to encourage their problem-solving skills. - Build mathematical thinking with our 'Toolkit' and mathematical exploration chapter, along with our new toolkit feature of questions, investigations and activities. - Develop understanding with key concepts and applications integrated throughout, along with TOK links for every topic. - Prepare your students for assessment with worked examples, extended essay support and colour-coded questions to highlight the level of difficulty and the different types of questions. - Check understanding with review exercise midway and at the end of the textbook. Follows the new 2019 IB Guide for Mathematics: applications and interpretation Standard Level Available in the series Mathematics for the IB Diploma: Applications and interpretation SL Student Book ISBN: 9781510462380 Student Book Boost eBook ISBN: 9781398334359 Exam Practice Workbook SL: 9781398321892 Exam Practice Workbook SL Boost eBook: 9781398342323 Mathematics for the IB Diploma: Applications and interpretation HL Student Book ISBN: 9781510462373 Student Book Boost eBook ISBN: 9781398334366 Exam Practice Workbook HL: 9781398321885 Exam Practice Workbook HL Boost eBook: 9781398342354 SL & HL Boost Subscription: 9781398341272

This book "Advanced Applications of Computational Mathematics" covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms. The book will be very useful to advanced students, researchers and practitioners who are involved in the areas of computational and applied mathematics and engineering.

-Offers an innovative introduction to the psychology of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. - In clear, engaging writing, award-winning mathematician and educator Norton Anderson explores the psychological basis for mathematics at every level, relevant for pre-service and in-service secondary and elementary math teachers, math teacher educators, and anyone interested in the nature of mathematics. -Reflections and exercises are included in each chapter, as well as footnotes for those interested in building off their understanding with related research.

An Outline of a General Theory of Models. Translation of Stabilit tructurelle et Morphog'se.

Exam Board: OCR Level: A-level Subject: Mathematics First Teaching: September 2017 First Exam: June 2018 An OCR endorsed textbook Boost your students' knowledge, skills and understanding so that they can reason and apply mathematical techniques in solving problems; with resources developed specifically for the OCR specification by subject experts and in conjunction with MEI (Mathematics in Education and Industry). - Boosts students' confidence approaching assessment with plenty of practice questions and skill-focused exercises. - Build connections between topics with points of interest and things to notice such as links to real world examples and noticing patterns in the mathematics. - Ensure targeted development of problem-solving, proof and modelling with dedicated sections on these key areas. - Help students to overcome misconceptions and develop insight into problem-solving with annotated worked examples. - Enhance individual understanding with discussion points designed for the classroom and end of chapter summaries of the key points. - Tackle the new statistics requirements with five dedicated statistics chapters and questions around the use of large data sets. - Address the use of technology in Mathematics with a variety of questions based around the use of spreadsheets, graphing software and graphing calculators. - Provide clear paths of progression that combine pure and applied maths into a coherent whole.

"Welcome to the maze.

A logical maze, a magical maze. A maze of the mind.

The maze is mathematics. The mind is yours. Let's see what happens when we put them together.

What is mathematics? What do mathematicians do?

What is a mathematician? Someone who does mathematics?

Not exactly. That's too easy an answer, and it creates too simple a maze—a circular loop of self-referential logic. No, a mathematician is more than just somebody who does mathematics. Think of it this way: what is a businessperson? Someone who does business? Yes, but not just that. A businessperson is someone who sees an opportunity for doing business where the rest of us see nothing; while we're complaining that there's no restaurant in the area, he or she is organizing a telephone pizza delivery service. Similarly, a mathematician is someone who sees opportunities for doing mathematics that the rest of us miss.

I want to open your mind to some of these opportunities."—from The Magical Maze

Praise for Ian Stewart's Previous Books

About Nature's Numbers: "Stewart achieves what other popular mathematics writers merely strive for: an accurate, informative portrayal of contemporary mathematics without a single equation in sight."—Nature

About The Problems of Mathematics:

"From one of mathematics' most gifted expositors . . . challenging and interesting. Those with no knowledge of the subject will be able to glimpse its beauty and appeal."—New Scientist

About The Collapse of Chaos:

"This ambitious book fearlessly asks some big questions, challenging us to look at science a new way."—San Francisco Chronicle

About Another Fine Math You've Got Me Into:

"Ian Stewart's quirky humor and imaginative storytelling entice readers into a fascinating world of mathematical curiosities."—Ivars Peterson author of The Jungles of Randomness

Enter the magical maze of mathematics and explore the surprising passageways of a fantastical world where logic and imagination converge. For mathematics is a maze—a maze in your head—a maze of ideas, a maze of logic. And that maze in your mind is a powerful tool for understanding an even bigger maze—the maze of cause and effect that we call "the universe." That is its special kind of magic. Real magic. Strange magic. Infinitely fascinating magic.

In this adventure of a book, acclaimed author Ian Stewart leads you swiftly and humorously through the junctions, byways, and secret passages of the magical maze to reveal its beauty, its surprise, and its power. Along the way, he reveals the infinite possibilities that arise from what he calls "the two-way trade between the natural world and the human mind."

On your travels you will encounter number magic—both the stage-act variety and the deeper magic of animals, plants, and the physical world. You will come to understand the amazing pattern-forming abilities of the humble slime mold, the numerology of flowers, and the feeding habits of pigs and panthers. You will discover how to solve puzzles the algorithmic way, the artistic way, and the army way. You will be amazed by the deep connections between the founding of Carthage, soap bubbles, and communications networks. You will discover how to use a toy train set as a computer, and find out why this implies that there are unavoidable limits to mathematics. You will join the controversy over cars and goats, find out the terrible truth about confessions, and win endless bets about birthdays. You will see how a new idea about ferns can lead to a multi-million-dollar computer graphics company, and how Jupiter and Mars can combine forces to hurl cosmic rocks at Earth. And you will never again be able to watch a kitten, a kangaroo, or a Chihuahua without noticing the delightfully rhythmic patterns with which they move their feet.

If you've always loved mathematics, you will find endless delights in the twists and turns of The Magical Maze. If you've always hated mathematics, a trip through this marvelous book will do much to change your mind.

A database management system (DBMS) is a collection of programs that enable users to create and maintain a database; it also consists of a collection of interrelated data and a set of programs to access that data. Hence, a DBMS is a general-purpose software system that facilitates the processes of defining, constructing, and manipulating databases for various applications. The primary goal of a DBMS is to provide an environment that is both convenient and efficient to use in retrieving and storing database information. It is an interface between the user of application programs, on the one hand, and the database, on the other. The objective of Database Management System: An Evolutionary Approach, is to enable the learner to grasp a basic understanding of a DBMS, its need, and its terminologies discern the difference between the traditional file-based systems and a DBMS code while learning to grasp theory in a practical way study provided examples and case studies for better comprehension This book is intended to give under- and postgraduate students a fundamental background in DBMSs. The book follows an evolutionary learning approach that emphasizes the basic concepts and builds a strong foundation to learn more advanced topics including normalizations, normal forms, PL/SQL, transactions, concurrency control, etc. This book also gives detailed knowledge with a focus on entity-relationship (ER) diagrams and their reductions into tables, with sufficient SQL codes for a more practical understanding.

From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.

This book explores the idea that mathematics educators and teachers are also problem solvers and learners, and as such they constantly experience mathematical and pedagogical disturbances. Accordingly, many original tasks and learning activities are results of personal mathematical and pedagogical disturbances of their designers, who then transpose these disturbances into learning opportunities for their students. This learning-transposition process is a cornerstone of mathematics teacher education as a lived, developing enterprise. Mathematical Encounters and Pedagogical Detours unfold the process and illustrate it by various examples. The book engages readers in original tasks, shares the results of task implementation and describes how these results inform the development of new tasks, which often intertwine mathematics and pedagogy. Most importantly, the book includes a dialogue between the authors based on the stories of their own learning, which triggers continuous exploration of learning opportunities for their students.

Mathematics teacher education includes the mathematics content teachers need to understand, ways that pedagogical approaches are developed, messages about the nature of mathematics teaching and learning, and interfaces between tertiary preparation and school contexts. Scholars from Sweden, France, Malawi, Singapore, New Zealand, Brazil, the USA, and Canada provide insights for the mathematics education community's understanding of how teacher educators structure, develop, and implement their respective mathematics teacher education programs. Several themes emerged across the chapters, including: varied approaches to developing culturally responsive pedagogies and/or Indigenous perspectives; issues and challenges in fostering partnerships and collaborations; strategies for developing mathematics knowledge for teaching; and preparing flexible and resourceful teachers

Special functions are mathematical functions that have established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. Each chapter finishes with a description of how the function is most commonly applied and a set of examples for the student to work through.

This book provides a common language for and makes connections between transfer research in mathematics education and transfer research in related fields. It generates renewed excitement for and increased visibility of transfer research, by showcasing and aggregating leading-edge research from the transfer research community. This book also helps to establish transfer as a sub-field of research within mathematics education and extends and refines alternate perspectives on the transfer of learning. The book provides an overview of current knowledge in the field as well as informs future transfer research.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

Mathematics Education for Sustainable Economic Growth and Job Creation considers the need for young employees to be capable and confident with transferable knowledge and skills in mathematics and statistics in order to support economic growth in developing countries in an increasingly digital age. This book draws on differing international perspectives in relation to mathematics education for sustainable economic growth and job creation. The contributors include education researchers and those involved in policymaking for both developing countries and beyond. Within each chapter, there is a reflection from the authors on their experiences in educational systems and policy development or research studies, which contribute to sustainable economic growth in different countries. As well as considerations of economies and job creation, the scholarship delves further into developing a critically aware citizenship through mathematics education. Extending current thinking about the role of mathematics education and educating students for future needs, this book will be of great interest for academics, researchers and postgraduate students in the field of mathematics education, STEM education and sustainability education.

Asia is the largest continent in the world. Five out of the top ten high performing economies in the Programme for International Student Assessment (PISA) 2018 are located in Asia. Why do Asian students perform so well in STEM-related subjects? This book answers this by examining the STEM education policies and initiatives in Asian economies, as well as the training programmes undertaken by STEM teachers in Asia. The book is broken into four sections, each accompanied by a passage of commentary that summarizes the key takeaways of the chapters. Section one focuses on STEM policy environments and how various countries have developed policies that promote STEM as an integral part of national economic development. Section two focuses on STEM teacher education in the Philippines and Thailand, while section three focuses on STEM curriculum design, context, and challenges in four Asian economies. The fourth and final section focuses on presenting snapshots of STEM education research efforts in Malaysia, South Korea, and Singapore. Written by Asian academics, this book will provide valuable insights to policy makers, educators, and researchers interested in the topic of STEM education, especially in the Asian context. Chapters 7 and 11 of this book are freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com

Chemometric Techniques for Quantitative Analysis shows how to produce and use quantitative analytical calibrations in a laboratory or production environment following a variety of methods, how to estimate the time and resources needed to develop analytical calibrations, and how to employ the quantitative software provided with a wide range of instruments and commercial software packages. Among several, this bestselling volume covers basic and classical approaches, component regression; PCR in action; partial least squares; PLS in action. An extensive appendix offers a glossary, a list of errors and tests for reduced Eigenvalues.

This book develops foundational concepts in probability and statistics with primary applications in mechanical and aerospace engineering. It develops the mindset a data analyst must have to interpret an ill-defined problem, operationalize it, collect or interpret data, and use this evidence to make decisions that can improve the quality of engineered products and systems. It was designed utilizing the latest research in statistics learning and in engagement teaching practices The author's focus is on developing students' conceptual understanding of statistical theory with the goal of effective design and conduct of experiments. Engineering statistics is primarily a form of data modeling. Emphasis is placed on modelling variation in observations, characterizing its distribution, and making inferences with regards to quality assurance and control. Fitting multivariate models, experimental design and hypothesis testing are all critical skills developed. All topics are developed utilizing real data from engineering projects, simulations, and laboratory experiences. In other words, we begin with data, we end with models. The key features are: Realistic contexts situating the learning of the statistics in actual engineering practice. A balance of rigorous mathematics, conceptual scaffolding, and real, messy data, to ensure that students learn the important concepts and can apply them in practice. The consistency of text, lecture notes, data sets, and simulations yield a coherent set of instructional resources for the instructor and a coherent set of learning experiences for the students. MatLab is used as a computational tool. Other tools are easily substituted. Table of Contents 1. Introduction 2. Dealing with Variation 3. Types of Data 4. Introduction to Probability 5. Sampling Distribution of the Mean 6. The Ten Building Blocks of Experimental Design 7. Sampling Distribution of the Proportion 8. Hypothesis Testing Using the 1-sample Statistics 9. 2-sample Statistics 10. Simple Linear Regression 11. The General Linear Model: Regression with Multiple Predictors 12. The GLM with Categorical Independent Variables: The Analysis of Variance 13. The General Linear Model: Randomized Block Factorial ANOVA 14. Factorial Analysis of Variance 15. The Bootstrap 16. Data Reduction: Principal Components Analysis Index Author Biography James A. Middleton is Professor of Mechanical and Aerospace Engineering and former Director of the Center for Research on Education in Science, Mathematics, Engineering, and Technology at Arizona State University. Previously, he held the Elmhurst Energy Chair in STEM education at the University of Birmingham in the UK. He received his Ph.D. from the University of Wisconsin-Madison. He has been Senior co-Chair of the Special Interest Group for Mathematics Education in the American Educational Research Association, and as Chair of the National Council of Teachers of Mathematics' Research Committee. He has been a consultant for the College Board, the Rand Corporation, the National Academies, the American Statistical Association, the IEEE, and numerous school systems around the United States, the UK, and Australia. He has garnered over $30 million in grants to study and improve mathematics education in urban schools.

This book explicates some of the fundamental philosophical tenets underpinning key theoretical frameworks, and demonstrates how these tenets inform particular kinds of research practice in mathematics education research. We believe that a deep understanding of significant theories from the humanities and social sciences is crucial for doing high-quality research in education. For that reason, this book focuses on six key theoretical sources, unpacking their relevance and application to specific research examples. We situate these key theorists within a larger framework pertaining to the history of thought more generally, and discuss how competing theories of teaching and learning differ in terms of their philosophical assumptions. In so doing, we offer context and motivation for particular research methods, with the agenda of helping researchers reflect on why particular approaches and not others might work for them.