Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research. Requiring only a moderate familiarity with functional analysis and general topology, the author begins with an introduction to infinite dimensional Lie theory with emphasis on the relationship between Lie groups and Lie algebras. A detailed examination of smooth homogeneous spaces follows. This study is illustrated by familiar examples from operator theory and develops methods that allow endowing such spaces with structures of complex manifolds. The final section of the book explores equivariant monotone operators and Kahler structures. It examines certain symmetry properties of abstract reproducing kernels and arrives at a very general version of the construction of restricted Grassmann manifolds from the theory of loop groups. The author provides complete arguments for nearly every result. An extensive list of references and bibliographic notes provide a clear picture of the applicability of geometric methods in functional analysis, and the open questions presented throughout the text highlight interesting new research opportunities. Daniel Beltita is a Principal Researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucharest, Romania.

Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. Offering an introductory review of historic research, Shock Waves and Explosions brings analytic and computational methods to a wide audience in a clear and thorough way. Beginning with an overview of the research on combustion and gas dynamics in the 1970s and 1980s, the author brings you up to date by covering modeling techniques and asymptotic and perturbative methods and ending with a chapter on computational methods. Most of the book deals with the mathematical analysis of explosions, but computational results are also included wherever they are available. Historical perspectives are provided on the advent of nonlinear science, as well as on the mathematical study of the blast wave phenomenon, both when visualized as a point explosion and when simulated as the expansion of a high-pressure gas. This volume clearly reveals the ingenuity of the human mind to conceptualize, model, and mathematically analyze highly complicated nonlinear phenomena such as nuclear explosions. It presents a solid foundation of knowledge that encourages further research and original ideas.

Sports Analytics in Practice with R A practical guide for those looking to employ the latest and leading analytical software in sport In the last twenty years, sports organizations have become a data-driven business. Before this, most decisions in sports were qualitatively driven by subject-matter experts. In the years since numerous teams found success with "Money Ball" analytical perspectives, the industry has sought to advance its analytical acumen to improve on- and off-field outcomes. The increasing demand for data to inform decisions for coaches, scouts, and players before and during sporting events has led to intriguing efforts to build upon this quantitative approach. As this methodology for assessing performance has matured and grown in importance, so too has the open-source R software emerged as one of the leading analytical software packages. In fact, R is a top 10 programming language that is useful in academia and industry for statistics, machine learning, and rapid prototyping. Sports Analytics in Practice with R neatly marries these two advances to teach basic analytics for sports-related use--from cricket to baseball, from basketball to tennis, from soccer to sports gambling, and more. Sports Analytics in Practice with R readers will also find: A broad perspective of sports, focusing on a wide range of sports rather than just one The first book of its kind that features coding examples Case study approach throughout the book Companion website including data sets to work through alongside the explanations Sports Analytics in Practice with R is a helpful tool for students and professionals in the sports management field, but also for sports enthusiasts who have a coding background.

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

Although the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.

This second collection of interesting mathematical puzzles continues the tribute to Martin Gardner, who has provided us with original puzzles and puzzling stories ever since he created and produced the "Mathematical Games" column in Scientific American. The international community of puzzle enthusiasts has gathered once again to celebrate Martin Gardner's continued contribution and, most fittingly, has done so in kind, by providing new challenges to our inquiring minds. We proudly present this collection to the mathemagicians of the world for their enjoyment, as a playful provocation.

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

Since it was first published three decades ago, Excursions Into Mathematics has been one of the most popular mathematical books written for a general audience. Taking the reader for short "excursions" into several specific disciplines of mathematics, it makes mathematical concepts accessible to a wide audience. The Millennium Edition is updated with current research and new solutions to outstanding problems that have been discovered since the last edition was printed, such as the solution to the well-known "four-color problem." Excursions Into Mathematics: The Millennium Edition is an exciting revision of the original, much-loved classic. Everyone with an interest in mathematics should read this book.

This book provides in-depth coverage of Pure Mathematics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study. Exam Board: Cambridge Assessment International Education First teaching: 2018 First examination: 2020 This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 first examination from 2020. This title is endorsed by Cambridge Assessment International Education. Written by expert authors, this Student Book: • covers all the content of Pure Mathematics 1 with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus • sets mathematics in real-world contexts that emphasise practical applications and career paths, with inspiring case studies and discussion activities that showcase how mathematics is relevant to different roles • develops the key A Level mathematical skills of mathematical modelling, problem-solving and communication through dedicated questions and teaching • helps you master mathematics with varied practice to develop understanding, exam-style questions to test comprehension, and selected Cambridge past paper questions to help prepare for examination • gives you control of your learning with prior knowledge checks to assess readiness and end-of-chapter summaries that test understanding • supports you through the course with detailed explanations, clear worked examples and plenty of graduated practice on each topic with full workings shown for each answer • provides clear progression from IGCSE® Mathematics and develops confident, independent and reflective mathematicians through extension questions and group discussions • supports mathematical communication and literacy with key terms for each topic explained and supported by a comprehensive glossary.

Numeracy in Children s Nursing and Healthcare is a handy, practical book which highlights the importance of numbers, numeracy and calculations in children s nursing practice, instilling nursing students and qualified nurses with confidence and competence when working with numbers and calculating drug doses. This accessible guide covers all aspects of numeracy from basic skills through to complex drug administration, and provides case studies throughout enabling the reader to apply the theory to practice. Each chapter adopts the same accessible and easy-to-follow format, featuring learning outcomes, a case scenario, key numeracy information, hints and tips, activities and exercises, and a glossary of terms.

Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal's triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin's sequence, and Rook and Queen paths and the equivalent Nim and Wythoff's Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon's theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

Statistical inference carries great significance in model building from both the theoretical and the applications points of view. Its applications to engineering and economic systems, financial economics, and the biological and medical sciences have made statistical inference for stochastic processes a well-recognized and important branch of statistics and probability. The class of semimartingales includes a large class of stochastic processes, including diffusion type processes, point processes, and diffusion type processes with jumps, widely used for stochastic modeling. Until now, however, researchers have had no single reference that collected the research conducted on the asymptotic theory for semimartingales. Semimartingales and their Statistical Inference, fills this need by presenting a comprehensive discussion of the asymptotic theory of semimartingales at a level needed for researchers working in the area of statistical inference for stochastic processes. The author brings together into one volume the state-of-the-art in the inferential aspect for such processes. The topics discussed include: Asymptotic likelihood theory Quasi-likelihood Likelihood and efficiency Inference for counting processes Inference for semimartingale regression models The author addresses a number of stochastic modeling applications from engineering, economic systems, financial economics, and medical sciences. He also includes some of the new and challenging statistical and probabilistic problems facing today's active researchers working in the area of inference for stochastic processes.

This conference proceedings focuses on enabling science and mathematics practitioners and citizens to respond to the pressing challenges of global competitiveness and sustainable development by transforming research and teaching of science and mathematics. The proceedings consist of 82 papers presented at the Science and Mathematics International Conference (SMIC) 2018, organised by the Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, Indonesia. The proceedings are organised in four parts: Science, Science Education, Mathematics, and Mathematics Education. The papers contribute to our understanding of important contemporary issues in science, especially nanotechnology, materials and environmental science; science education, in particular, environmental sustainability, STEM and STEAM education, 21st century skills, technology education, and green chemistry; and mathematics and its application in statistics, computer science, and mathematics education.

MATLAB The tremendously popular computation, numerical analysis, signal processing, data analysis, and graphical software package-allows virtually every scientist and engineer to make better and faster progress. As MATLAB's world-wide sales approach a half-million with an estimated four million users, it becomes a near necessity that professionals and students have a level of competence in its use. Until now, however, there has been no book that quickly and effectively introduces MATLAB's capabilities to new users and assists those with more experience down the path toward increasingly sophisticated work. Basics of MATLAB and Beyond is just such a book. Its hands-on, tutorial approach gently takes new users by the hand and leads them to competence in all the fundamentals of MATLAB. Then, with equal effectiveness, it covers the advanced topics that lead to full, creative exploitation of MATLAB's awesome power. With this book, readers will: Solve more problems with MATLAB-and solve them faster Create clearer, more beautiful graphics with control over every detail Create their own MATLAB code Share their work by exporting data and graphics to other applications Develop graphical user interfaces Based on the latest 5.x release, Basics of MATLAB and Beyond supplies both novice and experienced users the tools they need to gain proficiency, increase productivity, and ultimately have more fun with MATLAB.

This volume contains the best lectures from the Summer School Lectures volumes dealing with the theme of pattern formation. Topics include self-organization by simulated evolution, nonlinear dynamics of pattern formation in physics and biology, and the emergence of computational ecologies.

The study of complex systems has attracted a broad range of researchers from many disciplines spanning both the hard and soft sciences. In the Autumn of 1997, 300 of these researchers came together for the First International Conference on Complex Systems. The proceedings of this conference is the first book in the New England Complex Systems Institute Series on Complexity and includes more than 100 presentations and papers on topics like evolution, emergence, complexity, self-organization, scaling, informatics, time series, emergence of mind, and engineering of complex systems.

The International Conference on Complex Systems provides a unique opportunity for scientists to rise above the disciplinary boundaries and explore unity in complex systems. This volume contains the proceedings of the Second International Conference on Complex Systems. The sessions ranged from the opening talk by Nobel laureate Philip Anderson on emergence and the relevance of complex systems to physics to the final panel that included many of the great management gurus of this generation. The plenary session topics for the second conference were emergence, description and modeling, self-organization, networks, time series, agents in action, and complexity and management. Talks in these sessions often focused on contributions in specific disciplines, but each session contained a diverse set of disciplines to show the strategies and concepts that can be applied generally to complex systems. Overall, the conference presentations dealt with issues of significant public interest, including individual psychology, dynamics of social and economic change, the human genome, and ecology.The New England Complex Systems Institute is an independent educational and research institution dedicated to advancing the study of complex systems, including new concepts and methodologies that are affecting all fields of science and engineering, and are being applied to technology, business, and even social policy. NECSI organizes conferences, workshops, short courses, and other activities from which books will be produced for the NECSI Series on Complexity. The books will range from conference proceedings and graduate textbooks to general-audience trade books, and will address fundamental concepts, new frontiers, and innovative applications of complex systems.

Ein unverzichtbarer Leitfaden bei der Anwendung computergestutzter Statistik in der modernen Datenwissenschaft In Computational Statistics in Data Science prasentiert ein Team aus bekannten Mathematikern und Statistikern eine fundierte Zusammenstellung von Konzepten, Theorien, Techniken und Praktiken der computergestutzten Statistik fur ein Publikum, das auf der Suche nach einem einzigen, umfassenden Referenzwerk fur Statistik in der modernen Datenwissenschaft ist. Das Buch enthalt etliche Kapitel zu den wesentlichen konkreten Bereichen der computergestutzten Statistik, in denen modernste Techniken zeitgemass und verstandlich dargestellt werden. Daruber hinaus bietet Computational Statistics in Data Science einen kostenlosen Zugang zu den fertigen Eintragen im Online-Nachschlagewerk Wiley StatsRef: Statistics Reference Online. Ausserdem erhalten die Leserinnen und Leser: * Eine grundliche Einfuhrung in die computergestutzte Statistik mit relevanten und verstandlichen Informationen fur Anwender und Forscher in verschiedenen datenintensiven Bereichen * Umfassende Erlauterungen zu aktuellen Themen in der Statistik, darunter Big Data, Datenstromverarbeitung, quantitative Visualisierung und Deep Learning Das Werk eignet sich perfekt fur Forscher und Wissenschaftler samtlicher Fachbereiche, die Techniken der computergestutzten Statistik auf einem gehobenen oder fortgeschrittenen Niveau anwenden mussen. Zudem gehoert Computational Statistics in Data Science in das Bucherregal von Wissenschaftlern, die sich mit der Erforschung und Entwicklung von Techniken der computergestutzten Statistik und statistischen Grafiken beschaftigen.

This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations.

This book provides different mathematical frameworks for addressing supervised learning. It is based on a workshop held under the auspices of the Center for Nonlinear Studies at Los Alamos and the Santa Fe Institute in the summer of 1992.

Mental Arithmetic provides rich and varied practice to develop pupils' essential maths skills and prepare them for all aspects of the Key Stage 2 national tests. It may also be used as preparation for the 11+, and with older students for consolidation and recovery. Tailored to meet the requirements of the National Curriculum for primary mathematics, each book contains 36 one-page tests. Each test is presented in a unique three-part format comprising: questions where use of language is kept to a minimum; questions using number vocabulary; questions focusing on one- and two-step word problems. Structured according to ability rather than age, the series allows children to work at their own pace, building confidence and fluency. Two Entry Tests are available in the Mental Arithmetic Teacher's Guide and on the Schofield & Sims website, enabling teachers, parents and tutors to select the appropriate book for each child. All the books can be used flexibly for individual, paired, group or whole-class maths practice, as well as for homework and one-to-one intervention.Mental Arithmetic 6 Answers contains answers to all the questions included in the Mental Arithmetic 6 pupil book, as well as guidance on how to use the series and measure progress. Answers are clearly laid out in the format of a correctly completed pupil book making marking quick and easy, while a card cover ensures durability.

This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences," that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.

Interactively Run Simulations and Experiment with Real or Simulated Data to Make Sequential Analysis Come Alive Taking an accessible, nonmathematical approach to this field, Sequential Methods and Their Applications illustrates the efficiency of sequential methodologies when dealing with contemporary statistical challenges in many areas. The book first explores fixed sample size, sequential probability ratio, and nonparametric tests. It then presents numerous multistage estimation methods for fixed-width confidence interval as well as minimum and bounded risk problems. The book also describes multistage fixed-size confidence region methodologies, selection methodologies, and Bayesian estimation. Through diverse applications, each chapter provides valuable approaches for performing statistical experiments and facilitating real data analysis. Functional in a variety of statistical problems, the authors' interactive computer programs show how the methodologies discussed can be implemented in data analysis. Each chapter offers examples of input, output, and their interpretations. Available online, the programs provide the option to save some parts of an output so readers can revisit computer-generated data for further examination with exploratory data analysis. Through this book and its computer programs, readers will better understand the methods of sequential analysis and be able to use them in real-world settings.