With breathtaking detail, Maria Georgiadou sheds light on the work and life of Constantin Carathéodory, who until now has been ignored by historians. In her thought-provoking book, Georgiadou maps out the mathematician’s oeuvre, life and turbulent historical surroundings. Descending from the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a lifetime to mathematics and education. He significantly contributed to: calculus of variations, the theory of point set measure, the theory of functions of a real variable, pdes, and complex function theory. An exciting and well-written biography, once started, difficult to put down.

This volume consists of seven papers related in various matters to the research work of Kostia Beidar, a distinguished ring theorist and professor of National Ching Kung University (NCKU). Written by leading experts in these areas, the papers also emphasize important applications to other fields of mathematics. Most papers are based on talks that were presented at the memorial conference which was held in March 2005 at NCKU.

The first book of its kind, "New Foundations in Mathematics: The Geometric Concept of Number" uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner.

"New Foundations in Mathematics" will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.
Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.
The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.
One volume, unified treatment of essential topicsClearly and comprehensively covers material beyond standard textbooksWorked examples, challenges and exercises throughout

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.

This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.

This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates more generally the development of mathematical scientists for a variety of workplaces, and includes the experiences of those who were not successful in the transition to the workplace as mathematicians. The research presented is based on interviews, observations and surveys of students and graduates as they are finding their identity as a mathematician. The book contains material from the research carried out in South Africa, Northern Ireland, Canada and Brunei as well as Australia.

The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical "research agenda projects," which seek to outline specific research questions that the field should address around a central topic.

Contents -
Preface -
1. REVIEW OF BASIC MATERIAL - FUNCTIONS, INEQUALITIES - 2. DIFFERENTIAL CALCULUS - 3. INTEGRATION - 4. FUNCTIONS OF MANY VARIABLES; PARTIAL DIFFERENTIATION - 5. VECTORS - 6. SERIES, TAYLOR-MACLAURIN SERIES - 7. COMPLEX NUMBERS - 8. ORTHOGONAL FUNCTIONS AND FOURIER SERIES - 9. DETERMINANTS - 10. MATRICES - 11. DIFFERENTIAL EQUATIONS - 12. PARTIAL DIFFERENTIAL EQUATIONS - 13. NUMERICAL METHODS - 14. ELEMENTARY STATISTICS AND ERROR ANALYSIS - Problems for Solution - Bibliography - Answers to Problems - Index

Reveal the insights behind your company's data with Microsoft Power BI Microsoft Power BI allows intuitive access to data that can power intelligent business decisions and insightful strategies. The question is, do you have the Power BI skills to make your organization's numbers spill their secrets? In Microsoft Power BI For Dummies, expert lecturer, consultant, and author Jack Hyman delivers a start-to-finish guide to applying the Power BI platform to your own firm's data. You'll discover how to start exploring your data sources, build data models, visualize your results, and create compelling reports that motivate decisive action. Tackle the basics of Microsoft Power BI and, when you're done with that, move on to advanced functions like accessing data with DAX and app integrations Guide your organization's direction and decisions with rock-solid conclusions based on real-world data Impress your bosses and confidently lead your direct reports with exciting insights drawn from Power BI's useful visualization tools It's one thing for your company to have data at its disposal. It's another thing entirely to know what to do with it. Microsoft Power BI For Dummies is the straightforward blueprint you need to apply one of the most powerful business intelligence tools on the market to your firm's existing data.

This tenth volume in the Poincare Seminar Series describes recent developments at one of the most challenging frontiers in statistical physics - the deeply related fields of glassy dynamics, especially near the glass transition, and of the statics and dynamics of granular systems. These fields are marked by a vigorous interchange between experiment, theory, and numerical studies, all of which are well represented by the leading experts who have contributed articles to this volume. These articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a Galilean dialogue on the mean field and competing theories of the glass transition, a wide-ranging survey of colloidal glasses, and experimental as well as theoretical treatments of the relatively new field of dense granular flows. This book should be of broad general interest to both physicists and mathematicians.

This bestselling series is written by an experienced team of Scottish authors and examiners. This Student Book includes: Complete coverage of the higher course, whilst the Revision Book gives plenty of confidence-building practice. Multiple-choice questions to offer complete support for the new multiple-choice paper. Worked examples and exam questions help consolidate learning and provide thorough exam preparation. 'Test-yourself' questions presenting opportunities for self-assessment. Clear diagrams convey key teaching points and help students to learn. Answers to all the questions are supplied for all-round support.

1 Arithmetic Review.- 1.1 Basis Rules.- 1.2 Division, Fractions, and Exponents.- 1.3 Percentages.- 1.4 Rates.- 2 Prime Numbers and Fractions.- 2.1 Prime Numbers and Factorization.- 2.2 Greatest Common Factor.- 2.3 Rationals and Irrationals.- 3 The Pythagorean Theorem and Square Roots.- 3.1 The Theorem.- 3.2 Square Roots Which Are Irrational.- 3.3 Computation of Square Roots by Successive Approximation.- 4 Elementary Equations.- 4.1 Equations in One Unknown.- 4.2 The Use of Two or More Unknowns.- 4.3 Graphing.- 5 Quadratic Polynomials and Equations.- 5.1 Solution of Quadratic Equations.- 5.2 Applications of Quadratic Equations.- 5.3 Quadratic Polynomials.- 6 Powers and Geometric Sequences.- 6.1 Applications of Powers.- 6.2 More on Half-Lives.- 6.3 Compound Interest and Related Matters.- 6.4 IRAs and Similar Tax Sheltered Accounts.- 6.5 Geometric Series-the "Sum" of a Geometric Sequence.- 7 Areas and Volumes.- 7.1 Areas.- 7.2 Volumes.- 7.3 Surface Area of a Solid (versus Volume).- 7.4 Computation of Cube Roots.- 8 Galilean Relativity.- 8.1 Displacement and Velocity Vectors.- 8.2 Doppler Effect.- 8.3 Components of Vectors.- 9 Special Relativity.- 9.1 Simultaneity and Einstein's Postulate.- 9.2 Time Dilation.- 9.3 Length Contraction.- 10 Binary Arithmetic.- 10.1 Decimal, Binary, and Ternary Representation of Integers.- 10.2 Subtraction and Division in Base Two.- 10.3 Applications.- 11 Sets and Counting.- 11.1 Set Notation.- 11.2 Counting.- 12 Probability.- 12.1 Elementary Ideas and Examples.- 12.2 Mutually Exclusive Events.- 12.3 The Basic Rules.- 12.4 Quality Control (optional).- 12.5 Expectation.- 12.6 Conditional Probability.- 13 Cardinality.- 13.1 Countable Sets.- 13.2 Countably Many Countable Sets.- 13.3 The Reals vs. the Rationals.- Answers to Odd-Numbered Problems.

In the last 15 years we have seen a major transformation in the world of music. - sicians use inexpensive personal computers instead of expensive recording studios to record, mix and engineer music. Musicians use the Internet to distribute their - sic for free instead of spending large amounts of money creating CDs, hiring trucks and shipping them to hundreds of record stores. As the cost to create and distribute recorded music has dropped, the amount of available music has grown dramatically. Twenty years ago a typical record store would have music by less than ten thousand artists, while today online music stores have music catalogs by nearly a million artists. While the amount of new music has grown, some of the traditional ways of ?nding music have diminished. Thirty years ago, the local radio DJ was a music tastemaker, ?nding new and interesting music for the local radio audience. Now - dio shows are programmed by large corporations that create playlists drawn from a limited pool of tracks. Similarly, record stores have been replaced by big box reta- ers that have ever-shrinking music departments. In the past, you could always ask the owner of the record store for music recommendations. You would learn what was new, what was good and what was selling. Now, however, you can no longer expect that the teenager behind the cash register will be an expert in new music, or even be someone who listens to music at all.

This book provides a platform for international scholars to share evidence for effective practices in integrated STEM education and contributes to the theoretical and practical knowledge gained from the diversity of approaches. Many publications on STEM education focus on one or two of the separate STEM disciplines without considering the potential for delivering STEM curriculum as an integrated approach.This publication analyzes the efficacy of an integrated STEM curriculum and instruction, providing evidence to examine and support various integrations. The volume focuses on the problems seen by academics working in the fields of science, technology, engineering and mathematics (STEM) and provides valuable, high quality research outcomes and a set of valued practices which have demonstrated their use and viability to improve the quality of integrated STEM education.

This book is the "Study Book" of ICMI-Study no. 20, which was run in cooperation with the International Congress on Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organiser of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over world. This content was selected by the editors as especially pertinent to the study each individual chapter represents a significant contribution to current research.

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.

This volume contains refereed papers submitted by participants of the third week of a six week workshop on Statistics in the Health Sciences held by the Institute of Mathematics and its Applications in Minneapolis, Minnesota during July of 1997. This week was devoted to the closely related topics of Diagnosis and Prediction. Theoretical and applied statisticians from universities, medical and public health schools, government and private research institutions, and pharmaceutical companies involved in prediction problems in the life and social sciences and in diagnostic and screening tests were brought together to discuss and exchange new results and information on these important issues. A number of papers with applications were presented and especially lively discussions ensued involving the critical issues and difficulties in using and interpreting diagnostic tests and implementing mass screening programs. Both frequentist and Bayesian approaches were employed. The importance of predicting or controlling future events such as survival, comparative survival and survival post intervention for a disease or even for certain biological or natural events is growing rapidly. This area of concern was also represented by participants who presented work that devised predictive methodology for a variety of problems mainly from a Bayesian perspective.