This second book on Unity Root Matrix Theory extends its original three-dimensional formulation, as given in the first book, to an arbitrary number of higher dimensions. Unity Root Matrix Theory is formulated with strong adherence to concepts in mathematical physics and it is thought it may provide a discrete formulation of physical phenomena at the Planck level and upward. Consequently, it is essential that the theory incorporates the geometric dimensionality present in established physical theories. In particular, it must naturally embody the four-dimensional spacetime of Special Relativity, the five dimensions of Kaluza-Klein theory, and the eleven or more dimensions of Grand Unified Theories such as String Theory. Not only has an n-dimensional extension of Unity Root Matrix Theory successfully been achieved, whilst retaining all the three-dimensional mathematical and physical properties detailed in the first book, but a complete n-dimensional solution has been obtained which exhibits the geometric property of compactification, or dimensional reduction. This solution shows that dimensional shrinkage of higher dimensions may occur over long evolutionary timescales. The emergence of compactification and other physical phenomena gives further confidence that n-dimensional Unity Root Matrix Theory may, indeed, offer a discrete formulation of Physics starting at its most elemental level.

This market-leading text continues to provide students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one-term course that prepares students for further study in mathematics, the new ninth edition retains the features that have always made COLLEGE ALGEBRA a complete solution for both students and instructors: interesting applications, pedagogically effective design, and innovative technology combined with an abundance of carefully developed examples and exercises.

Developed on surprisingly simple but fundamental concepts, it provides a rich mathematical and physical structure, justifying it as a subject to be studied in its own right by physicists and mathematicians alike. Ultimately, it is thought that unity root matrix theory may provide an alternative reformulation of some fundamental concepts in physics and an integer-based escape from the current, unification impasse.

Literary Nonfiction. Philosophy. Economics & Statistics. Translated from the German by Karen Leeder. Acclaimed poet, essayist, and cultural critic Hans Magnus Enzensberger takes a fresh, sobering look at our faith in statistics, our desire to predict the future, and our dependence on fortuitousness. Tracing the interface between chance and probability in medical diagnostics, risk models, economics, and the fluctuations of financial markets, FATAL NUMBERS goes straight to the heart of what it means to live, plan, and make decisions in a globalized, digitized, hyperlinked, science-driven, and uncertain world. Foreword by Gerd Gigerenzer. Illustrations by David Fried.

MURDEROUS MATHS: The Magic of Maths is full of incredible tricks to wow children and teachers alike. With a fabulous brand-new cover design for 2019, children can: discover how to use the power of maths to beat the calculator perform amazing card tricks read minds - using the power of maths! Illustrated by Rob Davis and presented in a bold, funky and accessible way so children can find out why maths is marvellous, a new generation of Kjartan Poskitt fans will be able to discover the world of MURDEROUS MATHS. Get ready to be amazed!

For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better.

Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back.

Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.

What is time? The Janus Point offers a ground-breaking solution to one of the greatest mysteries in physics. For over a century, the greatest minds have sought to understand why time seems to flow in one direction, ever forward. In The Janus Point, Julian Barbour offers a radically new answer: it doesn't. At the heart of this book, Barbour provides a new vision of the Big Bang - the Janus Point - from which time flows in two directions, its currents driven by the expansion of the universe and the growth of order in the galaxies, planets and life itself. What emerges is not just a revolutionary new theory of time, but a hopeful argument about the destiny of our universe. 'Both a work of literature and a masterpiece of scientific thought' Lee Smolin, author of The Trouble with Physics 'Profound...original...accessible to anyone who has pondered the mysteries of space and time' Martin Rees, Astronomer Royal 'Takes on fundamental questions, offering a new perspective on how the Universe started and where it may be headed' Science Magazine

Designed for the three-semester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 5e, International Edition continues to offer instructors and students innovative teaching and learning resources. The Larson team always has two main objectives for text revisions: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the fifth of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 5e, International Edition has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.

Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.

Ages: 7–11 Level: KS2 Subject: Maths  Power Maths is a leading primary maths mastery scheme, developed in partnership with White Rose Maths.   This edition is fully aligned with the new White Rose Maths schemes of learning (version 3.0) and has been updated in response to current mastery best practice and feedback from teachers.  The Power Maths Teacher Guides provide expert support for day-to-day teaching and continual professional development, including: How to implement a mastery approach using the Textbooks and Practice Books. Advice and commentary for each Textbook and Practice Book page, including ‘Strengthen’ and ‘Deepen’ ideas for children that need more support or stretch. A guide to the concepts introduced in each unit, including important structures and representations, key language, common misconceptions and intervention strategies. Support with key strategies such as modelling a growth mindset, assessing mastery, speedy same-day intervention, and using the Concrete-Pictorial-Abstract approach to embed deep understanding. Templates for teacher reflection, lesson study, and tracking pupil progress.

This resource has been developed to fully cover unit A2 2: Applied Mathematics of the CCEA specification, addressing both mechanics and statistics. For each topic, the book begins with a logical explanation of the theory, examples to reinforce the explanation, and any key words and definitions that are required. Examples and definitions are clearly differentiated to ease revision and progression through the book. The material then flows into exercises, before introducing the next topic. In this way, the student is guided through the subject. The book contains a large number of exercises in order to provide teachers with as much flexibility as possible for their students. Answers to the questions are included at the back of the book. Contents: 1 Kinematics; 2 Projectiles; 3 Moments; 4 Impulse and Momentum; 5 Probability; 6 Statistical Distributions; 7 Statistical Hypothesis Testing

Stand out, showcase your ability and succeed in your university admissions test. Whether you're taking STEP, MAT or TMUA, this essential guide reveals tried-and-tested strategies for building the problem-solving skills you need to secure a high score. Containing expert advice and worked examples, followed by multiple-choice and extended questions that replicate the exams, this guide is designed to improve your understanding of the admissions tests and help to build the skills universities are looking for. - Learn to think like a university student - detailed guidance, thought-provoking questions and worked solutions show you how to advance your mathematical thinking - Improve your mathematical reasoning - practise the problem-solving skills you need with 'Try it out' activities throughout the book and end-of-chapter exercises to track progress - Build a path through every problem - our authors guide you through each type of problem so that you can approach questions confidently, think on the spot and apply your knowledge to new contexts - Maximise marks and make the most of the time you have - at the end of each chapter, our authors give advice on how to tackle questions in the most time-efficient way and help you to figure out which ones will show off your ability What are the STEP (Sixth Term Examination Paper), MAT (Mathematics Admissions Test) and TMUA (Test of Mathematics for University Admission) admissions tests? These admissions tests are used by universities as part of the application process to test problem-solving skills and identify candidates with the highest ability, motivation and ingenuity. MEI (Mathematics in Education and Industry) endorses this book and provided two of the authors. MEI is a charity and works to improve maths education, offering a range of support for teachers, including expertly written resources. OUR AUTHORS David Bedford has a PhD in Combinatorics and has been a mathematics lecturer in UK universities for over 30 years. He is also an A level examiner and has extensive experience in preparing students for mathematics admissions tests. David is the author of the Hodder 'MEI Further Mathematics: Extra Pure Maths' textbook. Phil Chaffe is the Advanced Maths Support Programme 16-19 Student Support and Problem Solving Professional Development Lead. He is the creator and lead writer for the Problem Solving Matters course which is designed to prepare students for mathematics admissions tests and is run in partnership with the Universities of Oxford, Warwick, Durham, Manchester, Bristol and Imperial College London. He is also the course designer for Imperial College's A* in A Level Mathematics course. He is also the MEI University Sector Lead. Tim Honeywill has been teaching at King Henry VIII School, Coventry, since 2008. Before that, he was the Coventry and Warwickshire Centre Manager for the Further Mathematics Network (now the AMSP), based at the University of Warwick where he did his PhD. He leads a ten-week Problem Solving course for Year 12 students and is a presenter on both the Problem Solving Matters course and on a STEP support course for Year 13 students. Richard Lissaman has a PhD in Ring Theory, a branch of abstract algebra. He has over 10 years' experience as a mathematics lecturer in UK universities and 20 years' experience of supporting students with A level Mathematics, Further Mathematics and mathematics admissions tests.

Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model a la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.

Dr Zoltan Dienes is a world-famous theorist and tireless practitioner of the 'new mathematics' - an approach to mathematics learning which uses games, songs and dance to make it more appealing to children. Holder of numerous honorary degrees, Dr Dienes has had a long and fruitful career, breaking new ground and gaining many followers with his revolutionary ideas of learning often complex mathematical concepts in such fun ways that children are often unaware that they are learning anything. This is an honest account of an academic radical, covering his sometimes unconventional childhood in Hungary, France, Germany and Britain, his peripatetic academic career, his successes and failures and his personal affairs. Occasionally sad or moving, frequently amusing and always fascinating, this autobiography shares some of the intelligence, spirit and humanity that have made Dr Dienes such a landmark figure in mathematics education. A 'must-read' for anyone with a professional interest in the field, this is also an absorbing and frank book for anyone interested in the life of a man of ideas who was not afraid to take on the might of the traditionalist educational establishment.

Quantitative techniques form the backbone of all statistical, economic and management models according to which forecasts and management decisions are made. Quantitative statistical techniques aims to help readers not only master these techniques, but also understand the role of each technique. Quantitative principles are stated simply and are specifically directed at the first-year student who is contemplating a career in the business sector. The topics that are dealt with reflect the relevant quantitative background specifically demanded by business careers. Guidelines describing how calculations can be performed with computer software are integrated throughout the text.

In this work Zoltan Paul Dienes enlivens the world of algebra and examines some of the mysteries of mathematical constructions in a new and exciting fashion. Step by step, equation by equation, diagram by diagram, he strips away all the unintelligible jargon and brings each task and problem to life. If algebra lessons were viewed with dread at school, this is the book to make you reconsider. The informal style, clear diagrams and comprehensive explanations make understanding easy, while innovative games and intriguing puzzles ensure that learning is no longer a chore but a pleasure. Although predominantly aimed at those already equipped with basic algebra skills, beginners and experts alike will find much to interest and test them.

A valuable, bilingual guide to the most useful statistical tables.

An introduction to Applied Calculus for Social and Life Sciences, the revised edition, contains all the material in the original version and now contains answers to odd numbered exercises. The book additionally contains selected worked out examples available from the publisher's website. The book is designed primarily for students majoring in Social Sciences and Life Sciences. It prepares students to deal with mathematical problems which arise from real-life problems encountered in other areas of study, such as Agriculture, Forestry, Biochemistry, Biology and the Biomedical Sciences. It is also of value to anyone intending to develop foundational undergraduate calculus for the Physical Sciences.

The UK's most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson's own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Decision Mathematics 1 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 1 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel's interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well as supporting the large data set and calculators. They are packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises. There are full worked solutions to every question available free and online for quick and easy access. You will also have access to lots of free additional online content with GeoGebra interactives and Casio calculator tutorials. There are separate Pure and Applied textbooks for AS and A level Maths, and a textbook per option for AS and A level Further Maths. Practice books are also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions. Pearson's revision resources are the smart choice for those revising for Pearson Edexcel AS and A level Mathematics - there is a Revision Workbook for exam practice and a Revision Guide for classroom and independent study. Practice Papers Plus+ books contain additional full length practice papers, so you can practice answering questions by writing straight into the book and perfect your responses with targeted hints, guidance and support for every question, including fully worked solutions.