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Edexcel and A Level Modular Mathematics C4 features: Student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample exam papers for thorough exam preparation. Regular review sections consolidate learning. Opportunities for stretch and challenge presented throughout the course. 'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.
Target success in OCR B (MEI) A Level Mathematics with this proven formula for effective, structured revision; key content coverage and plentiful worked examples are combined with exam-style and multiple choice questions to create a revision guide that students can rely on to review, strengthen and test their knowledge. - Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators). - Strategically target revision with diagnostic questions to establish which areas need focus. - Get assessment-ready with exam-style questions and advice on common examination pitfalls. - Embed knowledge and identify weaknesses with hundreds of multiple choice 'Test Yourself' questions, all carefully written to elicit misconceptions; full worked solutions online offer detailed, instructive explanations for all choices (whether they are correct or incorrect) - Consolidate revision with summaries for each topic that focus on what to concentrate on in the build-up to exams, with special focus on common pitfalls such as how to show correct workings. -Access answers at the back of the book, with detailed step-by-step worked solutions for ALL questions available for free online.
Larson's PRECALCULUS WITH LIMITS, 3E, International Edition is known for delivering the same sound, consistently structured explanations and exercises of mathematical concepts as the market-leading PRECALCULUS, 9E, International Edition with a laser focus on preparing students for calculus. In LIMITS, the author includes a brief algebra review to the core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus. With the third edition, Larson continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.
In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.
Transform your approach to oprisk modelling with a proven, non-statistical methodology Operational Risk Modeling in Financial Services provides risk professionals with a forward-looking approach to risk modelling, based on structured management judgement over obsolete statistical methods. Proven over a decade's use in significant banks and financial services firms in Europe and the US, the Exposure, Occurrence, Impact (XOI) method of operational risk modelling played an instrumental role in reshaping their oprisk modelling approaches; in this book, the expert team that developed this methodology offers practical, in-depth guidance on XOI use and applications for a variety of major risks. The Basel Committee has dismissed statistical approaches to risk modelling, leaving regulators and practitioners searching for the next generation of oprisk quantification. The XOI method is ideally suited to fulfil this need, as a calculated, coordinated, consistent approach designed to bridge the gap between risk quantification and risk management. This book details the XOI framework and provides essential guidance for practitioners looking to change the oprisk modelling paradigm. Survey the range of current practices in operational risk analysis and modelling Track recent regulatory trends including capital modelling, stress testing and more Understand the XOI oprisk modelling method, and transition away from statistical approaches Apply XOI to major operational risks, such as disasters, fraud, conduct, legal and cyber risk The financial services industry is in dire need of a new standard -- a proven, transformational approach to operational risk that eliminates or mitigates the common issues with traditional approaches. Operational Risk Modeling in Financial Services provides practical, real-world guidance toward a more reliable methodology, shifting the conversation toward the future with a new kind of oprisk modelling.
Edexcel's own course for the GCE specification. Providing the best match to the specification, this book motivates students by making maths easier to learn. Written by chief examiners, it provides student-friendly worked examples and solutions, leading to a wealth of practice questions. Sample past exam papers are included for thorough exam preparation, and regular review sections help to consolidate learning. Opportunities for stretch and challenge are presented throughout the course, and an interactive FREE LiveText CD-ROM contains everything students need to motivate and prepare themselves. The all new Exam Cafe gives students revision advice, key ideas summaries and an abundance of exam practice, with hints and tips.
Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
New from James Stewart and Dan Clegg, BRIEF APPLIED CALCULUS, International Edition takes an intuitive, less formal approach to calculus without sacrificing the mathematical integrity. Featuring a wide range of applications designed to motivate students with a variety of interests, clear examples detailing important mathematical processes, and a vast collection of exercises appropriate for students with disparate skill sets, this first edition is perfect for students who need to learn how to apply calculus concepts rather than replicate the formal proofs behind the techniques. Early coverage of exponential and logarithmic functions allows for the inclusion of many interesting applications throughout the text. Available with a range of supplements including Enhanced WebAssign, BRIEF APPLIED CALCULUS, International Edition makes calculus approachable so any student can understand the concepts and be successful in the course.
This book is intended for readers who have had a course in iso-differential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with exact iso-differential equations, while first-order iso-differential equations are studied in Chapter 2 and Chapter 3. Chapter 4 discusses iso-integral inequalities. Many iso-differential equations cannot be solved as finite combinations of elementary functions. Therefore, it is important to know whether a given iso-differential equation has a solution and if it is unique. These aspects of the existence and uniqueness of the solutions for first-order initial value problems are considered in Chapter 5. Iso-differential inequalities are discussed in Chapter 6. Continuity and differentiability of solutions with respect to initial conditions are examined in Chapter 7. Chapter 8 extends existence-uniqueness results and continuous dependence on initial data for linear iso-differential systems. Basic properties of solutions of linear iso-differential systems are given in Chapter 9. Chapter 10 deals with the fundamental matrix solutions. In Chapter 11, necessary and sufficient conditions are provided so that a linear iso-differential system has only periodic solutions. The asymptotic behaviour of the solutions of linear systems is investigated in Chapter 12. Chapters 13 and 14 are devoted to some aspects of the stability of solutions of iso-differential systems. The last major topic covered in this book is that of boundary value problems involving second-order iso-differential equations. After linear boundary value problems are introduced in Chapter 15, Green's function and its construction is discussed in Chapter 16.
Exam Board: Edexcel Level: AS and A level Subject: Further Mathematics First teaching: September 2017 First exams: Summer 2018 With over 1.3 million copies sold of the previous edition, Pearson's textbooks are the market-leading and most trusted resources for AS and A level Further Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Further Mechanics 1 exams. Fully updated to match the 2017 specifications, with more of a focus on problem-solving and modelling. FREE additional online content to support your independent learning, including full worked solutions for every question in the book (SolutionBank) and GeoGebra interactives. Includes access to an online digital edition (valid for 3 years once activated). Includes worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises.
An exploration of one of the most celebrated and well-known theorems in mathematics By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof-if indeed he had one-is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.
ELEMENTARY TECHNICAL MATHEMATICS helps students with minimal math background successfully prepare for technical, trade, allied health or tech prep programs. Author Dale Ewen focuses on fundamental concepts in basic arithmetic: the metric system and measurement, algebra, geometry, trigonometry and statistics. Thousands of examples, exercises and applications cover such fields as industrial and construction trades, electronics, agriculture/horticulture, allied health, CAD/drafting, HVAC, welding, auto/diesel service, aviation, natural resources, culinary arts and business/personal finance--to engage students and provide them with the math background they need to succeed in future courses and careers.
The maths needed to succeed in A Level Science is harder now than ever before. Suitable for all awarding bodies, this practical handbook addresses all of the maths skills needed for A Level Physics specifications. Worked examples, practice questions, 'remember points' and 'stretch yourself' questions give students the key knowledge and then the opportunity to practise and build confidence.
This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
Master the art and science of data storytelling--with frameworks and techniques to help you craft compelling stories with data. The ability to effectively communicate with data is no longer a luxury in today's economy; it is a necessity. Transforming data into visual communication is only one part of the picture. It is equally important to engage your audience with a narrative--to tell a story with the numbers. Effective Data Storytelling will teach you the essential skills necessary to communicate your insights through persuasive and memorable data stories. Narratives are more powerful than raw statistics, more enduring than pretty charts. When done correctly, data stories can influence decisions and drive change. Most other books focus only on data visualization while neglecting the powerful narrative and psychological aspects of telling stories with data. Author Brent Dykes shows you how to take the three central elements of data storytelling--data, narrative, and visuals--and combine them for maximum effectiveness. Taking a comprehensive look at all the elements of data storytelling, this unique book will enable you to: Transform your insights and data visualizations into appealing, impactful data stories Learn the fundamental elements of a data story and key audience drivers Understand the differences between how the brain processes facts and narrative Structure your findings as a data narrative, using a four-step storyboarding process Incorporate the seven essential principles of better visual storytelling into your work Avoid common data storytelling mistakes by learning from historical and modern examples Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals is a must-have resource for anyone who communicates regularly with data, including business professionals, analysts, marketers, salespeople, financial managers, and educators.
Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insights emerging from Franklin's treatment make it a valuable teaching resource.
Presenting theory while using "Mathematica" in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray's famous textbook, covers how to define and compute standard geometric functions using "Mathematica" for constructing new curves and surfaces from existing ones. Since Gray's death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the "Mathematica" code and added a "Mathematica" notebook as an appendix to each chapter. They also address important new topics, such as quaternions.
The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi's formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but"Mathematica "handles it easily, either through computations or through graphing curvature. Another part of "Mathematica" that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.
Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use "Mathematica" to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples.It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
This Student Book provides full support for both AQA's new linear AS Level Further Maths specification, and for the first year of the full A Level course. Covering both the compulsory content (further pure) and all the optional content (mechanics, statistics and discrete maths), each chapter starts with an Orientation box, clarifying which A Level Maths topics are being built on, and what learning objectives will be covered. Each chapter section starts with a clear and concise explanation of the maths, with an emphasis on visual presentation. Abundant worked examples show how key techniques can be used and common pitfalls to avoid. Separate exercises allow students to practise first their fluency and skills, and then the new exam-style problem-solving and modelling questions. The problem-solving is supported by Strategy boxes, which provide guidance on how best to approach these questions. Answers are given in the back of the book, while full step-by-step solutions to every single question can be found online. This Student Book provides a complete course for AS Level Further Maths and is the ideal way for a student to become a mathematician.
Pre-Algebra Essentials For Dummies (9781119590866) was previously published as Pre-Algebra Essentials For Dummies (9780470618387). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need to a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.
This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.
This revision of QUANTITATIVE METHODS FOR BUSINESS provides students with a conceptual understanding of the role that quantitative methods play in the decision-making process. This text describes the many quantitative methods that have been developed over the years, explains how they work, and shows how the decision-maker can apply and interpret data. Written with the non-mathematician in mind, this text is applications-oriented. Its Problem-Scenario Approach motivates and helps students understand and apply mathematical concepts and techniques. In addition, the managerial orientation motivates students by using examples that illustrate situations in which quantitative methods are useful in decision making.
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