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'One of the best books on evolutionary biology for a broad readership ever written' Edward O. Wilson A dazzling tour of evolution in action that sheds light on one of the greatest debates in science The natural world is full of fascinating instances of convergence: phenomena like eyes and wings and tree-climbing lizards that have evolved independently, multiple times. Convergence suggests that evolution is predictable, and if we could replay the tape of life, we would get the same outcome. But there are also many examples of contingency, cases where the tiniest change - a random mutation or an ancient butterfly sneeze - caused evolution to take a completely different course. In Improbable Destinies, renowned researcher Jonathan Losos reveals what the latest breakthroughs in evolutionary biology tell us about one of the greatest ongoing debates in science. Evolution can occur far more rapidly than Darwin expected, which has opened the door to something that was previously thought impossible: experimental studies of evolution in nature. Drawing on his own work with anole lizards on the Caribbean islands, as well as studies of guppies, foxes, field mice and others being conducted around the world, Losos reveals just how rapid and predictable evolution can be. By charting the discoveries of the scientists who are rewriting our understanding of evolutionary biology, Improbable Destinies will change the way we think and talk about evolution.
It's a big step up from GCSE Maths to the new AS-Level and A-level Maths courses - which is why we've rustled up this brilliant Head Start book! It recaps all the crucial topics students will need to remember from GCSE, and gives them a taste of how they're used at A-Level. Packed with study notes, examples and practice questions, it's the perfect way for students to get off to a flying start in September.
Elementary Differential Equations with Boundary Value Problems integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors.
This book introduces readers to the ways probability is applied to practical problems in science, business, and engineering. The author includes interesting examples that show applications of probability theory in all these fields. The emphasis throughout is on modeling and interpretation of data rather than of abstract mathematics, stressing uses of the computer for analysis.
This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Loef in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
This Student Book provides full support for year two of an AQA A Level course. Covering all the pure maths, mechanics and statistics content needed, the book provides dedicated exercises in every chapter for exam-style problem-solving and modelling questions. Dedicated revision exercises test synoptically across the curriculum. Throughout the book, the explanatory text is clear and concise, with abundant worked examples to show how key techniques can be used and common pitfalls to avoid. Short answers are in the back of the book, while full step-by-step solutions are provided online. MyMaths links appear at the bottom of all exercises, providing a quick route to further practice and support.
Barron's revised SAT Math Workbook provides realistic questions for all math topics on the SAT. This edition features: Hundreds of revised math questions with answer explanations Math strategies to help test-takers approach and correctly answer all of the question types on the SAT Answers and explanations for all questions This is an intensive preparation for the SAT's all-important Math section, and a valuable learning tool for college-bound students who may need extra help in math or who want to improve their math scores.
"Introduction to Statistics for Forensic Scientists" is an essential introduction to the subject, gently guiding the reader through the key statistical techniques used to evaluate various types of forensic evidence. Assuming only a modest mathematical background, the book uses real-life examples from the forensic science literature and forensic case-work to illustrate relevant statistical concepts and methods. Opening with a brief overview of the history and use of statistics within forensic science, the text then goes on to introduce statistical techniques commonly used to examine data obtained during laboratory experiments. There is a strong emphasis on the evaluation of scientific observation as evidence and modern Bayesian approaches to interpreting forensic data for the courts. The analysis of key forms of evidence are discussed throughout with a particular focus on DNA, fibres and glass.An invaluable introduction to the statistical interpretation of forensic evidence, this book will be invaluable for all undergraduates taking courses in forensic science. It includes an introduction to the key statistical techniques used in the evaluation of forensic evidence. It also includes end of chapter exercises to enhance student understanding. Numerous examples are taken from forensic science to put the subject into context.
This CGP Complete Revision & Practice book is a fantastic all-in-one guide to AS & A-Level Edexcel Further Maths (for courses starting in 2017 and beyond). It's bursting with crystal-clear revision notes and worked examples for the Core Pure topics as well as the Further Pure 1, Further Statistics 1, Further Mechanics 1 and Decision Mathematics 1 options. There are also plenty of exam-style questions to test students on what they've learned (including step-by-step answers at the back). And to top things off, the book comes with a free Online Edition - just use the code printed inside the book to read it on a PC, Mac or tablet.
This book is an introduction to real analysis for a one-semester course aimed at students who have completed the calculus sequence and preferably one other course, such as linear algebra. It does not assume any specific knowledge and starts with all that is needed from sets, logic, and induction. Then there is a careful introduction to the real numbers with an emphasis on developing proof-writing skills. It continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions. A theme in the book is to give more than one proof for interesting facts; this illustrates how different ideas interact and it makes connections among the facts that are being learned. Metric spaces are introduced early in the book, but there are instructions on how to avoid metric spaces for the instructor who wishes to do so. There are questions that check the readers' understanding of the material, with solutions provided at the end. Topics that could be optional or assigned for independent reading include the Cantor function, nowhere differentiable functions, the Gamma function, and the Weierstrass theorem on approximation by continuous functions.
Exam Board: Pearson Edexcel Academic Level: A level Subject: Mathematics First teaching: September 2017 First Exams: Summer 2018 This Revision Workbook is suitable for classroom and independent study, and is the smart choice for those revising for A level Mathematics. Organise their revision with the one topic-per-page format Speed up their revision with summary notes in short, memorable chunks Track their revision progress with at-a-glance check boxes Check their understanding with worked examples Develop their exam technique with exam-style practice questions and answers
Mathematical Methods for Physics and Engineering, Third Edition is a highly acclaimed undergraduate textbook that teaches all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. This solutions manual accompanies the third edition of Mathematical Methods for Physics and Engineering. It contains complete worked solutions to over 400 exercises in the main textbook, the odd-numbered exercises, that are provided with hints and answers. The even-numbered exercises have no hints, answers or worked solutions and are intended for unaided homework problems; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
Exam Board: Pearson Edexcel Academic Level: AS level Subject: Mathematics First teaching: September 2017 First Exams: Summer 2018 Each book contains complete sets of practice papers with full worked solutions and hints and notes on the marks allocated directly alongside the relevant steps of the solution, so your students can make most sense of them and build their confidence. Designed to survive the rigours of the classroom and home, all the papers are bound into a durable book. Accessible write-in format allows students to take an active role in their revision.
Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics.
This new, revised edition of the bestselling "Speed Mathematics" features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With "Speed Mathematics" you'll discover methods to make maths easy and fun. This book is perfect for students, parents, teachers and anyone who enjoys working with figures and even those who are terrified of numbers
In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really "six degrees of separation" between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, the number of guards needed to protect an art gallery, problematic election results and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.
Exam board: Edexcel Level: A-level Subject: Mathematics First teaching: September 2017 First exams: Summer 2018 Target success in Edexcel 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. Includes all Year 1 and Year 2 A-level Maths content.
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Gain an in-depth understanding of converter-interfaced energy storage systems with this unique text, covering modelling, dynamic behaviour, control, and stability analysis. Providing comprehensive coverage, it demonstrates the technical and economic aspects of energy storage systems, and provides a thorough overview of energy storage technologies. Several different modelling techniques are presented, including power system models, voltage-sourced converter models, and energy storage system models. Using a novel stochastic control approach developed by the authors, you will learn about the impact of energy storage on the dynamic interaction of microgrids with distribution and transmission systems. Compare the numerous real-world simulation data and numerical examples provided with your own models and control strategies. Accompanied online by a wealth of numerical examples and supporting data, this is the ideal text for graduate students, researchers, and industry professionals working in power system dynamics, renewable energy integration, and smart grid development.
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrodinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrodinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research. "
This new edition of Conceptual Developments of 20th Century Field Theories explores the conceptual foundations and historical roots of fundamental field theories. It also uncovers the underlying issues, logic and dynamics in fundamental physics. In response to new advances in the field over the past twenty years, the sections on gauge theory and quantum field theory have been thoroughly revised and elaborated. The chapter on ontological synthesis and scientific realism has also been reconsidered, now suggesting a new approach that goes beyond structuralism and historicism. Providing an integrated picture of the physical world, it is a valuable resource for theoretical physicists and philosophers of science with an interest in the development of twentieth century mathematical physics. It also provides professional historians and sociologists of science with a basis for further historical, cultural and sociological analysis of the theories discussed.
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.
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