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Understanding Maple
by Ian ThompsonMaple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author's personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.
Understanding Markov Chains: Examples and Applications
by Nicolas PrivaultThis book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.
Understanding Markov Chains: Examples and Applications (Springer Undergraduate Mathematics Series)
by Nicolas PrivaultThis book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
Understanding Mathematical Concepts in Physics: Insights from Geometrical and Numerical Approaches (Lecture Notes in Physics #1030)
by Sanjeev DhurandharModern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy’s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.
Understanding Mathematical Proof
by null John Taylor null Rowan GarnierThe notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techn
Understanding Mathematics: Grade 6
by Rod Staff Publishers Inc.New concepts are taught in the following areas. Numbers, Fractions, Decimals, Percents, Measures, Geometry, and Graphs.
Understanding Mathematics: Grade 6 Chapter Tests (Mathematics for Christian Living Series)
by Rod Staff Publishers StaffContains chapter tests with plenty of problem solving illustrations.
Understanding Mathematics and Science Matters (Studies in Mathematical Thinking and Learning Series)
by Thomas A. Romberg, Thomas P. Carpenter and Fae DremockThe research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world.The National Center for Improving Student Learning in Mathematics and Science--established in 1996 as a research center and funded by the U.S. Department of Education--was instrumental in developing instructional practices supportive of high student achievement in and understanding of mathematics and science concepts. NCISLA researchers worked with teachers, students, and administrators to construct learning environments that exemplify current research and theory about effective learning of mathematics and science. The careful programs of research conducted examined how instructional content and design, assessment, professional development, and organizational support can be designed, implemented, and orchestrated to support the learning of all students. This book presents a summary of the concepts, findings, and conclusions of the Center's research from 1996-2001.In the Introduction, the chapters in Understanding Mathematics and Science Matters are situated in terms of the reform movement in school mathematics and school science. Three thematically structured sections focus on, respectively, research directed toward what is involved when students learn mathematics and science with understanding; research on the role of teachers and the problems they face when attempting to teach their students mathematics and science with understanding; and a collaboration among some of the contributors to this volume to gather information about classroom assessment practices and organizational support for reform.The goal of this book is to help educational practitioners, policymakers, and the general public to see the validity of the reform recommendations, understand the recommended guidelines, and to use these to transform teaching and learning of mathematics and science in U.S. classrooms.
Understanding Mathematics for Young Children
by Derek Haylock Anne CockburnIf you are a teacher or student teacher in a nursery or primary school, you need a secure understanding of the mathematical ideas behind the material you will use in the classroom. To help young children develop their understanding of mathematics, you need to develop your own understanding of how mathematics is learnt. <P><P> In this indispensible book, the authors help you to understand mathematical concepts and how children come to understand them, and also help develop your own confidence with mathematical activities. <P> Each chapter of this book includes:<P> - Real-life examples and illustrations from children and teachers in the classroom <P> - The research behind some of the concepts and teaching approaches discussed <P> - Pauses to reflect and discuss your own mathematical knowledge and experience <P> - Age-appropriate classroom activities to try with your class or group.
Understanding Mathematics for Young Children: A Guide for Teachers of Children 3-7
by Derek Haylock Professor Anne CockburnHaving a deep understanding of the mathematical ideas and concepts taught in the classroom is vital as a nursery or primary school teacher. In order for children to get to grips with these concepts, trainee teachers need to be aware of how they come to interpret and understand them. Now in its 5th edition, this essential book helps trainee teachers develop their own knowledge of key mathematical ideas and concepts for the nursery and primary classroom. Now focusing specifically on ages 3-7, it also supports trainees with several age-appropriate classroom activities. As well as updates to further reading suggestions and research focuses, this revised edition includes new content on: Mastery in learning mathematics Simple fractions Roman numerals Money as a form of measurement
Understanding Mathematics for Young Children: A Guide for Teachers of Children 3-7
by Derek Haylock Professor Anne CockburnHaving a deep understanding of the mathematical ideas and concepts taught in the classroom is vital as a nursery or primary school teacher. In order for children to get to grips with these concepts, trainee teachers need to be aware of how they come to interpret and understand them. Now in its 5th edition, this essential book helps trainee teachers develop their own knowledge of key mathematical ideas and concepts for the nursery and primary classroom. Now focusing specifically on ages 3-7, it also supports trainees with several age-appropriate classroom activities. As well as updates to further reading suggestions and research focuses, this revised edition includes new content on: Mastery in learning mathematics Simple fractions Roman numerals Money as a form of measurement
Understanding Multivariate Research
by Mitchell Sanders William BerryAlthough nearly all major social science departments offer graduate students training in quantitative methods, the typical sequencing of topics generally delays training in regression analysis and other multivariate techniques until a student’s second year. William Berry and Mitchell Sanders’s Understanding Multivariate Research fills this gap with a concise introduction to regression analysis and other multivariate techniques. Their book is designed to give new graduate students a grasp of multivariate analysis sufficient to understand the basic elements of research relying on such analysis that they must read prior to their formal training in quantitative methods. Berry and Sanders effectively cover the techniques seen most commonly in social science journals--regression (including nonlinear and interactive models), logit, probit, and causal models/path analysis. The authors draw on illustrations from across the social sciences, including political science, sociology, marketing and higher education. All topics are developed without relying on the mathematical language of probability theory and statistical inference. Readers are assumed to have no background in descriptive or inferential statistics, and this makes the book highly accessible to students with no prior graduate course work.
Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis (Multivariate Applications Series)
by Geoff CummingThis is the first introductory statistics text to use an estimation approach from the start to help readers understand effect sizes, confidence intervals (CIs), and meta-analysis ('the new statistics'). It is also the first text to explain the new and exciting Open Science practices, which encourage replication and enhance the trustworthiness of research. In addition, the book explains NHST fully so students can understand published research. Numerous real research examples are used throughout. The book uses today's most effective learning strategies and promotes critical thinking, comprehension, and retention, to deepen users' understanding of statistics and modern research methods. The free ESCI (Exploratory Software for Confidence Intervals) software makes concepts visually vivid, and provides calculation and graphing facilities. The book can be used with or without ESCI. Other highlights include: - Coverage of both estimation and NHST approaches, and how to easily translate between the two. - Some exercises use ESCI to analyze data and create graphs including CIs, for best understanding of estimation methods. -Videos of the authors describing key concepts and demonstrating use of ESCI provide an engaging learning tool for traditional or flipped classrooms. -In-chapter exercises and quizzes with related commentary allow students to learn by doing, and to monitor their progress. -End-of-chapter exercises and commentary, many using real data, give practice for using the new statistics to analyze data, as well as for applying research judgment in realistic contexts. -Don't fool yourselftips help students avoid common errors. -Red Flagshighlight the meaning of "significance" and what pvalues actually mean. -Chapter outlines, defined key terms, sidebars of key points, and summarized take-home messages provide a study tool at exam time. -http://www. routledge. com/cw/cumming offers for students: ESCI downloads; data sets; key term flashcards; tips for using SPSS for analyzing data; and videos. For instructors it offers: tips for teaching the new statistics and Open Science; additional homework exercises; assessment items; answer keys for homework and assessment items; and downloadable text images; and PowerPoint lecture slides. Intended for introduction to statistics, data analysis, or quantitative methods courses in psychology, education, and other social and health sciences, researchers interested in understanding the new statisticswill also appreciate this book. No familiarity with introductory statistics is assumed.
Understanding Optics with Python (Multidisciplinary and Applied Optics)
by Ahmed Ammar Vasudevan Lakshminarayanan Hassen Ghalila L. VaradharajanOptics is an enabling science that forms a basis for our technological civilization. Courses in optics are a required part of the engineering or physics undergraduate curriculum in many universities worldwide. The aim of Understanding Optics with Python is twofold: first, to describe certain basic ideas of classical physical and geometric optics; second, to introduce the reader to computer simulations of physical phenomena. The text is aimed more broadly for those who wish to use numerical/computational modeling as an educational tool that promotes interactive teaching (and learning). In addition, it offers an alternative to developing countries where the necessary equipment to carry out the appropriate experiments is not available as a result of financial constraints. This approach contributes to a better diffusion of knowledge about optics. The examples given in this book are comparable to those found in standard textbooks on optics and are suitable for self-study. This text enables the user to study and understand optics using hands-on simulations with Python. Python is our programming language of choice because of its open-source availability, extensive functionality, and an enormous online support. Essentials of programming in Python 3.x, including graphical user interface, are also provided. The codes in the book are available for download on the book’s website. Discusses most standard topics of traditional physical and geometrical optics through Python and PyQt5 Provides visualizations and in-depth descriptions of Python’s programming language and simulations Includes simulated laboratories where students are provided a "hands-on" exploration of Python software Coding and programming featured within the text are available for download on the book’s corresponding website. "Understanding Optics with Python by Vasudevan Lakshminarayanan, Hassen Ghalila, Ahmed Ammar, and L. Srinivasa Varadharajan is born around a nice idea: using simulations to provide the students with a powerful tool to understand and master optical phenomena. The choice of the Python language is perfectly matched with the overall goal of the book, as the Python language provides a completely free and easy-to-learn platform with huge cross-platform compatibility, where the reader of the book can conduct his or her own numerical experiments to learn faster and better."— Costantino De Angelis, University of Brescia, Italy "Teaching an important programming language like Python through concrete examples from optics is a natural and, in my view, very effective approach. I believe that this book will be used by students and appreciated greatly by instructors. The topic of modelling optical effects and systems where the students should already have a physical background provides great motivation for students to learn the basics of a powerful programming language without the intimidation factor that often goes with a formal computer science course." — John Dudley, FEMTO-ST Institute, Besançon, France
Understanding Pendulums
by L. P. PookDespite their apparent simplicity, the behaviour of pendulums can be remarkably complicated. Historically, pendulums for specific purposes have been developed using a combination of simplified theory and trial and error. There do not appear to be any introductory books on pendulums, written at an intermediate level, and covering a wide range of topics. This book aims to fill the gap. It is written for readers with some background in elementary geometry, algebra, trigonometry and calculus. Historical information, where available and useful for the understanding of various types of pendulum and their applications, is included. Perhaps the best known use of pendulums is as the basis of clocks in which a pendulum controls the rate at which the clock runs. Interest in theoretical and practical aspects of pendulums, as applied to clocks, goes back more than four centuries. The concept of simple pendulums, which are idealised versions of real pendulums is introduced. The application of pendulums to clocks is described, with detailed discussion of the effect of inevitable differences between real pendulums and simple pendulums. In a clock, the objective is to ensure that the pendulum controls the timekeeping. However, pendulums are sometimes driven, and how this affects their behaviour is described. Pendulums are sometimes used for occult purposes. It is possible to explain some apparently occult results by using modern pendulum theory. For example, why a ring suspended inside a wine glass, by a thread from a finger, eventually strikes the glass. Pendulums have a wide range of uses in scientific instruments, engineering, and entertainment. Some examples are given as case studies.
Understanding Physics and Physical Chemistry Using Formal Graphs
by null Eric VieilThe subject of this book is truly original. By encoding of algebraic equations into graphs-originally a purely pedagogical technique-the exploration of physics and physical chemistry reveals common pictures through all disciplines. The hidden structure of the scientific formalism that appears is a source of astonishment and provides efficient simpl
Understanding Physics Using Mathematical Reasoning: A Modeling Approach for Practitioners and Researchers
by Andrzej SokolowskiThis book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students’ skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such trainingThe book draws on current research in developing students’ mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton’s laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.
Understanding Policy Decisions
by Bruno DenteThis book proposes a model for understanding how innovative policy decisions are taken in complex political and organizational systems as well as the possible strategies that the promoter of the innovation can employ in order to maximize the probability of successful adoption and implementation. It presents a conceptual framework for the analysis of decisional situations in order to design the most appropriate strategies for overcoming conflict (e. g. of the NIMBY variety) and/or increasing the engagement of potentially interested actors. The book includes a template for decisional case studies, a protocol for the definition of a decisional strategy, and an exercise in decisional analysis.
Understanding Proof: Explanation, Examples and Solutions of Mathematical Proof
by Ed Hall Tom BennisonProof is central to any mathematics curriculum and indeed, all mathematical thinking. Now we are delighted to provide an International Edition of our guide to proof for students...and for their teachers too. Contents: 1. Introduction to proof 2. Exploring Methods of Proof 3. Mathematical Language 4. Direct Proof 5. Indirect Proof 6. Proof by Induction 7. Proof and Applications of Pythagoras' Theorem 8. Proof in Calculus 9. Proving Trigonometric Identities 10. Proof in Statistics and Probability 11. Worked Solutions
Understanding Public Opinion Polls
by Jelke BethlehemPolls are conducted every day all around the world for almost everything (especially during elections). But not every poll is a good one. A lot depends on the type of questions asked, how they are asked and whether the sample used is truly representative. And these are not the only aspects of a poll that should be checked. So how does one separate the chaff from the wheat? That’s where Understanding Public Opinion Polls comes in. Written by a well-known author with over thirty years of experience, the book is built around a checklist for polls that describes the various aspects of polls to pay attention to if one intends to use its results. By comprehensively answering the questions in the checklist, a good idea of the quality of the poll is obtained. Features: Provides readers with a deeper understanding of practical and theoretical aspects of opinion polls while assuming no background in mathematics or statistics Shows how to determine if a poll is good or bad Provides a historical perspective and includes examples from real polls Gives special attention to online and election polls The book gives an overview of many aspects of polls – questionnaire design, sample selection, estimation, margins of error, nonresponse and weighting. It is essential reading for those who want to gain a better understanding of the ins and outs of polling including those who are confronted with polls in their daily life or work or those who need to learn how to conduct their own polls.
Understanding Randomness: EXERCISES FOR STATISTICIANS (Lecture Notes In Statistics Ser. #6)
by SalsburgThis concise, easy-to-follow book stimulates interest and develops proficiency in statisticalanalysis. Packed full of helpful exercises-covering a wide variety of conditions,random patterns, and simple models-Understanding Randomness presents a logical sequenceof study, through practice in interpreting random noise before progressing on toreal life problems ... demonstrates proper applications of numerous techniques throughworked out problems ... facilitates further work in statistics, keyed to standard references. . . and strengthens experience with unexpected results-fundamental for workingwith random events.Understanding Randomness serves as vital supplementary reading for both graduate andundergraduate students of statistics-with a standard statistics course as a prerequisiteandas a primary source for exercises in statistics laboratories. Moreover, it is importantfor industrial and mathematical training courses and society or association seminars, aswell as an invaluable workbook for statisticians, biostatisticians, biometricians, socialscientists concerned with improving their data analysis techniques-or anyone dealingwith evaluation of experimental data!
Understanding Real Analysis (Textbooks in Mathmatics)
by Paul ZornUnderstanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis. The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds.
Understanding Regression Analysis: A Conditional Distribution Approach
by Peter H. Westfall Andrea L. AriasUnderstanding Regression Analysis unifies diverse regression applications including the classical model, ANOVA models, generalized models including Poisson, Negative binomial, logistic, and survival, neural networks, and decision trees under a common umbrella -- namely, the conditional distribution model. It explains why the conditional distribution model is the correct model, and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books, this one from the outset takes a realistic approach that all models are just approximations. Hence, the emphasis is to model Nature’s processes realistically, rather than to assume (incorrectly) that Nature works in particular, constrained ways. Key features of the book include: Numerous worked examples using the R software Key points and self-study questions displayed "just-in-time" within chapters Simple mathematical explanations ("baby proofs") of key concepts Clear explanations and applications of statistical significance (p-values), incorporating the American Statistical Association guidelines Use of "data-generating process" terminology rather than "population" Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case) Clear explanations of probabilistic modelling, including likelihood-based methods Use of simulations throughout to explain concepts and to perform data analyses This book has a strong orientation towards science in general, as well as chapter-review and self-study questions, so it can be used as a textbook for research-oriented students in the social, biological and medical, and physical and engineering sciences. As well, its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples, it is also ideally suited to be a reference book for all scientists.
Understanding Relativity: A Conceptual Journey Into Spacetime, Black Holes and Gravitational Waves (The Frontiers Collection)
by Wouter SchmitzThis book bridges the huge gap between popular science and mathematical treatments of Einstein's theories. It explains special and general relativity, gravity, black holes, and gravitational waves, also presenting current ideas about dark matter and dark energy. The explanations are entirely non-mathematical, using many color pictures and clear concepts. In this way, the reader is led to a much deeper understanding than any popular science book can provide. The author has written this book for everyone who wants to go beyond superficial descriptions of relativity's remarkable phenomena, but is not equipped to read the professional literature and complicated math behind the theory. By providing a complete description in terms of concepts and pictures, the book answers many questions about why the theory works as it does. For example, it explains why and how momentum and pressure are related to gravity; why and how mass causes spacetime to curve and how curvature tells objects how to move; it also reveals the origin of the ring seen around the first ever image of a black hole. Not least, the reader will learn in detail how gravitational waves are produced and measured. Since their conception, the theories of relativity have appealed to the public's imagination. Thanks to this book, readers now have the opportunity to convert their fascination with the topic to a deep understanding.
Understanding Research Methods: An Overview of the Essentials (Ninth Edition)
by Mildred L. PattenUnderstanding Research Methods provides an overview of basic research methods.The updated text provides a detailed overview of all the important concepts traditionally covered in a research methods class. The numerous examples and large number of exercises help students master the material.