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Probably the Best Book on Statistics Ever Written: How to Beat the Odds and Make Better Decisions
by Haim ShapiraTaking an amusing and digestible look at the usually dry world of probability and statistics, this is the ultimate guide to how you can incorporate them into everyday life, from one of the world's most sought-after experts in game theory. This is the only book you need to become a statistics whizz! Numbers are everywhere – food packaging, weather forecasts, social media, adverts, and more. You can&’t escape them. But you can learn to understand them – and avoid being fooled! This book breaks down the key fundamentals in statistics in a fun and accessible way so that you can understand the numbers that occupy your life. • Make sense of sports stats – discover who is the greatest scorer of all time • Learn to interpret scientific studies and how they&’re reported in the media so you&’re never misled again • Discover tips and tricks to make you a more successful gambler • Explore what role stats has to play in flat-earth conspiracy arguments • Read about misunderstood probabilities in the Sally Clarke and OJ Simpson trials With easy-to-follow explanations, tables, graphs, and real-life examples, this book helps you evaluate your options, calculate your chances of success, and make better decisions.
Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum
by Maresuke ShiraishiThe non-Gaussianity in the primordial density fluctuations is a key feature to clarify the early Universe and it has been probed with the Cosmic Microwave Background (CMB) bispectrum. In recent years, we have treated the novel-type CMB bispectra, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance. On the basis of our current works, this thesis provides the general formalism for the CMB bispectrum sourced by the non-Gaussianity in the scalar, vector and tensor-mode perturbations. Applying this formalism, we calculate the CMB bispectra from the two scalars and a graviton correlation and primordial magnetic fields, and then outline new constraints on these magnitudes. Furthermore, this formalism can be easily extended to the cases where the rotational or parity invariance is broken. We also compute the CMB bispectra from the scalar-mode non-Gaussianities with a preferred direction and the tensor-mode non-Gaussianities induced by the parity-violating Weyl cubic terms. Here, we show that these bispectra include unique signals, which any symmetry-invariant models can never produce.
Problem-Based Learning: A Didactic Strategy in the Teaching of System Simulation (Studies in Computational Intelligence #824)
by Lorenzo Cevallos-Torres Miguel Botto-TobarThis book describes and outlines the theoretical foundations of system simulation in teaching, and as a practical contribution to teaching-and-learning models. It presents various methodologies used in teaching, the goal being to solve real-life problems by creating simulation models and probability distributions that allow correlations to be drawn between a real model and a simulated model. Moreover, the book demonstrates the role of simulation in decision-making processes connected to teaching and learning.
The Problem of Catalan
by Yuri F. Bilu Yann Bugeaud Maurice MignotteIn 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda MihÄfilescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2. In this book we give a complete and (almost) self-contained exposition of MihÄfilescu's work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
The Problem of Coronal Heating: A Rosetta Stone for Electrodynamic Coupling in Cosmic Plasmas (Astrophysics and Space Science Library #470)
by Philip Judge James A. IonsonThis book reflects on 8 decades of research on one of the longest-standing unsolved problems in modern astrophysics: why does the Sun form a hot corona? The authors give a critical overview of the field and offer suggestions on how to bridge the chasm between what we can measure, and what we can calculate. They go back to basics to explain why the problem is difficult, where we have made progress and where we have not, to help the next generation of scientists devise novel techniques to crack such a long-lasting problem. A way forward is formulated centered around refutation, using Bayesian methods to propose and to try to reject hypotheses and models, and avoiding seduction by ``confirmation bias’’.This book is aimed at physicists, students and researchers interested in understanding, learning from and solving the coronal heating problem, in an era of new dedicated facilities such as the Parker Solar Probe and the Daniel K. Inouye Solar Telescope. Thebook will appeal to those interested in understanding research methods and how they are changing in the modern academic environment, particular in astrophysics and Earth sciences where remote sensing is essential.
Problem Posing and Problem Solving in Mathematics Education: International Research and Practice Trends
by Tin Lam Toh Manuel Santos-Trigo Puay Huat Chua Nor Azura Abdullah Dan ZhangThis book presents both theoretical and empirical contributions from a global perspective on problem solving and posing (PS/PP) and their application, in relation to the teaching and learning of mathematics in schools. The chapters are derived from selected presentations in the PS/PP Topical Study Group in ICME14. Although mathematical problem posing is a much younger field of inquiry in mathematics education, this topic has grown rapidly. The mathematics curriculum frameworks in many parts of the world have incorporated problem posing as an instructional focus, building on problem solving as its foundation. The juxtaposition of problem solving and problem posing in mathematics presented in this book addresses the needs of the mathematics education research and practice communities at the present day. In particular, this book aims to address the three key points: to present an overview of research and development regarding students’ mathematical problem solving and posing; to discuss new trends and developments in research and practice on these topics; and to provide insight into the future trends of mathematical problem solving and posing.
Problem Posing and Solving for Mathematically Gifted and Interested Students: Best Practices, Research and Enrichment
by Deniz Sarikaya Lukas Baumanns Karl Heuer Benjamin RottMathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights.
Problem Solving: A statistician's guide, Second edition (Chapman & Hall/CRC Texts in Statistical Science)
by Chris ChatfieldThis book illuminates the complex process of problem solving, including formulating the problem, collecting and analyzing data, and presenting the conclusions.
Problem-solving 3-4
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusingmore on enquiry and skills-based approaches. Students, even at the early levels ofschooling, are expected to develop a range of skills, including problem solving skills.Creative thinking, using information appropriately and problem solving are important for students in the school curriculum and in daily life. This book will help students learn how to apply mathematical skills in different contexts and explain how they got to their solutions.This book is easy for parents and teachers to use, and teaches multiple strategies forsolving problems, using challenging but supportive contexts. The approach is underpinnedby the Five E's approach to learning.The course will help student to:· Engage with problems meaningfully· Explore different options for approaching and solving problems· Explain how they are thinking· Elaborate on their working and processes and see connections between different areasof mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes
Problem-solving 5-6
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusingmore on enquiry and skills-based approaches. Students, even at the early levels ofschooling, are expected to develop a range of skills, including problem solving skills.Creative thinking, using information appropriately and problem solving are important for students in the school curriculum and in daily life. This book will help students learn how to apply mathematical skills in different contexts and explain how they got to their solutions.This book is easy for parents and teachers to use, and teaches multiple strategies forsolving problems, using challenging but supportive contexts. The approach is underpinnedby the Five E's approach to learning.The course will help student to:· Engage with problems meaningfully· Explore different options for approaching and solving problems· Explain their thought processes · Elaborate on their working and processes and see connections between different areasof mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes
Problem Solving and Data Analysis Using Minitab: A Clear and Easy Guide to Six Sigma Methodology
by Rehman M. KhanSix Sigma statistical methodology using Minitab Problem Solving and Data Analysis using Minitab presents example-based learning to aid readers in understanding how to use MINITAB 16 for statistical analysis and problem solving. Each example and exercise is broken down into the exact steps that must be followed in order to take the reader through key learning points and work through complex analyses. Exercises are featured at the end of each example so that the reader can be assured that they have understood the key learning points. Key features: Provides readers with a step by step guide to problem solving and statistical analysis using Minitab 16 which is also compatible with version 15. Includes fully worked examples with graphics showing menu selections and Minitab outputs. Uses example based learning that the reader can work through at their pace. Contains hundreds of screenshots to aid the reader, along with explanations of the statistics being performed and interpretation of results. Presents the core statistical techniques used by Six Sigma Black Belts. Contains examples, exercises and solutions throughout, and is supported by an accompanying website featuring the numerous example data sets. Making Six Sigma statistical methodology accessible to beginners, this book is aimed at numerical professionals, students or academics who wish to learn and apply statistical techniques for problem solving, process improvement or data analysis whilst keeping mathematical theory to a minimum.
Problem-Solving and Selected Topics in Euclidean Geometry
by Michael Th. Rassias Sotirios E. Louridas"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.
A Problem Solving Approach to Mathematics for Elementary School Teachers
by Rick Billstein Barbara Boschmans Shlomo Libeskind Johnny W. LottA Problem Solving Approach to Mathematics for Elementary School Teachers not only helps students learn the math - it provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. <p><p> Revised throughout to prepare students more effectively for their own classrooms, the 13th Edition gives instructors a variety of approaches to teaching, and encourages discussion and collaboration among students and with their instructors. The MyLab(TM) Math course for this revision is updated extensively with new resources and features.
A Problem Solving Approach To Mathematics For Elementary School Teachers
by Rick Billstein Shlomo Libeskind Johnny LottA Problem Solving Approach to Mathematics for Elementary School Teachers
A Problem Solving Approach to Mathematics for Elementary School Teachers
by Shlomo Libeskind Rick Billstein Johnny LottMore than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts--it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments.
Problem Solving in Mathematics Education
by Peter Liljedahl Manuel Santos-Trigo Uldarico Malaspina Regina BruderThis survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled. "
Problem Solving in Mathematics, Grades 3-6: Powerful Strategies to Deepen Understanding
by Alfred S. Posamentier Stephen KrulikWith sample problems and solutions, this book demonstrates how teachers can incorporate nine problem solving strategies into any mathematics curriculum to help students succeed.
Problem Solving in Mathematics Instruction and Teacher Professional Development (Research in Mathematics Education)
by Peter Liljedahl Patricio Felmer Boris KoichuRecent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto—secondly—the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students’ engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences, combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.
Problem Solving In Operation Management
by Patricia Esperanza Balderas-Cañas Gabriel de las Nieves Sánchez-GuerreroThis volume examines problem solving and applied systems aimed at improving performance and management of organizations. The book’s eight chapters are integrated into two parts: methodologies and techniques that discuss complex dynamic analysis of the organizations, participative processes for building trend scenarios, consultancy as a systemic intervention process, processes to promote innovative goals in organizations, and analytical processes and solid mathematical representation systems. The authors also include a model to urban parks location, an analytic model to urban services location, and a system to forecast demand with fussy sets.Describes methodologies to analyze processes in complex dynamic organizations, including as participative, interventional, innovative, and analytical approaches;Clarifies a strategies for providing structure to complex organizations and applying analytical methods to decision making;Illustrates problem holistic solving strategies;Explains how to approach several problems from a holistic point of view and how analyze the subjacent processes to make decisions.
Problem Solving in Primary Mathematics: Learning to Investigate!
by Christine Edwards-Leis Debbie RobinsonProblem Solving in Primary Mathematics is an essential text designed to support new and experienced teachers in guiding pupils through mathematical investigations and problem solving, offering a framework that children themselves can begin to adopt as they progress to greater metacognitive awareness. Underpinned by the latest international research and theory, it examines how individual pupils think and act differently and offers guidance on how to promote independence and autonomy in the classroom. It examines key topics such as: Preparing for mathematical learning Designing learning material Assessing and evaluating learning Identifying key points for intervention What to do when learning is stalled Critical numeracy for real-world problem solving Mental Model Theory and the Mental Model Mode Different approaches to problem solving and investigating Aimed at new and experienced educators, particularly those with a maths specialism, and illustrated with investigations and activities, Problem Solving in Primary Mathematics demonstrates how frameworks can be used in key mathematical areas and assists students in progressing towards more meaningful problem solving.
Problem-solving K-2
by Hyacinth Dorleon Karen Morrison Rodney JulienWe live in an increasingly technological and information-rich world. Education is focusing more on enquiry and skills-based approaches. Students, even at the early levels of schooling, are expected to develop a range of skills, including problem solving skills. Creative thinking and problem solving are not only important elements in the curriculum but they are also crucial in daily life. Students need to learn basic mathematical skills, but they also have to be able to apply these in unfamiliar contexts, communicate their thinking and explain how they got to their solutions. This book is easy for parents and teachers to use, and teaches multiple strategies for solving problems, using challenging but supportive contexts. The approach is underpinned by the Five E's approach to learning. The course will help student to: · Engage with problems meaningfully · Explore different options for approaching and solving problems· Explain how they are thinking· Elaborate on their working and processes and see connections between different areas of mathematics· Evaluate what worked and what didn't, learning from mistakes as well as successes.
Problem-Solving Methods in Combinatorics
by Pablo SoberónEvery year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.
Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12: A Resource for the Mathematics Teacher
by Alfred S. Posamentier Stephen KrulikThis updated edition presents ten strategies for solving a wide range of mathematics problems, plus new sample problems.
Problem Solving Through Recreational Mathematics
by Bonnie Averbach Orin CheinHistorically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics -- problems, puzzles and games -- to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers' appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions, and other helpful addenda include hints and solutions, plus answers to selected problems. An extensive appendix on probability is new to this Dover edition.
The Problem with Math Is English: A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
by Concepcion MolinaTeaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. <P><P>Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.