These open-ended task cards encourage older students to think and work like scientists. Task Cards measure 4 by 6 inches. The limited size of each card leaves less room to tell students exactly what to do, and therefore more freedom for students to follow their own experimental strategies. Thorough, thoughtful teaching notes accompany each card, and the task cards are also reprinted 2 to a page at the back of each book for easy photocopying.
Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
This series is for maths teachers who want to develop their maths teaching skills. This book is for teachers and educators who want to develop their maths teaching skills where English is the language of instruction. It has been written by the international group of educators based at AIMSSEC, The African Institute for Mathematical Sciences Schools Enrichment Centre. The book provides practical classroom activities underpinned by sound pedagogy and recent research findings. The activities are designed for teachers working alone or in 'self-help' teachers' workshops. They are designed to develop mathematical thinking and offer immediate practical tools to help deliver this approach.
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
This book addresses an apparent paradox in the psychology of thinking. On the one hand, human beings are a highly successful species. On the other, intelligent adults are known to exhibit numerous errors and biases in laboratory studies of reasoning and decision making. There has been much debate among both philosophers and psychologists about the implications of such studies for human rationality. The authors argue that this debate is marked by a confusion between two distinct notions: (a) personal rationality (rationality1 Evans and Over argue that people have a high degree of rationality1 but only a limited capacity for rationality2. The book re-interprets the psychological literature on reasoning and decision making, showing that many normative errors, by abstract standards, reflect the operation of processes that would normally help to achieve ordinary goals. Topics discussed include relevance effects in reasoning and decision making, the influence of prior beliefs on thinking, and the argument that apparently non-logical reasoning can reflect efficient decision making. The authors also discuss the problem of deductive competence - whether people have it, and what mechanism can account for it. As the book progresses, increasing emphasis is given to the authors' dual process theory of thinking, in which a distinction between tacit and explicit cognitive systems is developed. It is argued that much of human capacity for rationality1 is invested in tacit cognitive processes, which reflect both innate mechanisms and biologically constrained learning. However, the authors go on to argue that human beings also possess an explicit thinking system, which underlies their unique - if limited - capacity to be rational.
An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions.
A comprehensive introduction to statistics that teaches the fundamentals with real-life scenarios, and covers histograms, quartiles, probability, Bayes' theorem, predictions, approximations, random samples, and related topics.
