It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Reflecting the need for even minor programming in today's model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.Web ResourceThe book is accompanied by an R package (rethinking) that is available on the author's website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

    Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    Theoretical, yet applied. Statistics for Business and Economics, Eleventh Edition, gives you the best of both worlds. Using a rich array of applications from a variety of industries, McClave/Sincich/Benson clearly demonstrates how to use statistics effectively in a business environment.The book focuses on developing statistical thinking so the reader can better assess the credibility and value of inferences made from data. As consumers and future producers of statistical inferences, readers are introduced to a wide variety of data collection and analysis techniques to help them evaluate data and make informed business decisions. As with previous editions, this revision offers an abundance of applications with many new and updated exercises that draw on real business situations and recent economic events. The authors assume a background of basic algebra.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    This is the only guide that includes 5 previously administered, full-length ACT tests written by the actual test maker (including 2 NEW practice tests). Also included is ACT content and procedures you'll follow when actually taking the test, along with in-depth review of the optional Writing Test and how it is scored; examples of all the question types; and suggestions on how you might approach the questions. The supplemental CD features a complete electronic copy of Peterson's Cool Colleges 101 and additional online college planning resources from Peterson's.The only guide that includes 5 previously administered, full-length ACT tests written by the actual test maker (including 2 NEW practice tests)ACT content and procedures you'll follow when actually taking the testValuable information about tuition payment plansAll the question types you can expect to find on the ACTSuggestions on how you might approach the questions and Peterson's tried-and-true test-taking strategies and tips

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    It also covers he nature of policy analysis and its practice, and gives students practical ways to think about public problems.

    Readerswill find information on frequency distributions; mean, median, and mode; range, variance, and standard deviation;probability; and more.-Emphasizes Microsoft Excel for number-crunching and computationsDownload a sample chapter.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    The book walks a teacher, either novice or veteran, through structuring and organizing a classroom for success that can be applied at any time of the year at any grade level, pre-K through college.The book is used in thousands of school districts, in over 116 countries, and in over 2,027 college classrooms. Its practical, yet inspiring. But most important, it works The new 4th edition includes updated research, photos, and more examples of "how-to" along with an implementation DVD, "Using The First Days of School" featuring Chelonnda Seroyer.This is the most requested book for what works in the classroom for teacher and student success.

    It's never too late."-Penny KittlePenny Kittle wants us to face the hard truths every English teacher fears: too many kids don't read the assigned texts, and some even manage to slip by without having ever read a single book by the time they graduate. As middle and high school reading declines, college professors lament students' inability to comprehend and analyze complex texts, while the rest of us wonder: what do we lose as a society when so many of our high school graduates have no interest in reading anything?In Book Love Penny takes student apathy head on, first by recognizing why students don't read and then showing us that when we give kids books that are right for them, along with time to read and regular response to their thinking, we can create a pathway to satisfying reading that leads to more challenging literature and ultimately, a love of reading. With a clear eye on the reality of today's classrooms, Penny provides practical strategies and advice on:increasing volume, capacity, and complexity over time creating a balance of independent reading, text study, and novel study helping students deepen their thinking through writing about reading building a classroom library with themes that matter to 21st century kids. Book Love is a call to arms for putting every single kid, no exceptions allowed, on a personal reading journey. But much more than that, it's a powerful reminder of why we became English teachers in the first place: our passion for books. Books matter. Stories heal. The right book in the hands of a kid can change a life forever. We can't wait for anyone else to teach our students a love of books-it's up to us and the time is now. If not you, who? For information about the Book Love Foundation, which provides classroom libraries to deserving teachers and schools, visit booklovefoundation.org.

    But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms. The book's examples are written in Processing, an open-source language and development environment built on top of the Java programming language. On the book's website (http://www.natureofcode.com), the examples run in the browser via Processing's JavaScript mode.