Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    Hinduism does not lend itself easily to a strictly chronological account: many of its central texts cannot be reliably dated even within a century; its central tenets—karma, dharma, to name just two—arise at particular moments in Indian history and differ in each era, between genders, and caste to caste; and what is shared among Hindus is overwhelmingly outnumbered by the things that are unique to one group or another. Yet the greatness of Hinduism—its vitality, its earthiness, its vividness—lies precisely in many of those idiosyncratic qualities that continue to inspire debate today. Wendy Doniger is one of the foremost scholars of Hinduism in the world. With her inimitable insight and expertise Doniger illuminates those moments within the tradition that resist forces that would standardize or establish a canon. Without reversing or misrepresenting the historical hierarchies, she reveals how Sanskrit and vernacular sources are rich in knowledge of and compassion toward women and lower castes; how they debate tensions surrounding religion, violence, and tolerance; and how animals are the key to important shifts in attitudes toward different social classes.The Hindus brings a fascinating multiplicity of actors and stories to the stage to show how brilliant and creative thinkers—many of them far removed from Brahmin authors of Sanskrit texts—have kept Hinduism alive in ways that other scholars have not fully explored. In this unique and authoritative account, debates about Hindu traditions become platforms from which to consider the ironies, and overlooked epiphanies, of history.

    It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

    Over sixty men were murdered, including the leader of the Winter Hill Gang, James "Buddy" McLean. The leadership of one of the most influential non-Italian crime organizations in the United States was inherited by his childhood friend, Howard T. "Howie" Winter. In CITIZEN SOMERVILLE the events during his tenure offer a true picture of an era in Boston's pre-Whitey Bulger history when the streets were protected by a close-knit group of Irish-Italian "businessmen." The son of one of Winter's closest friends, BOBBY MARTINI has laid his own history bare to depict a life of survival in the rough streets of Somerville, stopping just short of entering the Mob life. The death of Martini's two brothers as well as the murders and suicides of scores of others reveal the darker personal side of a small New England town. CITIZEN SOMERVILLE slices a layer deeper than a crime memoir by allowing a usually ostracized faction to speak - the women. After decades of silence, three strong and very different females lift the Mob veil and voice their own struggle to survive in Somerville's criminal circle. Often painfully poignant and yet frequently hilarious, CITIZEN SOMERVILLE is a microscopic view of a generation struggling to walk the moral tightrope between societal decency and the loyalty of criminality.

    In this title, the treatment is made easy-to-follow by giving step-by-step derivations, explanations and by avoiding advanced mathematics unfamiliar to students. It covers: math and physics thorough review sections; and worked examples, followed by a practice exercise.

    To reach this unique audience, Whitlock and Schluter motivate learning with interesting biological and medical examples; they emphasize intuitive understanding; and they focus on real data. The book covers basic topics in introductory statistics, including graphs, confidence intervals, hypothesis testing, comparison of means, regression, and designing experiments. It also introduces the principles behind such modern topics as likelihood, linear models, meta-analysis and computer-intensive methods. Instructors and students consistently praise the book's clear and engaging writing, strong visualization techniques, and its variety of fascinating and relevant biological examples.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Psychology of Learning for Instruction, Third Edition, focuses on the applications and implications of the learning theories. Using excellent examples ranging from primary school instruction to corporate training, this text combines the latest thinking and research to give readers the opportunity to explore the individual theories as viewed by the experts. Readers are encouraged to apply "reflective practice," which is designed to foster a critical and reflective mode of thinking when considering any particular approach to learning and instruction. Provides readers with the practical knowledge needed to apply learning theories to instruction. KEY TOPICS: This text addresses learning as it relates to behavior, cognition, development, biology, motivation and instruction. MARKET: Pre-service and in-service teachers, and educational psychologists.

    The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.