Presents essential ideas on critical phenomena developed over the last decade in simple, qualitative terms. This new edition maintains the simple structure of the first and puts new emphasis on pedagogical considerations. Thermostatistics is incorporated into the text without eclipsing macroscopic thermodynamics, and is integrated into the conceptual framework of physical theory.

    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.

    The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

    Theory has been provided in points between each chapter for clarifying relevant basic concepts. The book consist four parts algebra and trigonometry, fundamentals of analysis, geometry and vector algebra and the problems and questions set during oral examinations. Each chapter consist topic wise problems. Sample examples are provided after each text for understanding the topic well. The fourth part "oral examination problems and question" includes samples suggested by the higher schools for the help of students. Answers and hints are given at the end of the book for understanding the concept well. About the Book: Problems in Mathematics with Hints and Solutions Contents: Preface Part 1. Algebra, Trigonometry and Elementary Functions Problems on Integers. Criteria for Divisibility Real Number, Transformation of Algebraic Expressions Mathematical Induction. Elements of Combinatorics. BinomialTheorem Equations and Inequalities of the First and the SecondDegree Equations of Higher Degrees, Rational Inequalities Irrational Equations and Inequalities Systems of Equations and Inequalities The Domain of Definition and the Range of a Function Exponential and Logarithmic Equations and Inequalities Transformations of Trigonometric Expressions. InverseTrigonometric Functions Solutions of Trigonometric Equations, Inequalities and Systemsof Equations Progressions Solutions of Problems on Derivation of Equations Complex Numbers Part 2. Fundamentals of Mathematical Analysis Sequences and Their Limits. An Infinitely Decreasing GeometricProgression. Limits of Functions The Derivative. Investigating the Behaviors of Functions withthe Aid of the Derivative Graphs of Functions The Antiderivative. The Integral. The Area of a CurvilinearTrapezoid Part 3. Geometry and Vector Algebra Vector Algebra Plane Geometry. Problems on Proof Plane Geometry. Construction Problems Plane Geometry. C

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, -The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.- Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.In the paper, -On Computable Numbers, with an Application to the Entscheidungsproblem, - Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

    Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further."

    Laughlin transports us two centuries into the future, when we've ceased to use carbon from the ground--either because humans have banned carbon burning or because fuel has simply run out. Boldly, Laughlin predicts no earth-shattering transformations will have taken place. Six generations from now, there will still be soccer moms, shopping malls, and business trips. Firesides will still be snug and warm.How will we do it? Not by discovering a magic bullet to slay our energy problems, but through a slew of fascinating technologies, drawing on wind, water, and fire. Powering the Future is an objective yet optimistic tour through alternative fuel sources, set in a world where we've burned every last drop of petroleum and every last shovelful of coal.The Predictable: Fossil fuels will run out. The present flow of crude oil out of the ground equals in one day the average flow of the Mississippi River past New Orleans in thirteen minutes. If you add the energy equivalents of gas and coal, it's thirty-six minutes. At the present rate of consumption, we'll be out of fossil fuels in two centuries' time. We always choose the cheapest gas. From the nineteenth-century consolidation of the oil business to the California energy crisis of 2000-2001, the energy business has shown, time and again, how low prices dominate market share. Market forces--not green technology--will be the driver of energy innovation in the next 200 years. The laws of physics remain fixed. Energy will still be conserved, degrade entropically with use, and have to be disposed of as waste heat into outer space. How much energy a fuel can pack away in a given space is fixed by quantum mechanics--and if we want to keep flying jet planes, we will need carbon-based fuels. The Potential: Animal waste. If dried and burned, the world's agricultural manure would supply about one-third as much energy as all the coal we presently consume. Trash. The United States disposes of 88 million tons of carbon in its trash per year. While the incineration of waste trash is not enough to contribute meaningfully to the global demand for energy, it will constrain fuel prices by providing a cheap supply of carbon. Solar energy. The power used to light all the cities around the world is only one-millionth of the total power of sunlight pouring down on earth's daytime side. And the amount of hydropump storage required to store the world's daily electrical surge is equal to only eight times the volume of Lake Mead. PRAISE FOR ROBERT B. LAUGHLIN -Perhaps the most brilliant theoretical physicist since Richard Feynman---George Chapline, Lawrence Livermore National Laboratory -Powerful but controversial.--- Financial Times -[Laughlin's] company ... is inspirational.- --New Scientist

    

    Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge.Diaconis and Graham tell the stories--and reveal the best tricks--of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick--and much more.

    Shankar, a well-known physicist and contagiously enthusiastic educator, was among the first to offer a course through the innovative Open Yale Course program. His popular online video lectures on introductory physics have been viewed over a million times. In this concise and self-contained book based on his online Yale course, Shankar explains the fundamental concepts of physics from Galileo’s and Newton’s discoveries to the twentieth-century’s revolutionary ideas on relativity and quantum mechanics.   The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering, for motivated AP Physics students, and for general readers interested in advances in the sciences. Instructor resources--including problem sets and sample examinations--and more information about Professor Shankar's course are available at http://oyc.yale.edu/physics/phys-200.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    Johnson. It was the first book exclusively on the theory of NP-completeness and computational intractability. The book features an appendix providing a thorough compendium of NP-complete problems (which was updated in later printings of the book). The book is now outdated in some respects as it does not cover more recent development such as the PCP theorem. It is nevertheless still in print and is regarded as a classic: in a 2006 study, the CiteSeer search engine listed the book as the most cited reference in computer science literature.

    This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

    The addition of this book is a must for all upper-level Christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject, which cannot be taught from a distinctively Biblical perspective.