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

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincare conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.Poincare's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award.In telling the vibrant story of The Poincare Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.

    Peter Bernstein has written a comprehensive history of man's efforts to understand risk and probability, beginning with early gamblers in ancient Greece, continuing through the 17th-century French mathematicians Pascal and Fermat and up to modern chaos theory. Along the way he demonstrates that understanding risk underlies everything from game theory to bridge-building to winemaking.

    Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives—from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.Many of the greatest names in intellectual history—Pythagoras, Plato, Archimedes, Euclid— were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions—his famed Coxeter groups and Coxeter diagrams—have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

    It's about the broken, wrinkled, wiggly world - the uneven shapes of nature, unlike the idealized forms of Euclidean geometry. We see fractals everywhere; indeed we are fractal! Fractal Geometry is an extension of classical geometry. Using computers, it can make precise models of physical structures - from ferns to galaxies. Fractal geometry is a new language. Once you speak it, you can describe the shape of cloud as precisely as an architect can describe a house.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass.In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener.And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.