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

    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

    Streisand. Dylan. Pavarotti. McCartney. Sting. Madonna. What do these musicians have in common besides their super-stardom? They have all worked with legendary music producer Phil Ramone. For almost five decades, Phil Ramone has been a force in the music industry. He has produced records and collaborated with almost every major talent in the business. There is a craft to making records, and Phil has spent his life mastering it. For the first time ever, he shares the secrets of his trade.Making Records is a fascinating look "behind the glass" of a recording studio. From Phil's exhilarating early days recording jazz and commercial jingles at A&R, to his first studio, and eventual legendary producer status, Phil allows you to sit in on the sessions that created some of the most memorable music of the 20th century -- including Frank Sinatra's Duets album, Bob Dylan's Blood on the Tracks, Ray Charles's Genius Loves Company and Paul Simon's Still Crazy After All These Years. In addition to being a ringside seat for contemporary popular music history, Making Records is an unprecedented tutorial on the magic behind what music producers and engineers do. In these pages, Phil offers a rare peek inside the way music is made . . . illuminating the creative thought processes behind some of the most influential sessions in music history. This is a book about the art that is making records -- the way it began, the way it is now, and everything in between.

    It used to be that to diagnose an illness, interpret legal documents, analyze foreign policy, or write a newspaper article you needed a human being with specific skills—and maybe an advanced degree or two. These days, high-level tasks are increasingly being handled by algorithms that can do precise work not only with speed but also with nuance. These “bots” started with human programming and logic, but now their reach extends beyond what their creators ever expected. In this fascinating, frightening book, Christopher Steiner tells the story of how algorithms took over—and shows why the “bot revolution” is about to spill into every aspect of our lives, often silently, without our knowledge. The May 2010 “Flash Crash” exposed Wall Street’s reliance on trading bots to the tune of a 998-point market drop and $1 trillion in vanished market value. But that was just the beginning. In Automate This, we meet bots that are driving cars, penning haiku, and writing music mistaken for Bach’s. They listen in on our customer service calls and figure out what Iran would do in the event of a nuclear standoff. There are algorithms that can pick out the most cohesive crew of astronauts for a space mission or identify the next Jeremy Lin. Some can even ingest statistics from baseball games and spit out pitch-perfect sports journalism indistinguishable from that produced by humans. The interaction of man and machine can make our lives easier. But what will the world look like when algorithms control our hospitals, our roads, our culture, and our national security? What hap­pens to businesses when we automate judgment and eliminate human instinct? And what role will be left for doctors, lawyers, writers, truck drivers, and many others?  Who knows—maybe there’s a bot learning to do your job this minute.

    It's a thinking game. It's also a shifting game. Nowhere is this more evident than in the statistical revolution which has swept through the pastime in recent years, bringing metrics like WAR, OPS, and BABIP into front offices and living rooms alike. So what's on the horizon for a game that is constantly evolving? Positioned at the crossroads of sabermetrics and cognitive science, The Shift alters the trajectory of both traditional and analytics-based baseball thought. With a background in clinical psychology as well as experience in major league front offices, Baseball Prospectus' Russell Carleton illuminates advanced statistics and challenges cultural assumptions, demonstrating along the way that data and logic need not be at odds with the human elements of baseball—in fact, they're inextricably intertwined. Covering topics ranging from infield shifts to paradigm shifts, Carleton writes with verve, honesty, and an engaging style, inviting all those who love the game to examine it deeply and maybe a little differently. Data becomes digestible; intangibles are rendered not only accessible, but quantifiable. Casual fans and statheads alike will not want to miss this compelling meditation on what makes baseball tick.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

    He urges more frequent performance and more sensitive hearing of the music of new composers. He discusses sound media, new and old, and looks toward a musical future in which the timbres and intensities developed by the electronic engineer may find their musical shape and meaning. He considers the twentieth-century revolt against classical form and tonality, and the recent disturbing political interference with the form and content of music. He analyzes American and contemporary European music and the flowering of specifically Western imagination in Villa-Lobos and Charles Ives. The final chapter is an account, partially autobiographical, of the composer who seeks to find, in an industrial society like that of the United States, justification for the life of art in the life about him. Mr. Copeland, whose spectacular success in arriving at a musical vernacular has brought him a wide audience, will acquire as many readers as he has listeners with this imaginatively written book.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    Maths is about patterns, and our universe is extraordinarily patterned. With enthusiasm and wonder, Eddie is here to help us discover these patterns.With engaging clarity and entertaining anecdotes, Eddie demonstrates the intricacy of maths in all the things we love - from music in our iPods to our credit cards. Filled with humour and heart, this book will fascinate, entertain and illuminate the maths that surrounds us.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    This comprehensive boxed set assembles Books 1-4 of this classic method. The books feature colorful, amusing characters and illustrations, and the four accompanying CDs contain backing tracks to make learning and practicing even more fun. This unique package features a built-in storage carton!

    A one-of-a-kind book encompassing a wide scope of jazz topics, for beginners and pros of any instrument. A three-pronged approach was envisioned with the creation of this comprehensive resource: as an encyclopedia for ready reference, as a thorough methodology for the student, and as a workbook for the classroom, complete with ample exercises and conceptual discussion. Includes the basics of intervals, jazz harmony, scales and modes, ii-V-I cadences. For harmony, it covers: harmonic analysis, piano voicings and voice leading; modulations and modal interchange, and reharmonization. For performance, it takes players through: jazz piano comping, jazz tune forms, arranging techniques, improvisation, traditional jazz fundamentals, practice techniques, and much more! Customer reviews on amazon.com for Jazzology average a glowing 5 stars! Here is a typical reader comment: The book's approach is so intuitive, it almost leads you by the hand into the world of jazz. Certainly jazz is freedom of expression, but you have to know what you're doing and this book is the tool for that ... (it) should be standard in every high school with a jazz program and every college lab band.