This book explains how the test works, what the examiner wants to hear, and gives you strategies to organise your answers rapidly and effectively. It has many model answers from candidates speaking at Band 9 level, so that you can see what is possible. It has activities for you to practise our speaking strategies and compare to the Band 9 examples, including 2 complete model speaking tests for you to use. Even if your English is not perfect, you can transform your IELTS Band score by using the methods in this book. ABOUT THE AUTHORS: Cambridge IELTS Consultants are a team of IELTS trainers and past examiners based in Cambridge, United Kingdom. They have many years experience of preparing students for IELTS at University level, assessing the speaking tests and developing course books to guide candidates through the Cambridge IELTS process. They really are the experts!

    Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM

    It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the students existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research-based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

    The Americans were outsiders to the sport, the underdogs of the event, a 500-to-1 long shot. But they were also proud and loyal men -- to one another, to their communities, and certainly to their country. Facing almost no time to prepare, opponents with superior training, and skepticism from the rest of the world, this ragtag group of unknowns was inspired to a stunning victory over England and one of the most thrilling upsets in the history of sports.Written by critically acclaimed author Geoffrey Douglas, and now a film directed by David Anspaugh (Hoosiers), The Game of Their Lives takes us back to a time before million-dollar contracts and commercial endorsements, and introduces us to the athletes -- the Americans -- who showed the world just how far a long shot could really go.

    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.

    If you want to leverage OpenGL 2.1's major improvements, you really need the Fourth Edition. It's a comprehensive tutorial, systematic API reference, and massive code library, all in one. You'll start with the fundamental techniques every graphics programmer needs: transformations, lighting, texture mapping, and so forth. Then, building on those basics, you'll move towards newer capabilities, from advanced buffers to vertex shaders. Of course, OpenGL's cross-platform availability remains one of its most compelling features. This book's extensive multiplatform coverage has been thoroughly rewritten, and now addresses everything from Windows Vista to OpenGL ES for handhelds. This is stuff you absolutely want the latest edition for. A small but telling point: This book's recently been invited into Addison-Wesley's OpenGL Series, making it an "official" OpenGL book -- and making a powerful statement about its credibility. Bill Camarda, from the August 2007 href="http://www.barnesandnoble.com/newslet... Only

    In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    When Eddie's former caddie, "Fat Albert" Auberlain (a cross between Tiger Woods and John Daly), loses his PGA Tour card, his endorsements, and his composure after posting a twelve on a par three at the Fruit-of-the-Loom Waste Management Open, Eddie finds the sad sack on his doorstep. Fat Albert, in debt up to his eyeballs and with several needy relatives to feed, had barely been eking out a living on Tour as it was, and the pressure was threatening to make him implode altogether. Eddie takes pity on his protege but isn't quite sure what he can do, when along comes nuclear physicist Norman Standish with the most revolutionary advance in golf equipment since the double niblick-a golf ball they call Scratch. If Standish's claims are true, Eddie could make the killing of his strange and wonderful life and just possibly change the game forever. With McAllister's patented golf hustling hijinks, roller-coaster plotting, and laugh-out-loud skewering of pro sports hypocrisy, Eddie's die-hard fans and golf fiction aficionados will laugh all the way to the putting green. As Eddie himself puts it in The Foursome, "Why do you think they call the devil "Scratch"?"

    The Fireproof Your Marriage study integrates video clips from the movie FIREPROOF, along with key Scriptures, thought-provoking questions and devotionals. The Couple's Kit includes a six-session DVD and two Participant's guides. Also makes a great wedding or anniversary gift! Fireproof Your Marriage includes these six sessions: 1.) He Said/She Said: appreciating the God-designed differences between men and women. 2.) He First Loved Us: God's love for you and how it enables you to love others.3.) Love for a Lifetime: marriage as a lifelong covenant. 4.) Breaking Free: freeing yourself from temptations that can destroy a marriage. 5.) Forgiveness: offering and receiving forgiveness. 6.) A Better Way of Loving: unconditional love.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    This text is a lucid presentation of the principles of working of all types of sensors and transducers which form the prime components of the instrumentalisation systems.

    The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.