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

    Whether you are a patient struggling with miscarriages or a medical provider caring for patients with recurrent pregnancy loss, you will learn something from this resource. Dr. Shahine explains not only a typical Western medicine approach to evaluation and treatment for miscarriage but also includes Eastern approaches to care, lifestyle factors that will decrease your risk of miscarriage, and the emotional impact of recurrent pregnancy loss. You will finish this book feeling more empowered to be an advocate for your care and more hopeful than ever to continue towards your family goals. “I have one word to describe this fabulous book: FINALLY. Women with recurrent pregnancy loss have been needing this book for years.” – Dr. Alice Domar, associate professor of obstetrics, gynecology, and reproductive biology at Harvard Medical School and author of Conquering Infertility and Finding Calm for the Expectant Mom

    Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system.Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

    These kids often have violent outbursts, steal, engage in outlandish lying, play with feces, and hoard food. They are broken children who too often break even the most loving of caregivers. Many parents of these children feel utterly isolated as family, friends, and professionals minimize their struggles. Reactive Attachment Disorder (RAD) - The Essential Guide for Parents is written by a parent who is in the trenches with you. Keri has lived the journey of raising a son with RAD and has navigated the mental health system for over a decade. This is the resource you’ve been waiting for – you won’t find platitudes or false hopes. What you will find is essential information, practical suggestions, and resource recommendations to provide a way forward. If you desperately need help navigating the difficult RAD journey with your child, this book is for you.

     This graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, he crosses paths with thinkers like Gottlob Frege, David Hilbert & Kurt Gödel, & finds a passionate student in Ludwig Wittgenstein. But his most ambitious goal—to establish unshakable logical foundations of mathematics—continues to loom before him. Thru love & hate, peace & war, he persists in the mission threatening to claim both his career & happiness, finally driving him to the brink of insanity. This story is at the same time a historical novel & an accessible explication of some of the biggest ideas of mathematics & modern philosophy. With rich characterizations & atmospheric artwork, it spins the pursuit of such ideas into a satisfying tale. Probing, layered, the book throws light on Russell’s inner struggles while setting them in the context of the timeless questions he tried to answer. At its heart, Logicomix is a story about the conflict between ideal rationality & the flawed fabric of reality.

    Investigations into the causes of aircraft accidents have for decades focused on what happened and who did it - very rarely 'Why'? It is the question 'Why' that David Beaty has addressed here, fighting the misnomer of 'pilot error' and propounding that the cause should be sought deeper inside human beings who make apparently simple human errors.

    What hope do we have against superintelligent machines? But we aren't really on the path to developing intelligent machines. In fact, we don't even know where that path might be.A tech entrepreneur and pioneering research scientist working at the forefront of natural language processing, Erik Larson takes us on a tour of the landscape of AI to show how far we are from superintelligence, and what it would take to get there. Ever since Alan Turing, AI enthusiasts have equated artificial intelligence with human intelligence. This is a profound mistake. AI works on inductive reasoning, crunching data sets to predict outcomes. But humans don't correlate data sets: we make conjectures informed by context and experience. Human intelligence is a web of best guesses, given what we know about the world. We haven't a clue how to program this kind of intuitive reasoning, known as abduction. Yet it is the heart of common sense. That's why Alexa can't understand what you are asking, and why AI can only take us so far.Larson argues that AI hype is both bad science and bad for science. A culture of invention thrives on exploring unknowns, not overselling existing methods. Inductive AI will continue to improve at narrow tasks, but if we want to make real progress, we will need to start by more fully appreciating the only true intelligence we know--our own.

    First published in 1986, this mind-boggling and entertaining dictionary, arranged in order of magnitude, exposes the fascinating facts about certain numbers and number sequences - very large primes, amicable numbers and golden squares to give but a few examples.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    The absence of a book, explaining the techniques in a simple language, has been felt acutely for a long time. This book has been written using a step-by-step approach, and attempts to fill the existing void. It includes several solved problems in addition to 1000 practice problems with answers. It also includes a special chapter which shows the application of the techniques to problems set in competitive exams like CAT, CET etc.People from all walks of life including school and college students, teachers, parents and also those from non-mathematical areas of study will discover the joys of solving mathematical problems using the wonderful set of techniques called Vedic Maths.

    Perform this genius seemingly-mathematical feat on any napkin, any receipt, or even on your friend's arm.You can learn the famous Magic Square, and you can learn it in under 10 minutes.You will have a magician's Grand Finale, in your hands at any moment. This gets audible gasps, and you can wow people with this for the rest of your life...**************************THE PERFORMANCE:**************************Your friend will name a random number. You then speedily write 16 different numbers into a 4x4 grid. With a smug flourish, you then reveal that all combinations and directions within the grid add up to their chosen number. It is simply mind-blowing.Effortlessly perform a trick that it seems only a computer could perform, and learn how in 10 minutes from right now.

    This is the amazing story of how the "map problem" was solved.The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm.Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.

    As a professional C++ developer and former Harvard teaching fellow, I know what you need to know to be a great C++ programmer, and I know how to teach it, one step at a time. I know where people struggle, and why, and how to make it clear. I cover every step of the programming process, including:Getting the tools you need to program and how to use them*Basic language feature like variables, loops and functions*How to go from an idea to code*A clear, understandable explanation of pointers*Strings, file IO, arrays, references*Classes and advanced class design*C++-specific programming patterns*Object oriented programming*Data structures and the standard template library (STL)Key concepts are reinforced with quizzes and over 75 practice problems.

    The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.