In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa. A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.

    From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.

    From carrying a baby, delivering it, feeding it and raising it, Bec has experienced almost everything motherhood can throw at you and she wants to share the secrets and stories that she has learned along the way. Not to mention all those things about pregnancy, birth and motherhood that often come as a complete surprise. Join Bec and her dream team of experts (an obstetrician, a midwife, an ultrasound specialist, a women's health physio and a paediatric sleep specialist) as they take you month by month through your pregnancy. They will share their insider advice on the best ways to eat for two (or three!), stay in shape and get you and your baby sleeping well. This gorgeous, comprehensive handbook contains a wealth of honest, practical and sometimes hilarious advice to prepare you and your baby for life after birth.

    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."

    Julia Kelly is an Irish novelist; her partner was a successful artist whose increasingly disturbing behaviour is described quietly, in a series of dreadful epiphanies. A heartbreaking account of a destructive and distressing disease that affects 850,000 people in the UK alone, with numbers set to rise to over 1 million by 2025.

    Within that small, praying community known as Ffald-y-Brenin, the deaf hear, the blind see, and the broken receive healing. Roy Godwin reveals how God has given believers the authority to bless others. As the executive director of the Wales retreat center, he shares how this ministry began, stories of miraculous healings, and ways you can usher God’s presence into your community. It begins when we stop chasing blessings and become God’s conduit for blessing others.

    

    He broke their dreams. But they came back stronger.‘Terrie and Paul are two of the bravest people I have ever met. I have only shared the briefest glimpse into the true horrors this brother and sister have endured, but I rarely come across cases this bad. After the unspeakable abuse and shocking betrayals, two incredible human beings came through – to inspire us all.’Sara Payne OBE, co-founder of Phoenix SurvivorsTerrie and Paul’s step-father had been living with them for six months when the abuse and grooming began. What started as innocent conversations and goodnight kisses quickly developed into something far darker and depraved.Everyday Terrie was assaulted and abused; her rapes were photographed, filmed and shared. Paul was regularly taunted and mercilessly beaten. But despite the bruises and the scars, and the desperate pleas for help, no one saw their pain.But through it all they stuck together, battling for their childhoods for over a decade and masterminding creative ways to outwit their stepfather and buy themselves fleeting moments of joy.In March 2013, thirty years on, Terrie and Paul made the brave decision to give up their right to anonymity to tell of the years of abuse they endured at the hands of their recently convicted step-father and raise awareness for the ongoing battle for justice for victims of child abuse. A powerful testament of what can be achieved through courage and love, this is their inspiring story.

    Television shows and newspaper articles often gloss over the shocking details because it may be too grisly for the average viewer or reader.When researching these stories, I commonly use actual police reports, court documents, and first-hand descriptions. Some of the details can be disconcerting. I do my best to not leave out any of the details in my books, no matter how depraved they may be. My intent is not to shock, but to show precisely how twisted the mind of a killer can be.That being said, if you are overly squeamish, this may not be the book for you. If you’re okay with it, then let’s proceed.Volume 5 features: longer stories, more photos, a bonus chapter, and an online appendix with additional photos, videos, and documents. Volume Five features twelve of the most incomprehensible stories of the last fifty years.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    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.

    This fake book is a cornerstone for many musicians' libraries. With over 1200 songs in all styles of music, this fifth edition has been updated to include even more great songs and recent hits. From jazz standards to Broadway blockbusters and country classics to pop chart-toppers, this book has the songs you're looking for all in one convenient collection. It is comb-bound with locked tabs to ensure long-lasting durability. Songs include: All the Things You Are * Blue Skies * Body and Soul * Come Fly With Me * Endless Love * The Girl from Ipanema (Garota de Ipanema) * The House of the Rising Sun * Love and Marriage * Memory * Moon River * Mustang Sally * Night Moves * Over the Rainbow * Piano Man * Satin Doll * Shout * Smooth * Start Me Up * Strawberry Fields Forever * Tears in Heaven * Unforgettable * hundreds more!