Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Research has shown that the extraordinary sensory powers of our animal friends can help us better understand the same powers that lie dormant within us. From the harlequin mantis shrimp with its ability to see a vast range of colors, to the bloodhound and its hundreds of millions of scent receptors; from the orb-weaving spider whose eyes recognize not only space but time, to the cheetah whose ears are responsible for its perfect agility, these astonishing animals hold the key to better understanding how we make sense of the world around us. “An appealingly written, enlightening, and sometimes eerie journey into the extraordinary possibilities for the human senses” (Kirkus Reviews, starred), Sentient will change the way you look at humanity.

    Willingham on educational neuroscience? Written for busy teachers, trainers, managers and students, this dip-in dip-out guide makes theories of learning accessible and practical. It explores over 100 classic and contemporary learning theorists in an easy-to-use, bite-sized format with clear relevant illustrations on how each theory will benefit your teaching and learning.Each model or theory is explained in less than 350 words, many with accompanying diagrams, and the 'how to use it' sections, in less than 500 words. Every entry includes:Do it steps in order to apply the theory or modelReflection points & challenges to develop your understanding of how to apply itAnalogies & metaphors from which understanding and meaning can be drawnTips for the classroomFurther reading if you want to explore a theory in greater depth. More titles by Bob Bates: Educational Leadership Simplified A Quick Guide to Special Needs and Disabilities

    How did the replication bomb we call ”life” begin and where in the world, or rather, in the universe, is it heading? Writing with characteristic wit and an ability to clarify complex phenomena (the New York Times described his style as ”the sort of science writing that makes the reader feel like a genius”), Richard Dawkins confronts this ancient mystery.

    David Peat reveal sevenenlightening lessons for embracing the chaos of daily life.Be Creative:engage with chaos to find imaginative new solutions and live more dynamicallyUse Butterfly Power:let chaos grow local efforts into global resultsGo With the Flow:use chaos to work collectively with othersExplore What's Between:discover life's rich subtleties and avoid the traps of stereotypesSee the Art of the World:appreciate the beauty of life's chaosLive Within Time:utilize time's hidden depthsRejoin the Whole:realize our fractal connectedness to each other and the worldLife is impossible to control--instead of fighting this truth, Seven Life Lessons of Chaos shows you how to accept, celebrate, and use it to live life to its fullest.

    Regarded by many as the most gifted and influential author and journalist in America today, Gladwell's rare ability to connect with audiences of such varied interests has ensured that each title become a phenomenal bestseller with more than ten million copies in print combined. Now, Gladwell's landmark investigations into the world around us are collected together for the first time. Beautifully repackaged and redesigned, including for the first time illustrations throughout each book, MALCOLM GLADWELL: COLLECTED is a perfect treasury of prose and provocation for Gladwell fans old and new.

    It explores the three worlds which together shape a student’s learning – the public world of the teacher, the highly influential world of peers, and the student’s own private world and experiences. What becomes clear is that just because a teacher is teaching, does not mean students are learning.Using a unique method of data collection through meticulous recording -audio, video, observations, interviews, pre and posttests - and the collation and analysis of what occurred inside and outside the classroom, Graham Nuthall has definitively documented what is involved for most students to learn and retain a concept. In the author’s lifetime the significance of his discoveries and the rare mix of quantitative and qualitative methods were widely recognised and continue to be one of the foundation stones of evidence-based quality education.This book is the culmination of Professor Graham Nuthall’s forty years of research on learning and teaching. It is written with classroom teachers and teachers of teachers in mind. But realising time was short and that his life’s work was laid out in learned papers for fellow researchers, he wrote this brief but powerful book for a much wider audience as well: for all those who seek a better understanding of classroom learning.After completing his PhD at the University of Illinois, Graham Nuthall returned to take up academic positions at the University of Canterbury New Zealand. Throughout his long and distinguished career he continued to work closely with his academic colleagues in the USA and other countriesHe served on the editorial boards of international journals including Journal of Education for Teaching, Social Psychology of Education, Journal of Classroom Interaction and was Joint Editor of Teaching and Teacher Education: an International Journal of Research and Studies. His work has been translated into several languages and he was a visiting fellow at Stanford, London, Illinois and other universities. The recipient of many awards including The Royal Society of New Zealand’s Science and Technology Medal, The McKenzie Award for Excellence in Research in Education, Member of the New Zealand Order of Merit, his students and those he worked with remember him as warm, empathetic, and inspiring."Teachers who care about students and learning will be fascinated by the student voices that speak on the pages of this book, and what those voices reveal about learning in classroom settings, The Hidden Lives of Learners is a generous gift from Graham Nuthall to teachers everywhere."- Greta Morine-Dershimer

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    But where should you start? Americans are slowly becoming ill from impaired glucose metabolism that manifests itself as a debilitating illness or chronic condition. You may try to manage one problem after another– diuretics to treat blood pressure, statins to lower cholesterol, metformin and insulin to treat diabetes--without fully realizing that the root of these issues is insulin resistance which revs up inflammation, damages the immune system, and disrupts the whole hormonal/chemical system in the body.It's time to feel better and get healthy by following a simple step-by-step plan to a healthy lifestyle. Rob Thompson, MD and Dana Carpender create the ultimate dream team in your journey to wellness.The Insulin Resistance Solution offers a step-by-step plan and 75 recipes for reversing even the most stubborn insulin resistance.The Program:- Reduce Your Body's Demand for Insulin: This is the stumbling block of many other plans/doctor recommendations. Even "healthy" and "moderate" carb intake can continue to fuel insulin resistance.- Fat is Not the Enemy: Stop Worrying about Fat, Cholesterol, and Salt- Exercise--the RIGHT way:- Use Carb Blockers: Eat and Supplement to Slow Glucose Digestion and Lower Insulin Levels- Safe, Effective Medication

    Big and informative, "The New York Times Book of Mathematics" gathers more than 110 articles written from 1892 to 2010 that cover statistics, coincidences, chaos theory, famous problems, cryptography, computers, and many other topics. Edited by Pulitzer Prize finalist and senior "Times" writer Gina Kolata, and featuring renowned contributors such as James Gleick, William L. Laurence, Malcolm W. Browne, George Johnson, and John Markoff, it's a must-have for any math and science enthusiast!

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    The Complete Kobold Guide to Game Design offers 240 pages of in-depth essays on what makes RPGs tick. Get time-tested advice from the top designers in the industry. This compilation includes all three volumes of the Kobold Guide to Game Design series—now with all-new material by Wolfgang Baur, Mike Stackpole, and others! From core rules and magic systems to fantasy adventures, monster design, playtesting, and much more, these 40 essays cover every aspect of RPG design in clear, accessible language, to show you what it takes. The City Book Review called it "highly recommended for gaming nerds everywhere"! Pick up the Complete KOBOLD Guide to Game Design today, and starting designing your RPG tonight! Winner, 2012 Gold ENnie Award, Best RPG-Related Accessory

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    So he decided to write a book that is approachable and fun, centered on what people actually need to remember. In Remember It!, Dellis teaches us how to make the most of our memory, using his competition-winning techniques. Presenting the information in a user-friendly way, Dellis offers bite-size chapters, addressing things we wish we could remember but often forget: names, grocery lists, phone numbers, where you left your keys—you name it! This fast-paced, highly illustrated tour of the inner workings of the brain makes improving your memory simple and fun.