At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out the two appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    Adventures change you and how you see the world, and all you need is an open mind, bags of enthusiasm and boundless curiosity.So what’s a microadventure? It’s close to home, cheap, simple, short and 100% guaranteed to refresh your life. A microadventure takes the spirit of a big adventure and squeezes it into a day or even a few hours.The point of a microadventure is that you don’t need lots of time and money to meet a new challenge. This practical guide is filled with ideas for microadventures – for you to experience on your own or with friends and family – and over 150 stunning photographs, plus tips and advice on safety and kit.Whether it’s sleeping on a hilltop or going for a wild swim, cycling a lap of the Isle of Wight or walking home for Christmas, it’s time you discovered something new about yourself and the world outside your window. Adventure is everywhere, every day and it is up to us to find it.

    The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.

    Instead, we find that the wealthiest societies of the world have become depressed, anxious, sleep deprived, and overmedicated.Max Strom, author of A Life Worth Breathing and global teacher of personal transformation, reveals that we each have internal, human technology capable of empowering our lives and leading us to deeper levels of happiness. In his new book, There Is No App for Happiness, Strom illustrates three imperatives to take back control of our lives.Imperative One: Self-study. Overcoming our negative presets.Imperative Two: Live as if your time and your lifespan were the same thing.Imperative Three: Learn a daily regimen that heals and empowers you, and practice it one hour a day.Learn that joy and fulfillment require us to be active participants and that we should not strive for a virtual life—but a life truly lived. There Is No App for Happiness will propel you into a new and more meaningful experience of living.

    And yet the pursuit of both has never been more elusive. As work and personal demands rise, we try to keep up by juggling everything better, moving faster, and doing more. While we might succeed in the short term, it comes at a cost to our well-being, relationships, and, paradoxically, our productivity. In The Happiness Track, Emma Seppala, the science director of the Center for Compassion and Altruism Research and Education at Stanford University and director of the Yale College Emotional Intelligence Project, explains that our inability to achieve sustainable fulfillment is tied to common but outdated notions about success. We are taught that getting ahead means doing everything that’s thrown at us (and then some) with razor-sharp focus and iron discipline; that success depends on our drive and talents; and that achievement cannot happen without stress.The Happiness Track demolishes these counter-productive theories. Drawing on the latest findings from the fields of cognitive psychology and neuroscience—research on happiness, resilience, willpower, compassion, positive stress, creativity, mindfulness—Seppala shows that finding happiness and fulfillment may, in fact, be the most productive thing we can do to thrive professionally. Filled with practical advice on how to apply these scientific findings to our daily lives, The Happiness Track is a life-changing guide to fast tracking our success and creating the anxiety-free life we want.

    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.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    Parlez-vous Doggish? At long last, dogs will know just how smart their owners can be. By unlocking the secrets of the hidden language of dogs, psychologist Stanley Coren allows us into the doggy dialogue, or “Doggish,” and makes effective communication a reality. Drawing on substantial research in animal behavior, evolutionary biology, and years of personal experience, Coren demonstrates that the average house dog can understand language at about the level of a two-year-old human. While actual conversation of the sort Lassie seemed capable of in Hollywood mythmaking remains forever out of reach, Coren shows us that a great deal of real communication is possible beyond the giving and obeying of commands. How to Speak Dog not only provides the sounds, words, actions, and movements with which we can effectively communicate with our dogs, but also deciphers the signs that our dogs give to us. With easy-to-follow tips on how humans can mimic the language dogs use to talk with one another, original drawings illustrating the subtleties of their body language, and a handy visual glossary and “Doggish” phrasebook, How to Speak Dog gives dog lovers the skills they need to improve their relationships with their pets.

    Biologists have been trying to solve the mystery of how organisms have the ability to migrate and orient with such precision—especially since our own adventurous ancestors spread across the world without maps or instruments. O'Connor goes to the Arctic, the Australian bush, and the South Pacific to talk to masters of their environment who seek to preserve their traditions at a time when anyone can use a GPS to navigate.O'Connor explores the neurological basis of spatial orientation within the hippocampus. Without it, people inhabit a dream state, becoming amnesiacs incapable of finding their way, recalling the past, or imagining the future. Studies have shown that the more we exercise our cognitive mapping skills, the greater the grey matter and health of our hippocampus. O'Connor talks to scientists studying how atrophy in the hippocampus is associated with afflictions such as impaired memory, dementia, Alzheimer's Disease, depression, and PTSD.Wayfinding is a captivating book that charts how our species' profound capacity for exploration, memory, and storytelling results in topophilia, the love of place.

    For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

    James Paul Gee begins his new book with 'I want to talk about vide games- yes, even violent video games - and say some positive things about them'. With this simple but explosive beginning, one of America's most well-respected professors of education looks seriously at the good that can come from playing video games. Gee is interested in the cognitive development that can occur when someone is trying to escape a maze, find a hidden treasure and, even, blasting away an enemy with a high-powered rifle. Talking about his own video-gaming experience learning and using games as diverse as Lara Croft and Arcanum, Gee looks at major specific cognitive activities: How individuals develop a sense of identity; How one grasps meaning; How one evaluates and follows a command; How one picks a role model; How one perceives the world.

    Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications.Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability.The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.