Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    This began to change with the devising of methods to try to tap into what was going on in the 'black box' of the mind, and the development of 'cognitive psychology'. With the study of patients who had suffered brain damage or injury to limited parts of the brain, outlines of brain components and processes began to take shape, and by the end of the 1970s, a new science, cognitive neuroscience, was born. But it was with the development of ways of accessing activation of the working brain using imaging techniques such as PET and fMRI that cognitive neuroscience came into its own, as a science cutting across psychology and neuroscience, with strong connections to philosophy of mind. Experiments involving subjects in scanners while doing various tasks, thinking, problem solving, and remembering are shedding light on the brain processes involved. The research is exciting and new, and often makes media headlines. But there is much misunderstanding about what brain imaging tells us, and the interpretation of studies on cognition.In this Very Short Introduction Richard Passingham, a distinguished cognitive neuroscientist, gives a provocative and exciting account of the nature and scope of this relatively new field, and the techniques available to us, focusing on investigation of the human brain. He explains what brain imaging shows, pointing out common misconceptions, and gives a brief overview of the different aspects of human cognition: perceiving, attending, remembering, reasoning, deciding, and acting. Passingham concludes with a discussion of the exciting advances that may lie ahead.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

    Enthusiastic and informal accounts of the exciting discoveries and fascinating observations made by naturalists in the study of the behavior of animals in their natural surroundings

    It touches on its evolutionary development, its algorithmic nature and its scientific history by bridging ideas across Neuroscience, Computer Science, Biotechnology, Evolutionary History, Cognitive Science, Political Philosophy, and Artificial Intelligence.Never before had there been nearly as many scientists, resources or productive research focused on these topics, and humanity has achieved some understanding and some clarification. With the speed of progress it is timely to communicate an overreaching perspective, this book puts an emphasis on conveying the essential questions and what we know about their answers in a simple, clear and exciting way.Humans, along with the first RNA molecules, the first life forms, the first brains, the first conscious animals, the first societies and the first artificial agents constitute an amazing and crucial development in a path of increasingly complex computational intelligence. And yet, we occupy a minuscule time period in the history of Earth, a history that has been written by Genes, by Cultures and by Consciousnesses. If we abandon our anthropomorphic bias it becomes obvious that Humans are not so special after all. We are an important but short and transitory step among many others in a bigger story. The story of our computational minds, which is ours but not only ours. What is the relationship between computation, cognition and everything else? What is life and how did it originate? What is the role of culture in human minds? What do we know about the algorithmic nature of the mind, can we engineer it? What is the computational explanation of consciousness? What are some possible future steps in the evolution of minds? The underlying thread is the computational nature of the Mind which results from the mixture of Genes, Cultures and Consciousness. While these three interact in complex ways, they are ultimately computational systems on their own which appeared at different stages of history and which follow their own selective processes operating at different time scales. As technology progresses, the distinction between the three components materializes and will be a key determinant of the future.Among the many topics covered are the origin of life, the concept of computation and its relation to Turing Machines, cultural evolution and the notion of a Selfish Meme, free will and determinism, moral relativity, the hard problem of consciousness, the different theories of concepts from the perspective of cognitive science, the current status of AI and Machine Learning including the symbolic vs sub-symbolic dichotomy, the contrast between logical reasoning and neural networks, and the recent history of Deep Learning, Geoffrey Hinton, DeepMind and its algorithm AlphaGo. It also develops on the history of science and looks into the possible future building on the work of authors like Daniel Dennett, Yuval Harari, Richard Dawkins, Francis Crick, George Church, David Chalmers, Susan Carey, Stanislas Dehaene, Robert Boyd, Joseph Henrich, Daniel Kahneman, Moran Cerf, Josh Tenenbaum, David Deutsch, Steven Pinker, Ray Kurzweil, John von Neumann, Herbert Simon and many more. Andres Campero is a researcher and PhD student at the Brain and Cognitive Sciences Department and at the Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology (MIT).

    The text covers the neuroanatomy that medical and other healthcare students need, with expanded coverage of neurophysiology and inclusion of clinical content providing real-life application of neuroanatomy and neurophysiologic concepts to clinical neurologic disorders. Its readability and enhanced full-color illustrations make it a favorite among both students and faculty.Provides a single-author approach for a more consistent, readable text.Contains summary statement headings to help you find what you're looking for within the text.Provides an outline introducing each chapter to help students organize and stay focused as they learn.Includes appealing four-color, computerized three-dimensional images of the brain and brain structures fully integrated with the text.Complements an Electronic Image Bank that is also available separately.Includes more coverage of neurobiology and neurophysiology.Gives more clinical content, including many images depicting neurologic disorders.Features an expanded section on higher cortical function.Features an expanded section on learning and memory.Contains a new chapter on the development, maintenance, and repair of neural connections-an explosive area of research in neuroscience.Supplies a glossary of key terms.Replaces many of the older figures with new, computer-generated illustrations.

    Other bestselling works of neurobiology and the mind have focused on mental illness and abnormal behaviors—like the Oliver Sacks classic, The Man Who Mistook His Wife for a Hat—but The Other Side of Normal is an eye-opening, thought-provoking, utterly fascinating and totally accessible exploration of the universals of human experience. It will change forever our understanding of who we are and what makes us that way.

    These vignettes serve as springboards to many telling perspectives: simple arithmetic puts life-long habits in a dubious new light; higher dimensional geometry helps us see that we're all rather peculiar; nonlinear dynamics explains the narcissism of small differences cascading into very different siblings; logarithms and exponentials yield insight on why we tend to become bored and jaded as we age; and there are tricks and jokes, probability and coincidences, and much more.For fans of Paulos or newcomers to his work, this witty commentary on his life--and yours--is fascinating reading.From the Trade Paperback edition.

    Written by the well-known mathematics teacher consultant, this volume's collection of over 200 clearly illustrated mathematical ideas, concepts, puzzles, and games shows where they turn up in the real world. You'll find out what a googol is, visit hotel infinity, read a thorny logic problem that was stumping them back in the 8th century.THE JOY OF MATHEMATICS is designed to be opened at random...it's mini essays are self-contained providing the reader with an enjoyable way to explore and experience mathematics at its best.

    How to approach complex normal and abnormal behaviors through biology. How to integrate disciplines including sociobiology, ethology, neuroscience, and endocrinology to examine behaviors such as aggression, sexual behavior, language use, and mental illness.36 hours lectures

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del

    New findings in molecular biology challenge the gene-centered version of Darwinian theory according to which adaptation occurs only through natural selection of chance DNA variations. In Evolution in Four Dimensions, Eva Jablonka and Marion Lamb argue that there is more to heredity than genes. They trace four dimensions in evolution -- four inheritance systems that play a role in evolution: genetic, epigenetic (or non-DNA cellular transmission of traits), behavioral, and symbolic (transmission through language and other forms of symbolic communication). These systems, they argue, can all provide variations on which natural selection can act. Evolution in Four Dimensions offers a richer, more complex view of evolution than the gene-based, one-dimensional view held by many today. The new synthesis advanced by Jablonka and Lamb makes clear that induced and acquired changes also play a role in evolution. After discussing each of the four inheritance systems in detail, Jablonka and Lamb put Humpty Dumpty together again by showing how all of these systems interact. They consider how each may have originated and guided evolutionary history and they discuss the social and philosophical implications of the four-dimensional view of evolution. Each chapter ends with a dialogue in which the authors engage the contrarieties of the fictional (and skeptical) I.M., or Ifcha Mistabra -- Aramaic for the opposite conjecture -- refining their arguments against I.M.'s vigorous counterarguments. The lucid and accessible text is accompanied by artist-physician Anna Zeligowski's lively drawings, which humorously and effectively illustrate the authors' points.

    To start building a more straightforward, accurate understanding of current breakthroughs in neuroscience, you have to start by shattering popular brain myths.Each of these 24 lectures takes as its focus a single powerful, prevalent brain myth, and uses it as a launch pad from which to explore myriad topics in neuroscience: decision making, memory, dreams, emotions, neuroplasticity, consciousness, mental illness, and much more.Our memory is an accurate, objective record of the past. Our senses reflect the world as it really exists. Our dreams have hidden meanings. We are only using 10% of our total brain power. Modern technology (including social media) is making us less intelligent. Dr. Viskontas doesn't just settle for obliterating these and other myths. Instead, she replaces them with scientific facts gathered from experiments, research, and case studies. The result is an eye-opening adventure into the latest understanding of why the brain works the way it does.Whatever order you enjoy these lectures in, you'll be left with insights that will help you better determine the hard scientific truths behind the breaking news (and myths) of tomorrow.

    Richard Davenport-Hines, an eminent, prize-winning historian, uncovers the centrality of drug abuse in our modern industrial society, from the drug habits of Charles Dickens and John F. Kennedy to today's $400 billion annual worldwide trade in illicit drugs (the same volume as the oil industry). A vivid portrayal of the people and events that have shaped the history of narcotics, The Pursuit of Oblivion reveals that, contrary to the assumption underlying current drug policies, our need to escape reality and our body's need for physical pleasure are both ineradicable aspects of our humanity, unchangeable by government initiative.

    These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.