It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    It is a meditation on the infinite love of God and the infinite value of the human individual. Not only are we in God's hands, says Desmond Tutu, our names are engraved on the palms of God's hands. Throughout an often turbulent life, Archbishop Tutu has fought for justice and against oppression and prejudice. As we learn in this book, what has driven him forward is an unshakeable belief that human beings are created in the image of God and are infinitely valuable. Each one of us is a God-carrier, a tabernacle, a sanctuary of the Divine Trinity. God loves us not because we are loveable but because he first loved us. And this turns our values upside down. In this sense, the Gospel is the most radical thing imaginable.It is extremely moving that in this book Archbishop Tutu returns to something so simple and so profound after a life in which he has been involved in political, social, and ethical issues that have seemed to be so very complex.

    They will also develop a deeper understanding of the many interconnections that exist among the different areas of psychology. Goodwin's book not only provides accounts of the lives and contributions of psychology's pioneers set into historical context; it also contains original writings by these psychologists, interwoven with informative comments from the author. The text is written in a conversational and engaging style with discrete attention to recent scholarship in the history of psychology, especially that of the past 150 years.

    This new book takes place in Lockdown Three. This time Key can make Government-sanctioned expeditions out onto the streets of London (remember?). And it is there that the inaction takes place. Phone calls to his mother, promenades with his loyal friend, bubble-negotiations, sitting his fat arse down on benches, drinking mocha. Another three months of mind-freezing inertia. This time on the move. Conversations interspersed with poetry.

    Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.

    And it's easier than you think.If you're like most entrepreneurs, you started your business so you could be your own boss, make the money you deserve, and live life on your own terms. In reality, you're bogged down in the daily grind, constantly putting out fires, answering an endless stream of questions, and continually hunting for cash.Now, Mike Michalowicz, the author of Profit First and other small-business bestsellers, offers a straightforward step-by-step path out of this dilemma. In Clockwork, he draws on more than six years of research and real life examples to explain his simple approach to making your business ultra-efficient.Among other powerful strategies, you will discover how to:- Make your employees act like owners: Free yourself from micromanaging by using a simple technique to empower your people to make smart decisions without you.- Pinpoint your business's most important function: Unleash incredible efficiency by identifying and focusing everyone on the one function that is most crucial to your business.- Know what to fix next: Most entrepreneurs try to fix every inefficiency at once and end up fixing nothing. Use the weakest link in the chain method to find the one fix that will add the most value now.Whether you have a staff of one, one hundred, or somewhere in between, whether you're a new entrepreneur or have been overworked and overstressed for years, Clockwork is your path to finally making your business work for you.

    Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves – or discover for the first time – that maths is relevant to almost everything we do.Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

    Prepare to stretch your mind and challenge everything you think you know, as This Book Does Not Exist unveils just how weird a place the world of thought can be. Filled with philosophical and mathematical problems to baffle and delight you, This Book Does Not Exist is packed with thought experiments, real-life examples, and puzzles for you to try. It also introduces you to some of the great names in the field of paradoxes, from the ancient Greeks to Albert Einstein. Divided into eight mind-bending chapters, This Book Does Not Exist takes you on a journey from the counterintuitive to the downright absurd. On the way it will introduce you to topics such as impossible objects, how to expect the unexpected, and the trouble with time travel. This is a book that will change the way you think.

    In its scope and itnerest it can be compared with Freud's Totem and Taboo, the subtext Girard refutes with polemic daring, vast erudition, and a persuasiveness that leaves the reader compelled to respond, one way or another.This is the single fullest summation of Girard's ideas to date, the book by which they will stand or fall. In a dialogue with two psychiatrists (Jean-Michel Oughourlian and Guy Lefort), Girard probes an encyclopedic array of topics, ranging across the entire spectrum of anthropology, psychoanalysis, and cultural production.Girard's point of departure is what he calles "mimesis," the conflict that arises when human rivals compete to differentiate themselves from each other, yet succeed only in becoming more and more alike. At certain points in the life of a society, according to Girard, this mimetic conflict erupts into a crisis in which all difference dissolves in indiscriminate violence. In primitive societies, such crises were resolved by the "scapegoating mechanism," in which the community, en masse, turned on an unpremeditated victim. The repression of this collective murder and its repetition in ritual sacrifice then formed the foundations of both religion and the restored social order.How does Christianity, at once the most "sacrificial" of religions and a faith with a non-violent ideology, fit into this scheme? Girard grants Freud's point, in Totem and Taboo, that Christianity is similar to primitive religion, but only to refute Freud—if Christ is sacrificed, Girard argues, it is not becuase God willed it, but because human beings wanted it.The book is not merely, or perhaps not mainly, biblical exegesis, for within its scope fall some of the most vexing problems of social history—the paradox that violence has social efficacy, the function of the scapegoat, the mechanism of anti-semitism.

    What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    With engaging literary and everyday examples, inspirational prompts, and unforgettable insights, this course is the perfect reference guide for both professional and casual writers.Survey the ways five major literary genres-fiction, essay, poetry, drama, and autobiography-can show you the path to stronger persuasive and critical writing. Writing prompts and practice examples will help you better understand how to apply the insights you'll uncover by studying each genre. See how the art of rhetoric can help you adapt your writing to different situations. The increased awareness of classical rhetoric you gain will go a long way toward making you a stronger writer by calling your attention to the basics of compelling analytical writing. Take a step-by-step look at the four major stages of the writing process-researching, writing a first draft, editing, and rewriting.Chock full of useful strategies and real-world examples, this course is an invaluable tool for developing your effective writing skills so you can better express yourself to others.Listening Length: 12 hours and 7 minutes

    Simon Critchley skilfully probes some of the most perennial but least understood aspects of humour, such as our tendency to laugh at animals and our bodies, why we mock death with comedy and why we think it's funny when people act like machines. He also looks at the darker side of humour, as rife in sexism and racism and argues that it is important for reminding us of people we would rather not be.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.