The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    This is a presentation of the essential teaching of this direct path to freedom that focuses on the recognition and realization of the True Self. This book identifies the root cause of suffering as the identification with the mind and the belief that the psychological construct that is considered the "person" is actual. It is shown that this idea we have of who we are is an illusion that has been taken to be real and thus creates all forms of psychological suffering and confusion. The freedom from this illusion is shown to be available to anyone who is willing to recognize and realize the truth of who they are. This is a non-dual approach to psychological treatment that is becoming a new approach that has the potential to bring an end to all psychological disorders.

    The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh’s brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.

    Without knowledge, scientific enquiry is meaningless and we can’t begin to analyse the world around us. What is knowledge? How do you know you are not dreaming? Should we trust our senses? Presuming no prior experience of philosophy, this book covers everything in the topic from scepticism and possible worlds to Kant’s transcendentalism. Clear and readable, Epistemology: A Beginner’s Guide is essential reading for students and aspiring thinkers.

    The theory of karma is intellectually intriguing, but a practical understanding of how karma works can help us find hope and happiness in our lives. Eknath Easwaran is a foremost translator and interpreter of the Indian classics (the Bhagavad Gita, the Upanishads and the Dhammapada), and a highly respected teacher of meditation. This short ebook is one chapter from his forthcoming "Essence of the Dhammapada: The Buddha's Call to Nirvana."

    Based on the experience of the authors in teaching Mathematics Courses for almost four decades at the Institute of Technology, New Delhi, this text book rather than a guide/problem book, lays emphasis on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner.

    George Feuerstein has drawn short, memorable quotations from the key texts of this five-thousand-year-old legacy, with an emphasis on the wisdom of modern yoga masters.The quotations have been selected and arranged to address the needs of yoga practitioners in the twenty-first century.Among the many themes touched on in this treasure of a book: the process of inner growth; the value of silence; how to meditate; how to infuse everyday life with joy; universal kinship; overcoming suffering; dealing with grief, loss, anger, and jealousy; remembering and cultivating one’s true inner self; developing self-discipline; and bringing out the good in all you say and do.For both new and experienced yoga students alike, Yoga Gems is the perfect travel companion on the road to inner peace.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    

    From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a simple and lively way. Readers who are more mathematically adventurous will find optional sections introducing rather more challenging material. 'A lively and stimulating book' Philosophy

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.

    Brings insight and compassion to bear on the problems of insecurity and anxiety, and the solutions one finds through "attentiveness''--the key to true intelligence.

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    But since its birth was announced a century ago in 1898 by William James, pragmatism has played a vital role in almost every area of American intellectual and cultural life, inspiring judges, educators, politicians, poets, and social prophets.Now the major texts of American pragmatism, from William James and John Dewey to Richard Rorty and Cornel West, have been brought together and reprinted unabridged. From the first generation of pragmatists, including the Supreme Court Justice Oliver Wendell Holmes and the founder of semiotics, Charles Sanders Peirce, to the leading figures in the contemporary pragmatist revival, including the philosopher Hilary Putnam, the jurist Richard Posner, and the literary critic Richard Poirier, all the contributors to this volume are remarkable for the wit and vigor of their prose and the mind-clearing force of their ideas. Edited and with an Introduction by Louis Menand, Pragmatism: A Reader will provide both the general reader and the student of American culture with excitement and pleasure.

    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.