This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    In so doing, he reaches a provocative conclusion: science, the main tool we use to find answers, is fundamentally limited.These limits to our knowledge arise both from our tools of exploration and from the nature of physical reality: the speed of light, the uncertainty principle, the impossibility of seeing beyond the cosmic horizon, the incompleteness theorem, and our own limitations as an intelligent species. Recognizing limits in this way, Gleiser argues, is not a deterrent to progress or a surrendering to religion. Rather, it frees us to question the meaning and nature of the universe while affirming the central role of life and ourselves in it. Science can and must go on, but recognizing its limits reveals its true mission: to know the universe is to know ourselves.Telling the dramatic story of our quest for understanding, The Island of Knowledge offers a highly original exploration of the ideas of some of the greatest thinkers in history, from Plato to Einstein, and how they affect us today. An authoritative, broad-ranging intellectual history of our search for knowledge and meaning, The Island of Knowledge is a unique view of what it means to be human in a universe filled with mystery.