The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Inside: Logic Resource CD-ROM

    Dorman revises his textbook, which introduces and explains the classic doctrines of the historic Christian faith. While systematic in organization, the book remains written for students, aiming to bring them to an understanding of the central doctrines of the Christian church including the doctrines of Scripture, God, creation, humanity, atonement, salvation, and eschatology.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    Worked examples and exercises support the text. An ELBS/LPBB edition is available.

    Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

    stands as one of the most thorough books yet offered regarding how to make disciples. In thirty brief, hard-hitting but easily accessible chapters, the entire scope of disciple making is presented in a way that will inspire and inform the reader to obey the Great Commission with great passion.Grounded on a solid biblical foundation, authors Dave Earley and Rod Dempsey -- both veterans of one-on-one, collegiate, small group, and local church discipleship -- share their practical insights on how to best reproduce reproducers of Christ’s message.Each compelling entry is set up to finish the sentence that begins with the book’s title. For example, Disciple Making Is . . . "Embracing the Cross," "Forsaking All to Follow Jesus," "Living on Mission," "Launching an Unstoppable Force," "Mentoring Disciples as Jesus Did," "Multiplying Disciple-Makers as Paul Did," "Creating a Healthy Church," and more.

    Stars and galaxies have formed, and elements come forth from great stellar cauldrons. The necessary elements are present, the environment is fit for life, and slowly life forms have populated the earth. Are the creative forces purposeful, and in fact divine?Owen Gingerich believes in a universe of intention and purpose. We can at least conjecture that we are part of that purpose and have just enough freedom that conscience and responsibility may be part of the mix. They may even be the reason that pain and suffering are present in the world. The universe might actually be comprehensible.Taking Johannes Kepler as his guide, Gingerich argues that an individual can be both a creative scientist and a believer in divine design--that indeed the very motivation for scientific research can derive from a desire to trace God's handiwork. The scientist with theistic metaphysics will approach laboratory problems much the same as does his atheistic colleague across the hall. Both are likely to view the astonishing adaptations in nature with a sense of surprise, wonder, and mystery.In God's Universe Gingerich carves out "a theistic space" from which it is possible to contemplate a universe where God plays an interactive role, unnoticed yet not excluded by science.

    In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    Bryan Stone, however, argues that evangelism is the duty and call of the entire church as a body of witness. Evangelism after Christendom explores what it means to understand and put to work evangelism as a rich practice of the church, grounding evangelism in the stories of Israel, Jesus, and the Apostles. This thorough treatment is marked by an astute sensitivity to the ways in which Christian evangelism has in the past been practiced violently, intentionally or unintentionally. Pointing to exemplars both Protestant and Catholic, Stone shows pastors, professors, and students how evangelism can work nonviolently.

    We cannot choose to avoid philosophy, we can only choose whether we understand it or not. Stefan Molyneux, host of Freedomain Radio – the largest and most popular philosophy show in the world, with over 600 million views and downloads – takes you on a spectacular journey through the most foundational philosophical questions of the ages, clearing up and clarifying the most thorny problems posed by philosophers throughout history: -How do we know what is real? -How do we know what is true? -How do we know what is right? -How do we know what is good? -How do we know we even have a choice? -How do we convince others? These are all questions that we – as individuals and societies – wrestle with every day. These questions have challenged, motivated and plagued mankind for thousands of years. “Essential Philosophy” answers these questions with rigourous, illuminating and entertaining logic, reasoning from deep first principles to spectacular final conclusions. There is no need for confusion, there is no need for despair, there is no need for fear – pick up this book now, absorb the true power of philosophy, and live a rational moral life to the fullest. And then, give “Essential Philosophy” to others, so that the world may one day live in reason and peace.

    The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises. Solution ManualTable of Contents, Errata, and more...

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.