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.

    This text surveys the major ideologies which have shaped the political landscape, covering traditional ideologies including liberalism, conservatism, and socialism, and the newly emerging ideologies, like environmentalism.

    Thomas wrote, then turn to The One-Minute Aquinas, the fast-paced book that provides busy readers with simple, readable explanations of the truths that, for 750 years now, have caused the works of St. Thomas to be sought out by kings and popes, scholars and saints, as well as by ordinary souls like you — hungry to know God and to love him more and more.In this book’s lucid pages, author Kevin Vost gives you small, digestible portions of St. Thomas’s life-giving wisdom that you can enjoy one minute at a time. Tables and graphics will help you grasp and remember St. Thomas’s key ideas with a minimum of time and effort.Best of all, in The One-Minute Aquinas you’ll find quick, sure refutations of the countless relativistic, secular, and pseudoscientific ideas that are so influential in our culture today — and so shallow, contradictory, and wrong!Pope John Paul II declared that “the Church has been justified in consistently proposing St. Thomas as a master of thought and a model of the right way to do theology.” Now The One-Minute Aquinas enables even those with limited time and only a modest education to benefit from the wisdom of this great saint.Here, with minimal effort and among scores of other things, you’ll finally come to know and understand:--Why God permits evil--Heaven: what it is (and is not)--Five simple proofs that God exists--Why God became man--Why Jesus let himself be tempted--How you can grow quickly in virtue--Why all souls need the sacraments--Why Jesus let himself be crucified--The causes of lust--The natural law and the Commandments--The soul, free will, sin, and damnation--The angels, their ranks, and their powers--How God governs (and refrains from governing)--God’s power and its limits--The Bible: why didn’t Jesus just write it himself?--The surprising qualities of our resurrected bodies

    Inspired by and expanding on a series of lectures presented by Leonard Peikoff, David Harriman presents a fascinating answer to the problem of induction-the epistemological question of how we can know the truth of inductive generalizations.Ayn Rand presented her revolutionary theory of concepts in her book Introduction to Objectivist Epistemology. As Dr. Peikoff subsequently explored the concept of induction, he sought out David Harriman, a physicist who had taught philosophy, for his expert knowledge of the scientific discovery process.Here, Harriman presents the result of a collaboration between scientist and philosopher. Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.

    . . . We need a good book in cyberethics to deal with the present and prepare us for an uncertain future. Tavani's Ethics and Technology is such a book." --from the foreword by James Moor, Dartmouth College Is there privacy in a world of camera phones and wireless networking? Does technology threaten your civil liberties? How will bioinformatics and nanotechnology affect us? Should you worry about equity and access in a globalized economy? From privacy and security to free speech and intellectual property to globalization and outsourcing, the issues and controversies of the information age are serious, complex, and pervasive. In this new edition of his groundbreaking book, Herman Tavani introduces computer professionals to the emerging field of Cyberethics, the interdisciplinary field of study that addresses these new ethical issues from all perspectives: technical, social, and philosophical. Using fascinating real-world examples--including the latest court decisions in such cases as Verizon v. RIAA, MGM v. Grokster, Google versus the Bush Administration, and the Children's Online Pornography Act (CIPA) --as well as hypothetical scenarios, he shows you how to understand and analyze the practical, moral, and legal issues that impact your work and your life. Tavani discusses such cutting-edge areas as: * Globalization and outsourcing * Property rights and open source software * HIPAA (privacy laws) and surveillance * The Patriot Act and civil liberties * Bioinformatics and genomics research * Converging technologies--pervasive computing and nanocomputing * Children's online pornography laws Updating and expanding upon the previous edition, Ethics and Technology, Second Edition provides a much-needed ethical compass to help computer and non-computer professionals alike navigate the challenging waters of cyberspace. About the Author Herman T. Tavani is Professor of Philosophy at Rivier College and Co-Director of the International Society for Ethics and Information Technology (INSEIT). He is the author, editor, or co-editor of five books on ethical aspects of information technology. www.wiley.com/college/tavani

    With this long-awaited revision, the authors continue to present the theory in a concise and straightforward manner, now with an eye out for the practical applications. They have revised this book to make it more accessible to today's students, including the addition of more material on writing proofs, more figures and pictures to convey ideas, side-boxes to highlight other interesting material, and a less formal writing style. Exercises at the end of each chapter, including some new, easier exercises, help readers confirm and enhance their understanding of the material. *NEW! Completely rewritten to be less formal, providing more accessibility to todays students. *NEW! Increased usage of figures and pictures to help convey ideas. *NEW! More detail and intuition provided for definitions and proofs. *NEW! Provides special side-boxes to present supplemental material that may be of interest to readers. *NEW! Includes more exercises, including many at a lower level. *NEW! Presents program-like notation for PDAs and Turing machines. *NEW! Increas

    These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    It presents a profound and challenging investigation into the nature of human reason, its knowledge and its illusions. Reason, Kant argues, is the seat of certain concepts that precede experience and make it possible, but we are not therefore entitled to draw conclusions about the natural world from these concepts. The Critique brings together the two opposing schools of philosophy: rationalism, which grounds all our knowledge in reason, and empiricism, which traces all our knowledge to experience. Kant's transcendental idealism indicates a third way that goes far beyond these alternatives.

    Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

    Once again, Lemert has revised and updated Social Things, a best seller that is admired by teachers and students.

    Topics: elimination of metaphysics, function of philosophy, nature of philosophical analysis, the a priori, truth & probability, critique of ethics & theology, self & the common world etc.IntroductionThe elimination of metaphysicsThe function of philosophy The nature of philosophical analysisThe a priori Truth & probabilityCritique of ethics & theologyThe self & the common worldSolutions of outstanding philosophical disputesIndex

    Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

    This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.