Algorithms And Complexity In Mathematics Epistemology And Science

Download or read book Algorithms and Complexity in Mathematics, Epistemology, and Science written by Nicolas Fillion and published by Springer. This book was released on 2019-02-07 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Download or read book Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press. This book was released on 2020-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together — and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.

Download or read book Imitation of Rigor written by Mark Wilson and published by Oxford University Press. This book was released on 2022-01-27 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mark Wilson aims to reconnect analytic philosophy with the evolving practicalities within science from which many of its grander concerns originally sprang. He offers an alternative history of how the subject might have developed had the insights of its philosopher/scientist forebears not been cast aside in the vain pursuit of 'ersatz rigor'"--

Download or read book Causation with a Human Face written by James Woodward and published by Oxford University Press. This book was released on 2021-09-27 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past few decades have seen an explosion of research on causal reasoning in philosophy, computer science, and statistics, as well as descriptive work in psychology. In Causation with a Human Face, James Woodward integrates these lines of research and argues for an understanding of how each can inform the other: normative ideas can suggest interesting experiments, while descriptive results can suggest important normative concepts. Woodward's overall framework builds on the interventionist treatment of causation that he developed in Making Things Happen. Normative ideas discussed include proposals about the role of invariant or stable relationships in successful causal reasoning and the notion of proportionality. He argues that these normative ideas are reflected in the causal judgments that people actually make as a descriptive matter. Woodward also discusses the common philosophical practice-particularly salient in philosophical accounts of causation--of appealing to "intuitions" or "judgments about cases" in support of philosophical theses. He explores how, properly understood, such appeals are not different in principle from appeals to results from empirical research, and demonstrates how they may serve as a useful source of information about causal cognition.

Download or read book A Graduate Introduction to Numerical Methods written by Robert M. Corless and published by Springer Science & Business Media. This book was released on 2013-12-12 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

Download or read book Think Complexity written by Allen B. Downey and published by "O'Reilly Media, Inc.". This book was released on 2012-02-23 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expand your Python skills by working with data structures and algorithms in a refreshing context—through an eye-opening exploration of complexity science. Whether you’re an intermediate-level Python programmer or a student of computational modeling, you’ll delve into examples of complex systems through a series of exercises, case studies, and easy-to-understand explanations. You’ll work with graphs, algorithm analysis, scale-free networks, and cellular automata, using advanced features that make Python such a powerful language. Ideal as a text for courses on Python programming and algorithms, Think Complexity will also help self-learners gain valuable experience with topics and ideas they might not encounter otherwise. Work with NumPy arrays and SciPy methods, basic signal processing and Fast Fourier Transform, and hash tables Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines Get starter code and solutions to help you re-implement and extend original experiments in complexity Explore the philosophy of science, including the nature of scientific laws, theory choice, realism and instrumentalism, and other topics Examine case studies of complex systems submitted by students and readers

Download or read book Thinking about Godel and Turing written by Gregory J. Chaitin and published by World Scientific. This book was released on 2007 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as GAdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of GAdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity."