Gian-Carlo Rota

  • A New Era in Computation

    N. Metropolis and Gian-Carlo Rota

    The transition from serial to parallel computing in which many operations are performed simultaneously and at tremendous speed, marks a new era in computation. These original essays explore the emerging modalities and potential impact of this technological revolution. Daniel Hillis, inventor of the superfast Connection Machine®, provides a clear explanation of massively parallel computing. The essays that follow investigate the rich possibilities, as well as the constraints, that parallel computation holds for the future. These possibilities include its tremendous potential for simulating currently intractable physical processes and for solving "monster" scientific problems (involving new algorithms and ways of thinking about problem solving that will change the way we think about the world), and its use in the neural sciences (where the biological model for parallel computation is the brain). Essays also address the gap between the promise of this new technology and our current educational system and look at America's technological agenda for the 1990s. Daniel Hillis is Chief Scientist and James Bailey is Director of Marketing, both at Thinking Machines Corporation.

    Selected Essays: Preface, Stephen R. Graubard. What is Massively Parallel Computing, and Why Is It Important? W. Daniel Hillis. Complex Adaptive Systems, John H. Holland. Perspectives on Parallel Computing, Yuefan Deng, James Glimm, David H. Sharp. Parallel Billiards and Monster Systems, Brosl Hasslacher. First We Reshape Our Computers, Then Our Computers Reshape Us: The Broader Intellectual Impact of Parallelism, James Bailey. Parallelism in Conscious Experience. Robert Sokolowski. Of Time, Intelligence, and Institutions, Felix E. Browder. Parallel Computing and Education, Geoffrey C. Fox. The Age of Computing: A Personal Memoir, N. Metropolis. What Should the Public Know about Mathematics? Philip J. Davis. America's Economic-Technological Agenda for the 1990s, Jacob T. Schwartz.A Daedalus special issue

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  • George Pólya: Collected Papers, Volume 3


    George Pólya and Gian-Carlo Rota

    These two volumes complete the publication of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time.

    Norbert Wiener's scientific contributions not only spanned numerous branches of mathematics but also mathematical philosophy, quantum mechanics and relativity theory, and the field he christened "cybernetics" - a synthesis of communication and control engineering, the physiology of the heart and the nervous system, brain wave encephalography, and sensory prosthesis. His scholarly work also included incisive social, education, and literary essays. The object of these volumes of Collected Works is not only to reprint all of Wiener's scientific and scholarly papers but also to place them in the context of present-day research by means of commentaries written by contemporary authorities that trace both their genesis and their influence on subsequent work.

    Commentaries on the papers in Volume III were written by E. J. Akutowicz, D. Bohm, G. Freud, Sir Dennis Gabor, A. E. Heins, T. Hida, E. Hille, T. Kailath, G. Kallianpur, M. Kanter, P. Masani, L. T. McAuley, P. S. Muhly, E. Nelson, J. Pincus, E. E. Robinson, H. Salehi, A Siegel, A. H. Taub, and M. S. Vallarta. Volume I, published in 1976, included Wiener's contributions to mathematical philosophy and foundations, potential theory, Brownian movement, Wiener integrals, ergodic and chaos theories, and turbulence and statistical mechanics. Volume II collected his work on generalized harmonic analysis and Tauberian theory and on classical, harmonic, and complex analysis. A projected fourth and final volume will bring together Wiener's papers on cybernetics as well as essays and articles on nonscientific subjects.

    This book is twentieth in the series Mathematicians of Our Time.

    • Hardcover $65.00
  • George Pólya: Collected Papers, Volume 4

    Probability; Combinatorics; Teaching and Learning in Mathematics

    George Pólya and Gian-Carlo Rota

    The collected papers of George Pólya, one of the most influential mathematicians and teachers of our time.

    These two volumes complete the publication of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974. Volume III contains 58 papers spanning Pólya's career (the earliest is from 1913, the latest from 1976) and covering a wide range of subjects in mathematical analysis and mathematical physics. The commentaries on these papers attest to the fertility and continued importance of Pólya's ideas in current mathematics.

    Volume IV presents 20 papers on probability, 17 on combinatorics, and 18 on the teaching and learning of mathematics. Pólya has made a number of fundamental contributions to the first two fields, including perhaps the first use of the term "central limit theorem," but his major influence on mathematics has clearly been his approach to pedagogy. Many of the papers throughout these volumes have a strongly pedagogical flavor, but the papers in the third section of this volume focus squarely on the real business of how to do mathematics—how to formulate a problem and then create a solution.

    These volumes are the twenty-second and twenty-third in the series Mathematicians of Our Time, edited by Gian-Carlo Rota.

    • Hardcover $75.00
  • On The Foundations of Combinatorial Theory, Preliminary Edition

    Combinatorial Geometries

    Henry H. Crapo and Gian-Carlo Rota

    It has become clear within the last ten years that combinatorial geometry, together with its order-theoretic counter-part, the geometric lattice, can serve to catalyze the whole field of combinatorial theory, and a major aim of this preliminary edition is to present the theory in a form accessible to mathematicians working in disparate subjects.

    Earlier studies have been one-sided or restricted in their point of view; they were motivated primarily by the desire to extend the classical theory of graphs, or were lattice-theoretic approaches confined to axiomatics and algebraic dependence. These approaches largely ignored the original geometric motivations that gave impetus to the development of combinatorial theory.

    The present work brings all these aspects together in order to emphasize the many-sidedness of combinatorial geometry, and to point up the unifying role it may well play in current developments in combinatorics and its applications.

    The book defines the axiomatics of combinatorial geometry examples, and discusses the notion of a strong map between geometrics. In addition, there is a brief presentation of coordination theory and a sketch of two important lines of future work, the “critical problem” and matching theory. The full chapter titles are given below.

    Contents1. Introduction • 2. Geometries and Geometric Lattices • 3. Six Classical Examples • 4. Span, Bases, Bonds, Dependence, and Circuits • 5. Cryptomorphic Versions of Geometry • 6. Simplicial Geometries • 7. Semimodular Functions • 8. A Glimpse of Matching Theory • 9. Maps • 10. The Extension Theorem • 11. Orthogonality • 12. Factorization of Relatively Complemented Lattices • 13. Factorization of Geometries • 14. Connected Sets • 15. Representation • 16. The Critical Problem • 17. Bibliography

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