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75 Years of Mathematics of Computation
 
Edited by: Susanne C. Brenner Louisiana State University, Baton Rouge, LA
Igor Shparlinski The University of New South Wales, Sydney, Australia
Chi-Wang Shu Brown University, Providence, RI
Daniel B. Szyld Temple University, Philadelphia, PA
Front Cover for 75 Years of Mathematics of Computation
Available Formats:
Electronic ISBN: 978-1-4704-5637-5
Product Code: CONM/754.E
364 pp 
List Price: $120.00
MAA Member Price: $108.00
AMS Member Price: $96.00
Front Cover for 75 Years of Mathematics of Computation
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  • Front Cover for 75 Years of Mathematics of Computation
  • Back Cover for 75 Years of Mathematics of Computation
75 Years of Mathematics of Computation
Edited by: Susanne C. Brenner Louisiana State University, Baton Rouge, LA
Igor Shparlinski The University of New South Wales, Sydney, Australia
Chi-Wang Shu Brown University, Providence, RI
Daniel B. Szyld Temple University, Philadelphia, PA
Available Formats:
Electronic ISBN:  978-1-4704-5637-5
Product Code:  CONM/754.E
364 pp 
List Price: $120.00
MAA Member Price: $108.00
AMS Member Price: $96.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 7542020
    MSC: Primary 11; 16; 35; 41; 65;

    The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.

    The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions.

    On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

    Readership

    Graduate students and research mathematicians interested in computational mathematics.

  • Table of Contents
     
     
    • Articles
    • Markus Bachmayr and Wolfgang Dahmen - Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity
    • Fleurianne Bertrand and Daniele Boffi - The Prager–Synge theorem in reconstruction based a posteriori error estimation
    • Juan Pablo Borthagaray, Wenbo Li and Ricardo H. Nochetto - Linear and nonlinear fractional elliptic problems
    • Ronald Cools, Frances Y. Kuo, Dirk Nuyens and Ian H. Sloan - Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters
    • Qiang Du, Bjorn Engquist and Xiaochuan Tian - Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues
    • Michael Neilan - The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows
    • Peter Monk and Yangwen Zhang - Finite element methods for Maxwell’s equations
    • Adam M. Oberman - Partial differential equation regularization for supervised machine learning
    • Yousef Saad - Iterative methods for linear systems of equations: A brief historical journey
    • Jie Shen and Xiaofeng Yang - The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
    • Chi-Wang Shu - A class of bound-preserving high order schemes: The main ideas and recent developments
    • Olof B. Widlund - BDDC domain decomposition algorithms
    • Perlas Caranay, Matthew Greenberg and Renate Scheidler - Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields
    • Nicolas David and Paul Zimmermann - A new ranking function for polynomial selection in the number field sieve
    • Bettina Eick and Tobias Moede - A nilpotent quotient algorithm for finitely presented associative $\mathbb {Z}$-algebras and its application to integral group rings
    • Michael J. Mossinghoff and Timothy S. Trudgian - A tale of two omegas
  • Additional Material
     
     
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Volume: 7542020
MSC: Primary 11; 16; 35; 41; 65;

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.

The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions.

On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

Readership

Graduate students and research mathematicians interested in computational mathematics.

  • Articles
  • Markus Bachmayr and Wolfgang Dahmen - Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity
  • Fleurianne Bertrand and Daniele Boffi - The Prager–Synge theorem in reconstruction based a posteriori error estimation
  • Juan Pablo Borthagaray, Wenbo Li and Ricardo H. Nochetto - Linear and nonlinear fractional elliptic problems
  • Ronald Cools, Frances Y. Kuo, Dirk Nuyens and Ian H. Sloan - Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters
  • Qiang Du, Bjorn Engquist and Xiaochuan Tian - Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues
  • Michael Neilan - The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows
  • Peter Monk and Yangwen Zhang - Finite element methods for Maxwell’s equations
  • Adam M. Oberman - Partial differential equation regularization for supervised machine learning
  • Yousef Saad - Iterative methods for linear systems of equations: A brief historical journey
  • Jie Shen and Xiaofeng Yang - The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
  • Chi-Wang Shu - A class of bound-preserving high order schemes: The main ideas and recent developments
  • Olof B. Widlund - BDDC domain decomposition algorithms
  • Perlas Caranay, Matthew Greenberg and Renate Scheidler - Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields
  • Nicolas David and Paul Zimmermann - A new ranking function for polynomial selection in the number field sieve
  • Bettina Eick and Tobias Moede - A nilpotent quotient algorithm for finitely presented associative $\mathbb {Z}$-algebras and its application to integral group rings
  • Michael J. Mossinghoff and Timothy S. Trudgian - A tale of two omegas
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