Conceptual and Computational Mathematics†

[1]  T. Kuhn,et al.  The Structure of Scientific Revolutions. , 1964 .

[2]  Donald E. Knuth,et al.  Computer Science and its Relation to Mathematics , 1974 .

[3]  J. Marquis.  Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics , 2016, The Best Writing on Mathematics 2017.

[4]  Nicolas Fillion,et al.  The Vindication of Computer Simulations , 2017 .

[5]  Robert H. C. Moir,et al.  Explanation and abstraction from a backward-error analytic perspective , 2018, European Journal for Philosophy of Science.

[6]  The architecture of modern mathematics: Essays in history and philosophy , 2008 .

[7]  Nicolas Fillion,et al.  Numerical Methods, Complexity, and Epistemic Hierarchies , 2015, Philosophy of Science.

[8]  M. Carrier,et al.  Mathematics as a Tool: Tracing New Roles of Mathematics in the Sciences , 2017 .

[9]  Paul R. Halmos.  Problems for mathematicians, young and old , 1991 .

[10]  Lloyd N. Trefethen,et al.  The Definition of Numerical Analysis , 1992 .

[11]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

[12]  M. Viana.  What’s new on lorenz strange attractors? , 2000 .

[13]  Donald Gillies,et al.  Revolutions in Mathematics , 1975 .

[14]  Lenore Blum,et al.  Computing over the Reals: Where Turing Meets Newton , 2004 .

[15]  Richard Pettigrew,et al.  Accuracy and the credence-belief connection , 2015 .

[16]  Leo P. Kadanoff,et al.  Excellence in computer simulation , 2003, Computing in Science & Engineering.

[17]  Eric Winsberg,et al.  Holism, entrenchment, and the future of climate model pluralism , 2010 .

[18]  Anthony Ralston,et al.  The Influence of Computers and Informatics on Mathematics and Its Teaching. Science and Technology Education Series, 44. , 1986 .

[19]  Paul Humphreys,et al.  Extending Ourselves: Computational Science, Empiricism, and Scientific Method , 2004 .

[20]  Julie Jebeile,et al.  Empirical agreement in model validation. , 2016, Studies in history and philosophy of science.

[21]  Roman Frigg,et al.  The philosophy of simulation: hot new issues or same old stew? , 2009, Synthese.

[22]  Lenore Blum,et al.  Complexity and Real Computation , 1997, Springer New York.

[23]  M. F. Atiyah.  The Influence of Computers and Informatics on Mathematics and its Teaching: Mathematics and the Computer Revolution , 1986 .

[24]  Robert M. Corless,et al.  On the epistemological analysis of modeling and computational error in the mathematical sciences , 2013, Synthese.

[25]  Istituto Della Enciclopedia Italiana,et al.  Storia della scienza , 2001 .

[26]  M. Crowe.  Ten “Laws” concerning patterns of change in the history of mathematics , 1975 .

[27]  Robert I. Soare,et al.  The History and Concept of Computability , 1999, Handbook of Computability Theory.

[28]  Eike-Henner W. Kluge,et al.  On the foundations of geometry and formal theories of arithmetic , 1973 .

[29]  Paul Humphreys,et al.  The philosophical novelty of computer simulation methods , 2009, Synthese.

[30]  Thomas Tymoczko.  The Four-color Problem and Its Philosophical Significance , 1979 .

[31]  C. Pincock.  The Unsolvability of The Quintic: A Case Study in Abstract Mathematical Explanation , 2015 .

[32]  S. Smale.  Mathematical problems for the next century , 1998 .

[33]  Ian Stewart,et al.  Mathematics: The Lorenz attractor exists , 2000, Nature.

[34]  L. Laudan.  Progress and Its Problems , 1977 .

[35]  Edward R. Griffor.  Handbook of Computability Theory , 1999, Handbook of Computability Theory.