Joćo Fernando Ferreira

Joćo Ferreira Personal Web

Mathematical Methodology and Algorithmic Problem Solving

This page lists some useful resources on mathematical methodology and algorithmic problem solving. For more resources visit the webpages listed on Other websites. You can also find additional information in the homepages listed on section People.

Books

  • Predicate Calculus and Program Semantics, Edsger W. Dijkstra and Carel S. Scholten
    ( ACM link , Amazon link )

  • Program Construction (International Summer School), Edsger W. Dijkstra and David Gries, LNCS Springer
    E-book link

Articles and Notes

Documents named EWDxxx, where xxx is a positive natural number, are notes written by Edsger W. Dijkstra. Similarly:

  • JAWxxx - Jeremy Weissmann
  • JFFxxx - Joao Fernando Ferreira
  • WFxxx - Wim Feijen

Still to sort

  • Exercises in Quantifier Manipulation, Roland Backhouse and Diethard Michaelis, In Mathematics of Program Construction 2006, Tarmo Uustalu (Ed.), Springer-Verlag, LNCS 4014, pp. 70--81 © Springer-Verlag

  • Galois Connections and Logical Relations, Kevin Backhouse and Roland Backhouse, Int. Conf. on Mathematics of Program Construction, Dagstuhl, Germany, July 2002. Springer Verlag LNCS 2386, pp. 23--39. © Springer-Verlag

  • Fixed Point Calculus, Roland Backhouse, Presented at the Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, Oxford, April 11--14, 2000.

Mathematical Methodology

Introductory documents

The following documents introduce our line of thought.

  • Mathematics and Programming. A Revolution in the Art of Effective Reasoning, Roland Backhouse, Inaugural lecture, School of Computer Science and IT, University of Nottingham, 24th October 2001.
  • EWD619 - Essays on the nature and role of mathematical elegance (1) (HTML, PDF)
  • EWD641 - On the interplay between mathematics and programming (HTML, PDF)
  • EWD655 - Essays on the nature and role of mathematical elegance (3): On notation (A sequel to EWD619) (HTML, PDF)
  • EWD1059 - 0 Preface (Mathematical Methodology) (HTML, PDF)
  • EWD1063 - An introductory example (Mathematical Methodology) (PDF)
  • EWD1067 - A very first introductory example (Mathematical Methodology) (HTML, PDF)
  • The Calculational Method, Information Processing Letters, Volume 53, Issue 3, 10 February 1995, Page 121

Notation and Proof Formats

  • EWD1068 - On the quality criteria for mathematical writing (Mathematical Methodology) (HTML, PDF)
  • EWD999 - Our proof format (PDF)
  • EWD1070 - For brevity's sake (Mathematical Methodology) (HTML, PDF)
  • EWD1300 - The notational conventions I adopted, and why (HTML, PDF)

Monotonicity

  • JAW44 - Different types of symbol dynamics for Leibniz and monotonicity (PDF)

Algorithmic Problem Solving

People (alphabetical order of surname)

List of people interested in mathematical methodology and in particular, in the calculational method.

Tools

Other websites

-- JoaoFerreira - 30 May 2007

r2 - 07 Dec 2007 - 11:47:28 - JoaoFerreira
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