Mathematics & Computer Science

You will find here various articles about mathematics and computer science.

Before my own posts, here are a few interesting links:

Algorithms about groups and Rubik’s cube…

Algorithmic Number Theory and Computer Algebra

Symbolic Computation & Computer Algebra Systems

History, Famous Problems and General References

Other geek links

Articles

What we learned from 5 million books
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A new great tool to explore our lexical culture: the ngram viewer. Have a look to the following video first:

Stuxnet & sons: anatomy of computer viruses that can destroy plants
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Stuxnet is a very sophisticated virus, famous for having destroyed nuclear installations in Iran. Variants are now being developed. They can attack, as Stuxnet did, so called “SCADA” (Supervisory Control And Data Acquisition) IT systems, which are used to monitor, … Continue reading

The history of email
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Discover the history of email: More on this site.

How complex systems appear
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In a city such as New York alone, there are more than 10 billion distinct products or services being traded. How such a complex system can work? The story of the Universe in 17 minutes, to understand how complex systems … Continue reading

Digital art & dancing
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List Decoding of Algebraic Geometric Codes
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PhD of University Paris VI (now UPMC Sorbonne University) Research carried out, between 1997 and 2001, at Project CODES (now SECRET) at l’INRIA, under the supervision of Pascale Charpin, Research Director at INRIA, Project CODES Director, and of Daniel Augot, … Continue reading

Curves for Coding and Cryptography
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In this elementary and introductory talk at INRIA‘s Junior Colloquium, we present the usual problems that occur in the theory of error-correcting codes and of cryptography. We show how the use of effective algebraic geometry over finite fields can help … Continue reading

Building Algebraic-Geometric Codes with Magma
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I this talk given at the 3rd European Congress of Mathematics (3ECM, Barcelona, Spain, July 2000), we illustrate how the computer algebra system MAGMA can be used for the implementation of sophisticated algorithms requiring many primitives in various branches of effective … Continue reading

A Hensel Lifting for List Decoding
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This article describes an algorithmic improvement on Sudan’s algorithm for Reed-Solomon codes and its generalization to algebraic-geometric codes by Shokrollahi and Wasserman. Instead of completely factoring the interpolation polynomial over the function field of the curve, we compute fast sufficiently … Continue reading

Reed-Solomon coding and decoding in one page
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This mini-article (in French) presents the Reed-Solomon codes and the principle of their decoding (2006).

Aesthetic Hacking
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A few aesthacking examples A RPN Calculator in many languages by Frederik A RPN calculator in 30 languages:, Ada, Assembler (MC68000), AWK, Bash, Brainfuck, C, C#, C++, Chef, Common Lisp, Emacs Lisp, Erlang, Fortran, Haskell, Io, Java, JavaScript, K, O’Caml, … Continue reading

IT Architecture and Operating Systems
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Sorry, this entry is only available in Français.

Game Theory and Strategy
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Computing Oesterlé’s bounds
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This package contains two C programs. The first program computes a lower bound on the genus of a curve defined over a fixed finite field, given its number of points. The second one computes an upper bound on the number … Continue reading

Root finding algorithms over function fields of algebraic curves
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Talk at Journées Nationales de Calcul Formel, CIRM (November 2005) We propose an algorithm to find the roots of a univariate polynomial with coefficients in the function field of an algebraic curve (or more generally, in a discretely valued field). … Continue reading

Logics
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Logic handout, BSc in Computer Science and Mathematics Logics course, BSC in Computer Science and Mathematics, University Paris XII (2001-2003)

Functional Programming
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Functional Programming handout, BSc in Computer Science Functional Programming Course, BSc in Computer Science, University Paris XII (2001-2003) Découvrez Objective Caml Published in GNU/Linux & Hurd Magazine France n° 43 (Oct. 2002) Objective Caml (aka Ocaml) is a wonderful programming language: … Continue reading

Object Oriented Programming
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Mathematics of Secret
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Mathématiques du Secret Talk at Camille Sée High School, Paris (December 6th, 2002) This talk is made for students who specialize in mathematics during their last year in high school. We present fundamental principles of cryptology an describe precisely the … Continue reading

Algebra to correct errors
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L’algèbre qui corrige des erreurs Published in La Recherche n°393 (January 2006) This article is a non-technical introduction about the problem of detection and correction of errors in digital transmissions.

IT Humour
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Mathematical Humor
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A mind-reading machine
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Sorry, this entry is only available in Français.