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Algorithms

الكتاب المختصر في حساب الجبر والمقابلة

The success of computers is largely due to the existence of efficient algorithms for solving numerical and combinatorial problems. These algorithms are used billion of times per second. Many users (even among scientists) do not know them. One may find a list of algorithms on Wikipedia. Depending on your tastes, you may distinguish some favorite ones, for their simplicity, elegance, or versatility. Here are some few of my favorite algorithms and paradigms:

Ironically, the most used algorithms (if we measure say in Megawatt) concern coding, compression, cryptography, linked with what is often identified as “pure mathematics” (finite fields algebra, discrete linear algebra, discrete harmonic analysis). This does not mean that numerical algorithms, identified as “applied mathematics”, are not used! To me, what matters is the depth and beauty of concepts and the efficiency and versatility of implementations.

  • Iterative and non-iterative
  • Exact and approximate
  • Stochastic and deterministic
  • Integer and numerical
  • Euclid and Archimedes

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