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Introduction to Numbers, Errors, and Chaos for Non-ICT Specialists

Difficulty level

Computer arithmetic is necessarily performed using approximations to the real numbers they are intended to represent, and consequently it is possible for the discrepancies between the actual solution and the approximate solutions to diverge, i.e. to become increasingly different. This lecture focuses on how this happens and techniques for reducing the effects of these phenomena and discuss systems which are chaotic.

Topics covered in this lesson
  • Natural numbers, integers, rationals, and reals
  • Implementation of natural numbers: Peano arithmetic
  • Bijections
  • Irrational numbers
  • Computer numbers: integers and floating point types
  • Wrap-around errors
  • Cancellation errors
  • Practical problems with floating point numbers
  • Hybrid systems
  • Chaotic systems
  • Implications for simulation of neural systems
Lecture Slides (472.54 KB)