Unit 1: Systems Theory

Systems theory is the interdisciplinary study of systems. A system is an interconnected set of components that, under certain rules, look to achieve one same goal.

In systems theory, there are several key concepts:

  • Synergy, which is the cooperative action of independent sub-systems.
  • Having recursivity in a system means that every one of its components is independent and synergistic with each other.
  • Homoeostasis is the level of response and adaptation to context that a system has.
  • Semantics is a set of new words derived from new specialisations.
  • The wear and tear that a system suffers with time or as a byproduct of its own operation is known as entropy.
  • The principle that establishes that a system and its components must achieve the same goal is known as equifinality.

Operations research is the application of the scientific method to improve decision making, within the context of systems theory.

Unit 2: Mathematical Models

A mathematical model is an abstract representation of a problem. Mathematical models can be:

  • Normative, which describe a functional relation and prescribe a specific course of action.
  • Descriptive. which describe a functional relation but don’t prescribe any course of action.
  • Deterministic, which means that all of its parameters are known.

A linear function is a type of function where sums and scalar products behave nicely. Linear inequalities are similar.

With these two, we can model a linear programming problem (LPP), which is basically a problem where the optimum (maximum or minimum) of a linear function is sought for. The correct and adequate modelling of an LPP is crucial for its optimisation and is an essential concept for this course.