Theory of discrete mathematics

Table of contents:

• Sets & Relations.
• Finite-state-machines notations.
• Finite-state-machines examples.
• Finite sum notation (Riemann's Sum formula).
• Mathematical induction & rules of the finite-sum notation (Sigma or Σ).
• The fundamental theorem of calculus within the discrete mathematics context.
• Applications using the Automata4j API.
• Abstract algorithm analysis using Automata4j and the finite sum formula.

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1) Sets & Relations:

Advanced Life applications:

• Time-warp machines (TWM), a new subdivision branch of state-machines.
• Finite-state-machines in embedded systems (WIP).
• Finite-state-machines in ML algorithm processing (WIP).