This course is devoted to mathematical aspects laying at the basis of major programming theories.

In this course we will cover the following fundamental topics:

• Number representation in computer
• Linear algebra basics: vectors and matrices. And their role in computations.
• Graphs and trees.
• Algorithm complexity analysis. Big-O notation.
• Algorithmic strategies with connection to programming:
  • Recurrence relations and recursion in programs.
  • Brute force and it's practical improvements.
  • Heuristic algoritms.
  • Greedy algorithms and matroids.
• Formal models.
  • Finite State Automata.
  • Languages and Grammatics.

Original plan is located here.