• Asymptotics
  • The need for asymptotic notation: a case study
  • Big Oh
  • Big Omega
  • Multiple variables
  • Polynomial complexity
  • The negligible, the noticeable and the overwhelming
• Divisibility and modular arithmetics
  • Divisibility
  • Primes and divisibility
  • Greatest common divisor and least common multiple
  • Euclidean algorithm
  • Extended Euclidean algorithm
  • Modular arithmetics
• Finite fields
  • What are rings and fields?
  • Long division of polynomials
  • The general way of constructing finite fields
  • Isomorphisms, homomorphisms, automorphisms. Classification of all finite fields
  • Computations in finite fields
  • What is a group?
  • Multiplicative group in finite fields
  • Subfields
• Linear algebra
  • 1. Matrices
  • 2. Systems of linear equations and matrices
  • 3. Gaussian elimination algorithm
  • 4. Solving systems of linear equations via invertible matrices
• Number theory
• Probability theory
  • Event and probability
  • Probability of two events
  • Conditional probability
  • Total probability
  • Expected value
  • Inequalities
  • Game notation