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modular:06_modular_arithmetics
  • 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

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