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
