Educational guide 2023_24 School of Engineering

Contents

Topic	Sub-topic
The natural numbers	The natural numbers. Induction principle. Numerical semigroups. Open problems and applications.
Euclidean division	Euclidean division, divisibility, prime numbers, integer factorization, greatest common divisor.
Modular arithmetics	Congruences, modular arithmetics, invertibles elements and zero divisors, multiplicative order. Little Fermat's theorem and Euler's theorem.
Polynomials in modular rings	Polynomials in modular rings. Polynomial divisibility, irreducible polynomials and polynomial factorization.
Finite fields	Quocient rings of polynomials in modular rings. Construction of finite fields. Primitive elements and computations in finite fields.
Linear codes	Linear codes, generator matrix, parity check matrix, minimum distance, error detection and error correction. Cyclic codes, generator polynomial, systematic encoding.