Discrete MathematicsLaajuus (5 cr)

Objective

After completing the course the student: can some of the basic concepts of mathematical logic identifies some of basic concepts of sets can describe some of basic concepts of proof in mathematics can what means mathematical induction can describe what means concepts: permutation, combination, probability can describe some of basic concepts of number theory can describe what means concepts: group, ring, field and calculate basic exercises in finite fields can describe elements of coding theory and calculate linear codes: encoding and decoding can describe what means BCH codes and calculate BCH codes: encoding and decoding.

Content

mathematical logic: statements, truth tables, logical equivalences, valid arguments sets: subsets, the power set, operations on sets techniques of proofs in mathematics: mathematical induction permutations and combinations elementary probability number theory: divisibility and the Euclidean algorithm, prime numbers, congruence, applications of congruence basic concepts of modern algebra: group, ring and field coding theorem: linear codes and BCH codes Matlab programming in coding theory.