MATE-1102 Structural Mathematics

Sets, set operations, demonstration by elements, set algebra. Theory of numbers, principle of proper order, principles of induction, applications on counting. Divisibility, division algorithm, Euclid’s’ algorithm, prime numbers, congruencies, Chinese theorem of residuals, Fermat’s little theorem. Relationships, orders, equivalence relations, functions, applications on counting. Cardinality of finite and infinite sets, Cantor-Schröder-Bernstein theorem. Mathematical structures, isomorphism of structures, rudiments of group theory.