Apply logic and set theory|
Apply formal concepts of function and operation
Understand relations and their properties
This course concerns a continuation of Mathematics A / Introduction to Mathematics (Euclid) of Quartile 1 and consists of two parts. In the first part we start with logic, where the emphasis is laid on the translation of natural language into logical expressions and the formulation of logical derivations and counterexamples to false statements. Then we consider manipulations of set theoretic operations and formal proofs in set theory. In the second part we start with revisiting the technique of mathematical induction. Now more advanced examples are treated than those in Mathematics A/Introduction to Math. Next the formal concepts of function and operation and their properties are studied (one-to-one, onto, bijective, composition, inverse, preimage, commutativity, associativity, identity element). Finally, we study relations and their properties (reflexivity, (anti-)symmetry, transitivity) and consider representations of relations with matrices and graphs. Special attention is given to partial orders (Hasse diagrams) and equivalence relations (partitions).