- Apply logic and set theory
- Apply formal concepts of function and operation
- Understand relations and their properties
This course concerns a continuation of Introduction to Mathematics and Calculus 1A for CS 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 by revisiting the technique of mathematical induction. Now more advanced examples are treated than those in the Introduction to Mathematics and Calculus 1A course. 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).