The module consists of two parts, each of fundamental importance for any serious approach to Computer Science: Logic and Discrete Structures. Logic has been called the Calculus of Computer Science. It plays a very important role in computer architecture (logic gates), software engineering (specification and verification), programming languages (semantics, logic programming), databases (relational algebra and SQL the standard computer language for accessing and manipulating databases), artificial intelligence (automatic theorem proving), algorithms (complexity and expressiveness), and theory of computation (general notions of computability). Computer scientists use Discrete Mathematics to think about their subject and to communicate their ideas independently of particular computers and programs. They expect other computer scientists to be fluent in the language and methods of Discrete Mathematics. In the module we consider Propositional logic as well as Predicate Calculus. We will treat Propositional Logic and Predicate Calculus as formal systems. You will learn how to produce and annotate formal proofs. As application we will briefly consider the programming language Prolog. This module will also cover a variety of standard representations, operations, properties, constructions and applications associated with selected structures from Discrete Mathematics (sets, relations, functions, directed graphs, orders).

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