Semantics & Verification Research Group
Conversion Masters in IT


First Year

These credits are primarily aimed at instilling basic notions which will be necessary not only for the formal methods and theoretical computer science thread but also to full understanding of various areas in computer science and general IT. These credits are compulsory to all IT students.

  • Title: Mathematics of Discrete Structures (as part of xxx)
    Code: MIT xxx
    Credits: 4 ECTS
    Lectures: 24 hours
    Semesters: Held in the first semester
    Lecturer: Gordon Pace
    Examination: 30% exam in February, 70% exam in June. The resit will also be in the form of one exam covering 100% of the final mark.

    Syllabus: The course is primarily aimed to introduce the basic mathematical tools that are required for the formal and rigorous treatment of the various aspects of computing. The importance of formal reasoning is emphasised in the course, concentrating on syntax, and formal proofs. The course also explains various mathematical notions and structures that will be used in later courses. The course introduces fundamental mathematical concepts - the use of axioms, rules of inference and syntactic definitions to express concepts in a precise mathematical notation, thus making them amenable to formal reasoning and proof.

    • Propositional Calculus: The use of truth tables, axiomatic and algebraic approaches, including the concept of soundness and completeness of formal models.
    • Predicate Calculus: Axiomatic approach to typed predicate calculus.
    • Typed Set Theory: A definitional approach based on predicate calculus allowing reasoning about sets.
    • Relations and Functions: Reasoning about relations and functions in terms of sets.
    • Natural Numbers and cardinality
    • Sequences, multisets, graph theory: These concepts are formalised in terms of the notions formalised earlier in the course.
    • Principle of Induction

    Textbooks and recommended reading list:
    • Gordon Pace, Mathematics of Discrete Structures, Lecture Notes, 2006.
    • Andrew Simpson, Discrete Mathematics by Example, McGraw-Hill, ISBN 0-07-709840-4, 2002.