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.
|