Module Code - Title:
MS4111
-
DISCRETE MATHEMATICS 1
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
Rationale and Purpose of the Module:
The aim of this module is to introduce students to some of the language of Discrete Mathematics, and to show its relevance, particularly in the context of Computer Science. It is taught at a level that is appropriate to first year students, i.e. without an excess of formality. The module should re-inforce the development of the students "thinking" skills, and should enable them to undertake further study in the various applied areas of Discrete Mathematics (coding, graphs, logic and formal systems etc)
Syllabus:
Review of sets and operations on sets, power sets.
Propositional logic, truth tables, propositional calculus, equivalence.
Predicate logic, quantifiers, equivalence, application to (mathematical) proof.
Cartesian product of sets, relations, equivalence relations, matrix representation of
relations, composition of relations, functions, types of functions.
Number systems, natural numbers, integers, rationals, reals, axioms for N, proof by
induction, recursive definitions and algorithms, recurrence relations.
Representations of N (binary, octal, etc), other number "fields".
Introductory combinatorics, permutations, combinations.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
On successful completion of this module, students should be able to:
1. Use the language of Discrete Mathematics.
2. Formulate, analyse and solve problems in Discrete Mathematics.
3. Apply methods of Discrete Mathematics to solve problems in Computer Science.
4. Simplify compound propositions.
5. Use standard proof methods.
Affective (Attitudes and Values)
None
Psychomotor (Physical Skills)
None
How the Module will be Taught and what will be the Learning Experiences of the Students:
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Johnsonbaugh, R. (2008)
Discrete mathematics,
,
Other Relevant Texts:
Gersting, J.L. (2006)
Mathematical Structures for Computer Science
, Freeman
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Romina.Gaburro@ul.ie