Module: Discrete Mathematics

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Discrete Mathematics
Module Code	MTH1095 (ITS: MTH1090, MS342)
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	8	Credit Rating	5

Description

This module introduces students to some fundamental ideas and practices in the areas of Logic & Proof, Number Theory, Combinatorics and Graph Theory. Students will be expected to work collaboratively to discuss and reflect on their learning.

Learning Outcomes

1. Recall relevant mathematical facts in Set Theory, Logic & Proof, Number Theory, Combinatorics, and Graph Theory.
2. Apply concepts and processes related to these topics in both mathematical and non-mathematical contexts.
3. Analyse information and interpret results (related to these topics).
4. Explore patterns and formulate conjectures (related to these topics).
5. Present arguments, draw and justify conclusions (related to these topics).
6. Communicate ideas in Discrete Mathematics in writing.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	No Description
Tutorial	12	No Description
Assignment Completion	3	No Description
Guided learning activities	24	Completion of problem sets
Independent Study	62	No Description
Total Workload: 125

Section Breakdown
CRN	21467	Part of Term	Semester 2
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Sinead Breen	Module Teacher	Niamh O'Sullivan

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	n/a	10%	Week 7
Assignment	n/a	10%	Week 11
Formal Examination	n/a	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Set Theory
revision of basic definitions and operations

Logic & Proof
simple & compound propositions, conditional connectives, truth tables, argument validation, quantifiers, methods of proof (direct, contraposition, contradiction, induction), counterexamples

Number Theory
divisibility of integers, properties of primes, modular arithmetic & linear congruences, applications in cryptography

Graph Theory
introduction to graphs & terminology, Euler circuits & trails, isomorphism, planarity, adjacency matrices

Combinatorics
addition & multiplication principles, permutations & combinations, arrangements and selections with repetitions, distributions, Pigeonhole Principle

Indicative Reading List

Books:

Tucker, A: 0, Applied Combinatorics, Wiley,
Silverman, J.H: 0, A friendly introduction to Number Theory, Pearson,
Chartrand, G., Polimeni, A.D. & P. Zhang, P: 0, Mathematical proofs: A transition to advanced mathematics, Pearson,
Voloshin, V: 0, Introduction to Graph Theory, Nova Science,

Articles:
None

Other Resources

None