Module: Discrete Mathematics II

Latest Module Specifications

Current Academic Year 2025 - 2026

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

Description

This module entails the study of different mathematical concepts linked by the theme of discreteness, including sets and logic, combinatorics, probability and graphs. Students will be expected to work collaboratively to discuss and reflect on their learning.

Learning Outcomes

1. 1DE00AF1-188E-0001-B8AD-877C147011E2
2. Recall relevant mathematical facts in Set Theory and Logic, Combinatorics, Probability and Graph Theory.
3.
4. 7,6,8,11
5. 1
6. 1DE00AF1-1C9F-0001-A44E-1FF01EFAC760
7. Apply concepts and processes related to these topics in both mathematical and non-mathematical contexts.
8.
9. 7,6,8,11,9
10. 2
11. 1DE00AF1-2D24-0001-3284-EBA014AFF090
12. Analyse information and interpret results (related to these topics).
13.
14. 7,6,8,11,9
15. 3
16. 1E14BFDA-BEF1-0001-EEE4-A8C0151044E0
17. Explore patterns and formulate conjectures (related to these topics).
18.
19. 7,6,9
20. 4
21. 1E14BFDA-C209-0001-391D-18EF1B006720
22. Present arguments, draw and justify conclusions (related to these topics).
23.
24. 7,6,8,11,9
25. 5
26. 1E14BFDA-CB5D-0001-BFC7-140062001978
27. Communicate ideas in Discrete Mathematics in writing.
28.
29. 6
30. 6

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	No Description
Tutorial	12	No Description
Independent Study	88	No Description
Total Workload: 124

Section Breakdown
CRN	21256	Part of Term	Semester 2
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	N
Module Co-ordinator	Niamh O'Sullivan	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Assignment	n/a	10%	Week 4
Assignment	n/a	10%	Week 8
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

Sets, Modular Arithmetic, and equivalence relations
Definitions and theorems for sets. Introduction to modular arithmetic and the Euclidean algorithm. Definition and examples of relations.

Mathematical Proofs
Methods of Mathematical proof. Examples from combinatorics; including proofs relevant to second level education.

Combinatorics
Permutations and combinations; introduction to discrete probability; binomial coefficients and combinatorial identities; pigeonhole principle.

Graph Theory
Paths and cycles; travelling salesperson problem; shortest-path algorithm; representations of graphs; planar graphs; instant insanity and other games.

Indicative Reading List

Books:
None

Articles:
None

Other Resources

None