Module: Discrete Mathematics II

Module Specifications.

Current Academic Year 2024 - 2025

All Module information is indicative, and this portal is an interim interface pending the full upgrade of Coursebuilder and subsequent integration to the new DCU Student Information System (DCU Key).

As such, this is a point in time view of data which will be refreshed periodically. Some fields/data may not yet be available pending the completion of the full Coursebuilder upgrade and integration project. We will post status updates as they become available. Thank you for your patience and understanding.

Date posted: September 2024

Module Title	Discrete Mathematics II
Module Code	MS342 (ITS) / MTH1090 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Niamh O'Sullivan
Module Teachers	-
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination

Description

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

Learning Outcomes

1. Recall relevant mathematical facts in Set Theory and Logic, Combinatorics, Probability 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
Independent Study	89	No Description
Total Workload: 125

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.

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Written assessment	10%	Week 6
Assignment	Written assessment	10%	Week 10

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

R. Johnsonbaugh: 1993, Discrete Mathematics, Macmillan Publishing Company,
K. A. Ross, C. R. B. Wright: 1999, Discrete Mathematics, Prentice Hall,,
R. Diestel: 1997, Graph Theory, Springer N, New York,

Other Resources

65458, Website, 0, Primary resource: Course Notes on Loop;,