Module: Foundations of Linear Algebra

Module Specifications

Academic Year 2026 - 2027

Module Title	Foundations of Linear Algebra
Module Code	MTH2008
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	8	Credit Rating	5

Description

This module is a first course in Linear Algebra. It will introduce students to the notions of vectors, matrices and linear maps in the context of Euclidean Space. The module aims to give students a working knowledge of the methods and applications of linear algebra, with an emphasis on solving linear systems, curve fitting, and eigenvalues and eigenvectors. Students will attend lectures on the course material and will work, independently, to solve problems on topics related to the course material. The students will have an opportunity to review their solutions, with guidance, at weekly tutorials.

Learning Outcomes

1. Learn to solve and analyse systems of linear equations using matrix techniques
2. Develop an understanding of vectors and vector spaces, and associated vector operations
3. Understand linear transformations, matrices and matrix algebra.
4. Apply linear algebraic methods to solve problems in 2 and 3 dimensions
5. Understand eigenvalues and eigenvectors and how to determine them from a square matrix

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Students will attend lectures where new material will be presented and explained. Also attention will be drawn to various supporting material and tutorials as the course progresses.
Tutorial	12	Students will attempt homework questions in advance and will receive help with and feed-back on their solutions.
Independent Study	89	Corresponding to each lecture students will devote approximately one and a half additional hours of independent study to the material discussed in that lecture or to work on support material when attention is drawn to such in lectures. Before each tutorial students will devote approximately three and a half hours to solving homework problems which are to be discussed in that tutorial.
Total Workload: 125

Section Breakdown
CRN	21546	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	Ronan Egan	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	A mid term class test assessing progress with the first half of the module content.	20%	Week 25
Formal Examination	Final written exam on the module in its entirety	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

Systems of linear equations
Learn to solve systems of linear equations in several variables using gaussian elimination and matrix algebra techniques.

Matrices
Definitions and properties of matrices, matrix arithmetic, determinants, inverses.

Curve fitting
Using matrix algebra techniques to find the best fit of a curve (such as a line) to a set of data points.

Eigenvalues and eigenvectors
Definitions, properties, how to find eigenvalues and eigenvectors of a square matrix, and applications to problems such as Google's page rank algorithm.

Indicative Reading List

Books:
None

Articles:
None

Other Resources

None