Module: Linear Mathematics I

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Linear Mathematics I
Module Code	MTH1010 (ITS: MS103)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

The purpose of this module is to introduce students to matrix algebra and linearity. In this module students will gain a sound grasp of elementary linear algebra, and fundamental computational skills; it lays the foundations for further courses in linear algebra, calculus, probability and statistics. The module is aimed at students who have recently completed Leaving Certificate Honours Mathematics. The course is delivered through a combination of lectures, and tutorials facilitated by a tutor.

Learning Outcomes

1. demonstrate computational skills by solving wide range of drill problems involving topics in the indicative syllabus
2. state selected definitions and theorems related to the indicative syllabus
3. solve exercises that test understanding of these definitions and theorems
4. explain arguments used to prove selected theorems in special cases

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Lectures
Tutorial	11	Tutorial and examples class
Independent Study	44	Solving exercises on tutorial sheets
Independent Study	22	Preparation for class tests and final exam
Independent Study	24	Assimilating lecture content
Total Workload: 125

Section Breakdown
CRN	11191	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Ronan Egan	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Class test on matrices	20%	Week 7
Formal Examination	End-of-Semester Final Examination	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

Matrices and linear equations
Matrix algebra; invertibility; vectors; lines and planes; Gaussian elimination; elementary matrices and Gauss-Jordan method forfinding inverse; diagonal, triangular, symmetric and Hermitian matrices; triangular decompositions; symmetric positive and negative definite matrices

Geometry
Lines, planes, triangles, parallelograms

Determinants
Determinants by cofactor expansion; evaluating determinants using row and column operations; properties of determinants; adjugate; finding inverses; criteria involving principal minors for testing positive and negativeness

Indicative Reading List

Books:

H. Anton and C. Rorres: 2005, Elementary Linear Algebra - Applications Version, 9th or 10th, John Wiley & Sons, Inc.,

Articles:
None

Other Resources

None