Module: Linear Mathematics I

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Linear Mathematics I
Module Code	MS103 (ITS) / MTH1010 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	-
Module Teachers	Thomas Brady
NFQ level	6	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None
Examination in August repeat exam diet

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

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

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	Class test on matrices	20%	Week 7

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

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

Other Resources

None