Module: Linear Algebra I

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Linear Algebra I
Module Code	MTH1087 (ITS) / MTH1087 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Thomas Brady
Module Teachers	-
NFQ level	6	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None

Description

The purpose of this module is to introduce students to matrix algebra and linearity and to the notions of vector space and linear transformation.

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
5. Demonstrate an understanding of the mechanics of change of basis

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Lecture
Tutorial	12	Tutorial
Independent Study	170	Independent learning
Assignment Completion	2	Final Exam
Total Workload: 220

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

Vectors:
vectors in Euclidean space, linear combinations, dot product, orthogonality, one-dimensional projection, Cauchy-Schwarz Inequality.

Matrices and systems of equations:
Matrices, systems of linear equations, Gauss-Jordan elimination, invertible matrices, elementary matrices

Dimension:
subspaces, linear independence, basis, dimension, Rank-Nullity Theorem

Vector spaces
Abstract vector spaces and linear transformation. General rank-nullity Theorem.

Matrix representations
Coordinates, matrix representations, similarity

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	In class test	10%	Week 5
In Class Test	n/a	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

John B. Fraleigh,Raymond A. Beauregard: 1995, Linear Algebra, Addison Wesley, 0201526751
Gilbert Strang: 2023, Introduction to Linear Algebra, Wellesley-Cambridge Press, 1733146679
Howard Anton,Chris Rorres,Anton Kaul: 2019, Elementary Linear Algebra, John Wiley & Sons, 1119282365

Other Resources

None