Module: Linear Mathematics II

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Linear Mathematics II
Module Code	MS104 (ITS) / MTH1011 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	James O'Shea
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 to students who have successfully completed Linear Mathematics 1 further foundational topics in Linear Algebra. The emphasis is on students gaining a sound knowledge of basics and fundamental computational skills. Eigenvalues and eigenvectors are important in calculus of several variables, probability and statistics. 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 related to 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 material
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

Vector Spaces
Spaces of real and complex vectors; linear mappings; subspaces; linear independence; basis and dimension; row space, column space and null space; rank and nullity

Inner product spaces
standard inner products; Cauchy-Schwarz inequality; angle and orthogonality; orthonormal bases and Gram-Schmidt procedure; orthogonal matrices; positive and negative definite matrices; least squares approximation; least square solutions; orthogonal projections

Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors; diagonalisation; Diagonalisation of symmetric and Hermitian matrices

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Homework assignments and/or in-class tests	20%	As required

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