Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Linear Mathematics
Module Code	MS106
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: David Reynolds Semester 2: David Reynolds Autumn: David Reynolds
NFQ level	8	Credit Rating	10
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

The purpose of this module is to introduce students to Linear Algebra. 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 matrices and vectors
2. State selected definitions and theorems in linear algebra
3. Solve exercises that test understanding of these definitions and theorems
4. Explain arguments used to prove selected theorems in special cases

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	48	Lectures
Tutorial	24	Tutorial and examples class
Independent learning	120	Solving exercises on tutorial sheets
Independent learning	58	Preparation for class tests and final exam
Total Workload: 250

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 and matrices.
Matrices and matrix operations; Gaussian elimination; elementary matrices and Gauss-Jordan method forfinding inverse; diagonal, triangular and symmetric matrices; LU decompositions.

Determinants.
Determinants by cofactor expansion; evaluating determinants using row and column operations; properties of determinants.

Vectors in two and three dimensions.
Norms and inner products of vectors; vector products; lines and planes.

Vector subspaces.
Complex vectors; 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 andGram-Schmidt procedure; orthogonal matrices; positive and negative definite matrices; least squaresapproximation.

Eigenvalues and Eigenvectors.
Eigenvalues and eigenvectors; diagonalisation; orthogonal diagonalisation of symmetric matrices.

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Other	Participation in Semester 2 tutorials	5%	n/a
Other	Participation in Semester 1 tutorials	5%	n/a
In Class Test	2 x in class test in weeks 9 and 28 (approx)	15%	n/a

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List